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today's guest is professor richard

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borchardt

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of uc berkeley richard is one of the

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brightest people if not the brightest

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person that i've been lucky to speak to

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on this channel he's a fields medalist

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and a fields medal is essentially the

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nobel prize equivalent of mathematics

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he was awarded this medal due to him

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proving a speculative assertion at the

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time

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put forward by conway that the that

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there's a deep connection between the

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monster group

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and the j function which is a simple or

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one of the simplest modular forms

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this is called the monstrous moonshine

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conjecture and it was proven by

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professor borchards in the early 1990s

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when he was in his early 30s

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the monster group is the largest of all

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the sporadic simple groups

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and its order is of the size of pretty

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much all the atoms

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that comprise the earth so around 10 to

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the 53 if i'm not mistaken orchard also

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runs a wonderful youtube channel

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which the link is in the description

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it's essentially teaching graduate

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mathematics

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over the next few months i'll be asking

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mathematicians and physicists about how

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they think and how they study

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because if you're watching this you're

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likely a sagacious individual

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who knows the importance of self-study

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this is because it's often more

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important to know how to think about a

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problem

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rather than exactly how to solve this

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particular problem because the former

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generalizes to more problems and more

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solutions

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if you'd like to see more conversations

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like this then please consider

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supporting at

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patreon.com kurtjmungle right now

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there's the goal of hosting multiple

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intellectuals on

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simultaneously almost like theomaki so

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that they can battle it out in real time

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the first will be bernardo castro and

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donald hoffman and jonathan verveicky

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simultaneously if i'm lucky enough to

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reach

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around 50 patrons i'll be able to host

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this conversation thank you so much to

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all my current patrons

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i hope you enjoy part of this was filmed

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as a live stream so if it looks like i'm

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reading

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question enjoy

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first of all why don't you tell the

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audience a little bit about yourself

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your interest what field of math you

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study

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um math professor working mania and

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algebra number theory

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um i did some stuff on monstrous

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moonshine about 20 or 30 years ago and

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have been

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struggling to do something similar ever

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since

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similar as in you can't announce it or

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you can well um

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i i feel like one of these people

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you know that said that the worst thing

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that can happen to a musician is they

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have a big hit

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early in their career because they spend

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the rest of their time trying to

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equal that and i feel i'm in sort of

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that position that i did

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monstrous moonshine when i was young and

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i've been

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never managed to do anything similar

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since how did you get interested in

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mathematics

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um i've always been as long as i can

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remember i mean i i think someone was

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asking me this question why did i decide

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to become a mathematician i never did

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decide i just

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was a mathematician right you equated it

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to being a dolphin or a dolphin deciding

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something like that yeah how did you

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become interested in the particular

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field that you're interested in

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oh moonshine that that was sort of by

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accident

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um i i went to a talk by john conway as

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an undergraduate

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once you know he he

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he would sometimes give undergraduate

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talks and he mentioned this

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it was about finite simple groups which

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either sort of vague idea of what they

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were and he said well there was this

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monster group with this

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dimension living in dimension one nine

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six

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eight eight three and you also mentioned

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this is the same as the coefficient of

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the elliptic modular function i was just

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you know just completely blown away by

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this it was just

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you know that these were two

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areas of mathematics that had absolutely

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nothing to do with each other there was

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this bizarre coincidence going on

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so so that's how i got interested in it

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do you find that there's some connection

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between

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unifying different fields in math and

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unifying different fields in physics

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because as you know unification happens

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frequently in physics but it seems to

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also happen in math

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there's a sort of vague analogy i mean

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one of the things i've discovered in

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math is you really want to know

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little bits of lots of different areas

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because every now and then you find some

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bizarre connection between two

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apparently different areas

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and i would guess the same is sort of

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true in physics for instance

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you know maxwell unified light and

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electromagnetism

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and that there were two apparently

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completely different areas of physics

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but maxwell happened to know about both

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of them so he was able to unify them

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i guess gravitational quantum field

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theory is another very topical example

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that they you know general relativity

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looks quite different from

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quantum mechanics and it's a big problem

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trying to

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connect them what do your average days

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look like

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do you wake up at a particular time do

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you remember i wake up at random times

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and frankly

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most of my days spent procrastinating

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um i mean supposed to be doing

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mathematics research but mathematics

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research consists mainly of trying to do

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things that don't work

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and what do you procrastinate with what

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are your advices

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oh i can procrastinate by

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making youtube videos on mathematics or

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something like that

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do you play any video games or do you go

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for walks do you have pets or kids

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i go for walks i used to have chickens

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but they they all died a few years ago

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how much time do you spend studying

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versus

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well let's say you're doing research

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some of the research is studying

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some of the research is just writing

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some of it is thinking some of it is

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collaborating

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what does that look like for you and how

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much time do you get to spend in each

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let's say on a weekly basis

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yeah um i knew an accountant once who

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said they had to spend

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for every 15 minutes of the day they had

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to write down what they were doing

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and i've never done anything like that

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and i never dared to because if i did

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i would probably be horrified at what i

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was wasting my time on all the time

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um i i just don't know

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um i probably spend far less time doing

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useful stuff than i like to imagine

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so you don't feel like you manage your

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time well it's dreadful at it

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i'm poorly organized and have atrocious

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time management

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skills let's say that you had an ideal

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day

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in terms of process so not in terms of

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outcome because your ideal day may be

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solve the riemann hypothesis in the

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morning move on to so-and-so and solve

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it so forget about that

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process that is spend four hours

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writing spend two hours answering email

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i don't know whose ideal day would be

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emails i can't

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what would your idea look like i i can't

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spend four hours a day

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working on anything i i just get too

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fidgety and impatient

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um i mean ideal day would be if i was

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able to focus

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on something that well um yes

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i mean sometimes in the past when

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mathematics when research was going well

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i could spend you know

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12 or 16 hours a day working on a

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straight or with breaks well i'd have

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lunch

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occasionally and things like that but

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yeah yeah it was

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when i was younger i really was able to

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spend many hours straight working on

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something

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now is that a function of age that

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i don't know probably

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just getting less energetic as you get

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older or something

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are you more creative now than you were

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when you were younger i don't seem to be

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i mean when i was in my 20s and 30s i

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was getting all these ideas and they all

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worked and

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these days i'm getting loads and loads

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of ideas and they all fail

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can you give an example of what an idea

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that worked for an idea that failed

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recently let's say in the past two

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months past two months

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um well

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nothing very easy to explain i mean

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they're the

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they're all rather technical ideas i

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mean i mean that's fine

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i mean i i can tell you i mean i was

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trying to find an extension of the smith

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minkowski ziggler formula to give an

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exact number for class numbers rather

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than a

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weighted sum which probably means

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absolutely nothing to most people

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you'll find that much like the audience

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of yours the audience of this channel

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they comprise extremely bright people

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some post docs some

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even professors so don't worry if you

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feel like you're going above someone's

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head

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it seems like one of the appeals of this

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podcast is the fact that we do go into

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some technicalities unlike other

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podcasts which tend to stay at a fluffy

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or

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cosmetic level well i can go into

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technicalities if you want but i suspect

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your audience is going to plummet

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but whatever what do you feel like is

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your greatest

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greatest strength

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i'm really obstinate um that i can

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keep working on a problem for i can keep

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coming back to it

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year after year and sometimes you know

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when you come back to a problem for the

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tenth

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time you finally make some progress on

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it

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um weakness over too many to think of

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um as i said i've got lousy time

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management and work skills

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i don't collaborate with people nearly

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as much as i ought to

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you know most of the top mathematicians

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have this fantastic

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network of talking to other good

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mathematicians and

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i'd i do far too little of that why is

286
00:09:25,590 --> 00:09:22,480
that

287
00:09:27,430 --> 00:09:25,600
um poor social socials i guess social

288
00:09:28,949 --> 00:09:27,440
anxiety or just poor social skills or

289
00:09:31,829 --> 00:09:28,959
disagreeableness

290
00:09:33,509 --> 00:09:31,839
um just just not very good at

291
00:09:36,389 --> 00:09:33,519
interacting with people

292
00:09:36,710 --> 00:09:36,399
and i never quite figured out how to do

293
00:09:38,230 --> 00:09:36,720
it

294
00:09:40,310 --> 00:09:38,240
i was watching one of your q and a's and

295
00:09:41,590 --> 00:09:40,320
someone said what's or who is the nicest

296
00:09:43,509 --> 00:09:41,600
mathematician and you said

297
00:09:45,350 --> 00:09:43,519
they're all pretty much nice so then if

298
00:09:46,710 --> 00:09:45,360
they're all pretty much nice that to me

299
00:09:48,630 --> 00:09:46,720
implies that you get along with them

300
00:09:49,750 --> 00:09:48,640
unless you're not being nice in return

301
00:09:52,550 --> 00:09:49,760
so why is it that you don't get along

302
00:09:54,630 --> 00:09:52,560
with them i do get along with them just

303
00:09:57,110 --> 00:09:54,640
fine it's just kind of stressful

304
00:09:59,670 --> 00:09:57,120
interacting with people so i

305
00:10:00,710 --> 00:09:59,680
just just tend to not do it unless i

306
00:10:02,550 --> 00:10:00,720
have to

307
00:10:04,389 --> 00:10:02,560
what are the advantages of that see

308
00:10:06,389 --> 00:10:04,399
there's the soul mathematician or the

309
00:10:07,509 --> 00:10:06,399
soul physicist who in isolation comes up

310
00:10:10,230 --> 00:10:07,519
with the brilliant idea

311
00:10:10,870 --> 00:10:10,240
i believe max planck was a proponent of

312
00:10:12,710 --> 00:10:10,880
that

313
00:10:14,069 --> 00:10:12,720
but then all there are obviously others

314
00:10:15,829 --> 00:10:14,079
well people have different

315
00:10:17,829 --> 00:10:15,839
styles i mean there are some people like

316
00:10:19,110 --> 00:10:17,839
a tear and say who are fantastic at

317
00:10:20,550 --> 00:10:19,120
collaboration

318
00:10:23,030 --> 00:10:20,560
and there are other people i think i

319
00:10:24,630 --> 00:10:23,040
mean perilman is an obvious example he

320
00:10:26,790 --> 00:10:24,640
he just

321
00:10:27,670 --> 00:10:26,800
went off by himself didn't talk to

322
00:10:29,990 --> 00:10:27,680
anybody else

323
00:10:32,310 --> 00:10:30,000
work for 10 or 20 years and solve this

324
00:10:33,750 --> 00:10:32,320
absolutely fantastic problem i mean that

325
00:10:37,110 --> 00:10:33,760
that's that's the sort of

326
00:10:39,430 --> 00:10:37,120
idea of what that that's a sort of one

327
00:10:40,389 --> 00:10:39,440
ideal of mathematics research you you

328
00:10:42,150 --> 00:10:40,399
you just

329
00:10:43,829 --> 00:10:42,160
solve a problem by yourself by brute

330
00:10:45,509 --> 00:10:43,839
force but it's

331
00:10:49,190 --> 00:10:45,519
actually it's very rare that that

332
00:10:52,150 --> 00:10:49,200
happens nearly all mathematics is

333
00:10:54,550 --> 00:10:52,160
done very collaboratively these days are

334
00:10:57,670 --> 00:10:54,560
there any advantages to studying math

335
00:10:58,550 --> 00:10:57,680
later in life so for example starting in

336
00:11:01,350 --> 00:10:58,560
your 20s or

337
00:11:02,949 --> 00:11:01,360
starting in your 30s or even 40s we can

338
00:11:05,110 --> 00:11:02,959
take those as three different questions

339
00:11:07,269 --> 00:11:05,120
yeah i haven't heard of any

340
00:11:09,110 --> 00:11:07,279
mathematicians who started in their 30s

341
00:11:10,949 --> 00:11:09,120
or 40s there'd been a

342
00:11:13,190 --> 00:11:10,959
a few really good mathematicians who

343
00:11:14,230 --> 00:11:13,200
started in their 20s i mean i think ed

344
00:11:16,069 --> 00:11:14,240
whitman was

345
00:11:17,670 --> 00:11:16,079
doing history as an undergraduate or

346
00:11:20,069 --> 00:11:17,680
something and only started taking math

347
00:11:23,350 --> 00:11:20,079
seriously in his twenties

348
00:11:25,350 --> 00:11:23,360
so i mean it might be possible i just

349
00:11:28,069 --> 00:11:25,360
don't know of any cases i mean it may be

350
00:11:30,069 --> 00:11:28,079
something like learning languages you

351
00:11:31,430 --> 00:11:30,079
if you learn languages when you're young

352
00:11:33,829 --> 00:11:31,440
you're much much better

353
00:11:35,590 --> 00:11:33,839
than if you start when you're older did

354
00:11:37,670 --> 00:11:35,600
you enjoy your graduate studies more

355
00:11:40,829 --> 00:11:37,680
than your undergrad

356
00:11:44,710 --> 00:11:40,839
um they were both fun i mean

357
00:11:47,030 --> 00:11:44,720
um i wouldn't say either

358
00:11:48,389 --> 00:11:47,040
i enjoyed either more than the other

359
00:11:48,949 --> 00:11:48,399
when i was watching one of your talks

360
00:11:50,790 --> 00:11:48,959
you

361
00:11:52,069 --> 00:11:50,800
mentioned quite a few times and probably

362
00:11:54,150 --> 00:11:52,079
even in some of

363
00:11:55,670 --> 00:11:54,160
your non-q a videos you mentioned that

364
00:11:57,269 --> 00:11:55,680
interest matters so if you're gonna pick

365
00:11:58,069 --> 00:11:57,279
a problem pick one that you're terribly

366
00:12:00,230 --> 00:11:58,079
interested in

367
00:12:01,269 --> 00:12:00,240
because over the long run you'll be

368
00:12:03,509 --> 00:12:01,279
faced with

369
00:12:05,509 --> 00:12:03,519
you'll be set with problems and so on

370
00:12:09,590 --> 00:12:05,519
and it had me wondering

371
00:12:10,069 --> 00:12:09,600
did you either voluntarily like force

372
00:12:11,990 --> 00:12:10,079
yourself

373
00:12:13,190 --> 00:12:12,000
or it was forced upon you have to study

374
00:12:15,590 --> 00:12:13,200
some piece of math that you

375
00:12:17,030 --> 00:12:15,600
absolutely hated and now you abhor

376
00:12:17,829 --> 00:12:17,040
studying whatever you're not interested

377
00:12:20,389 --> 00:12:17,839
in

378
00:12:22,069 --> 00:12:20,399
well i i've never actually bothered

379
00:12:25,030 --> 00:12:22,079
studying math i didn't like

380
00:12:26,710 --> 00:12:25,040
i mean i don't remember anybody past

381
00:12:29,590 --> 00:12:26,720
high school telling me to

382
00:12:30,389 --> 00:12:29,600
study math that i didn't want to i mean

383
00:12:33,430 --> 00:12:30,399
at

384
00:12:36,629 --> 00:12:33,440
just

385
00:12:38,790 --> 00:12:36,639
what you want to study i mean

386
00:12:41,110 --> 00:12:38,800
high school yes i i was forced to study

387
00:12:44,710 --> 00:12:41,120
various bits of applied math that i

388
00:12:46,470 --> 00:12:44,720
can no longer stand often solving

389
00:12:47,430 --> 00:12:46,480
mathematical problems requires a certain

390
00:12:49,509 --> 00:12:47,440
state of mind

391
00:12:51,110 --> 00:12:49,519
do you find yourself going through

392
00:12:53,269 --> 00:12:51,120
periods where you feel like

393
00:12:54,949 --> 00:12:53,279
your mind is not creative enough not

394
00:12:57,910 --> 00:12:54,959
focused enough and how do you

395
00:12:59,269 --> 00:12:57,920
solve that yeah of course well you just

396
00:13:02,389 --> 00:12:59,279
have to go off and do something

397
00:13:03,829 --> 00:13:02,399
else so um

398
00:13:05,990 --> 00:13:03,839
there are several things you can do for

399
00:13:07,829 --> 00:13:06,000
this i mean john conway told me that

400
00:13:09,750 --> 00:13:07,839
that what he he did is he always had a

401
00:13:12,230 --> 00:13:09,760
sort of background calculation so he'd

402
00:13:14,470 --> 00:13:12,240
be calculating tables of knots or

403
00:13:16,550 --> 00:13:14,480
tables of lattices or something you can

404
00:13:18,230 --> 00:13:16,560
you you can do that even if you're not

405
00:13:20,710 --> 00:13:18,240
feeling inspired and

406
00:13:22,150 --> 00:13:20,720
i think richard feynman had this idea

407
00:13:23,110 --> 00:13:22,160
that you would always do teaching as a

408
00:13:25,190 --> 00:13:23,120
sort of background

409
00:13:26,470 --> 00:13:25,200
thing and the the point in both cases is

410
00:13:27,990 --> 00:13:26,480
so that you have

411
00:13:30,470 --> 00:13:28,000
something where you can see that you're

412
00:13:32,230 --> 00:13:30,480
making progress because the i mean the

413
00:13:34,150 --> 00:13:32,240
trouble with research is most of the

414
00:13:36,069 --> 00:13:34,160
time you're you're working hard and

415
00:13:38,790 --> 00:13:36,079
making no progress at all and this is

416
00:13:41,750 --> 00:13:38,800
psychologically kind of a bit depressing

417
00:13:43,189 --> 00:13:41,760
so you need to have something something

418
00:13:45,030 --> 00:13:43,199
else you can do where you can actually

419
00:13:47,430 --> 00:13:45,040
make visible progress on it

420
00:13:49,189 --> 00:13:47,440
what's the longest lull or the longest

421
00:13:51,110 --> 00:13:49,199
involuntary cognitive hiatus you've

422
00:13:54,629 --> 00:13:51,120
experienced

423
00:13:56,790 --> 00:13:54,639
well i'd say um hard to say i mean it

424
00:13:57,990 --> 00:13:56,800
might be now um i've been working on a

425
00:14:01,030 --> 00:13:58,000
problem for

426
00:14:02,870 --> 00:14:01,040
several years and i

427
00:14:04,790 --> 00:14:02,880
i i don't know what the progress is

428
00:14:06,790 --> 00:14:04,800
because you know 20 times i think i've

429
00:14:09,829 --> 00:14:06,800
solved it and got really excited

430
00:14:11,910 --> 00:14:09,839
and and then i start to write a top and

431
00:14:13,269 --> 00:14:11,920
geez there's this huge hole i somehow

432
00:14:15,110 --> 00:14:13,279
overlooked so i go back to being

433
00:14:18,790 --> 00:14:15,120
depressed for a bit and

434
00:14:20,389 --> 00:14:18,800
and so it keeps on switching backwards

435
00:14:22,069 --> 00:14:20,399
and forwards between thinking i solved

436
00:14:23,829 --> 00:14:22,079
and thinking i haven't and i

437
00:14:25,189 --> 00:14:23,839
you know i i sometimes think that that

438
00:14:27,189 --> 00:14:25,199
sooner or later i'm going to be

439
00:14:28,710 --> 00:14:27,199
get so senile that i can't actually

440
00:14:30,629 --> 00:14:28,720
figure out what's wrong with my solution

441
00:14:32,949 --> 00:14:30,639
and then i can publish it and

442
00:14:34,310 --> 00:14:32,959
you know you know the the the the this

443
00:14:35,750 --> 00:14:34,320
is what this is actually

444
00:14:37,670 --> 00:14:35,760
unfortunately what happens to some

445
00:14:39,509 --> 00:14:37,680
mathematicians when they get old

446
00:14:41,269 --> 00:14:39,519
they sort of lose this capacity to see

447
00:14:43,189 --> 00:14:41,279
what's wrong with what they're doing

448
00:14:44,310 --> 00:14:43,199
you mentioned depression i don't know if

449
00:14:45,670 --> 00:14:44,320
you just meant that as a throwaway

450
00:14:47,670 --> 00:14:45,680
comment but do you feel like

451
00:14:49,030 --> 00:14:47,680
you're characterized by depression or

452
00:14:49,430 --> 00:14:49,040
are you just using that in the informal

453
00:14:51,509 --> 00:14:49,440
sense

454
00:14:52,870 --> 00:14:51,519
i i don't feel i've ever had anything

455
00:14:54,870 --> 00:14:52,880
i'd call depression i mean

456
00:14:57,269 --> 00:14:54,880
of course you go through phases when

457
00:15:00,790 --> 00:14:57,279
you're feeling a little bit

458
00:15:03,509 --> 00:15:00,800
less happy than usual um actually i i

459
00:15:05,430 --> 00:15:03,519
don't know i mean i

460
00:15:07,030 --> 00:15:05,440
me maybe i'm just not very good at

461
00:15:08,949 --> 00:15:07,040
spotting symptoms of depression i

462
00:15:10,389 --> 00:15:08,959
remember seeing a poster once of saying

463
00:15:13,670 --> 00:15:10,399
you know

464
00:15:14,629 --> 00:15:13,680
um look out for these typical symptoms

465
00:15:16,310 --> 00:15:14,639
of depression i

466
00:15:17,509 --> 00:15:16,320
remember being really unimpressed by

467
00:15:18,069 --> 00:15:17,519
that because i was thinking that was

468
00:15:20,069 --> 00:15:18,079
sort of

469
00:15:23,269 --> 00:15:20,079
my normal state as a graduate student i

470
00:15:25,590 --> 00:15:23,279
didn't count that as being depressed so

471
00:15:26,949 --> 00:15:25,600
maybe i just don't recognize depression

472
00:15:28,790 --> 00:15:26,959
someone asked

473
00:15:30,710 --> 00:15:28,800
what's your iq and do you have any

474
00:15:35,110 --> 00:15:30,720
methods of increasing iq

475
00:15:37,509 --> 00:15:35,120
i've no idea what my iq is and

476
00:15:39,590 --> 00:15:37,519
as far as i know the only method of

477
00:15:41,749 --> 00:15:39,600
increasing iq is to go back in time

478
00:15:42,629 --> 00:15:41,759
because your iq steadily decreases as

479
00:15:44,150 --> 00:15:42,639
you get older

480
00:15:47,030 --> 00:15:44,160
have you taken any nootropics or

481
00:15:49,350 --> 00:15:47,040
supplements to try and either stave off

482
00:15:50,710 --> 00:15:49,360
cognitive deterioration or to improve

483
00:15:53,509 --> 00:15:50,720
your cognitive state

484
00:15:54,949 --> 00:15:53,519
no idea besides caffeine i don't take

485
00:15:57,430 --> 00:15:54,959
caffeine and i don't know what a new

486
00:15:59,829 --> 00:15:57,440
tropic is and i stay well clear of

487
00:16:01,189 --> 00:15:59,839
anything that's remotely mind-altering

488
00:16:04,310 --> 00:16:01,199
you don't drink coffee

489
00:16:04,949 --> 00:16:04,320
i don't drink coffee no tea you're

490
00:16:07,509 --> 00:16:04,959
british

491
00:16:07,990 --> 00:16:07,519
no tea well i i drink tea out of

492
00:16:09,990 --> 00:16:08,000
politeness

493
00:16:11,430 --> 00:16:10,000
if someone puts it in front of me do you

494
00:16:13,430 --> 00:16:11,440
find that depression is higher in

495
00:16:14,629 --> 00:16:13,440
mathematicians than in the general

496
00:16:18,470 --> 00:16:14,639
population

497
00:16:20,230 --> 00:16:18,480
um way outside my expertise i've no idea

498
00:16:22,069 --> 00:16:20,240
what the incidence of depression is in

499
00:16:24,550 --> 00:16:22,079
either the general population or

500
00:16:25,910 --> 00:16:24,560
mathematicians i've i've never noticed

501
00:16:26,870 --> 00:16:25,920
mathematicians being particularly

502
00:16:29,269 --> 00:16:26,880
depressed but i'm

503
00:16:30,870 --> 00:16:29,279
so clueless i probably wouldn't notice

504
00:16:32,870 --> 00:16:30,880
even if they were

505
00:16:34,470 --> 00:16:32,880
i mean the reason is that you mentioned

506
00:16:35,990 --> 00:16:34,480
you read the signs of depression one

507
00:16:37,430 --> 00:16:36,000
time on a bus ad or somewhere

508
00:16:39,030 --> 00:16:37,440
and you thought oh that's my entire

509
00:16:42,069 --> 00:16:39,040
department

510
00:16:44,310 --> 00:16:42,079
well yeah but i mean i

511
00:16:45,670 --> 00:16:44,320
i i it's it's not like i'm qualified to

512
00:16:47,509 --> 00:16:45,680
actually

513
00:16:48,949 --> 00:16:47,519
diagnose people with depression or not

514
00:16:50,710 --> 00:16:48,959
it was just

515
00:16:53,189 --> 00:16:50,720
you know you you go through periods

516
00:16:54,629 --> 00:16:53,199
where you you know depression is

517
00:16:56,230 --> 00:16:54,639
you know they have things like you go

518
00:16:57,910 --> 00:16:56,240
through periods when you're

519
00:17:00,069 --> 00:16:57,920
getting nowhere feel you're getting

520
00:17:01,829 --> 00:17:00,079
nowhere and so on and that that's just

521
00:17:04,470 --> 00:17:01,839
normal for research if you're

522
00:17:06,710 --> 00:17:04,480
researching anything serious

523
00:17:08,390 --> 00:17:06,720
what's your creative process like is it

524
00:17:11,270 --> 00:17:08,400
different depending on the problem or do

525
00:17:14,470 --> 00:17:11,280
you have a general framework

526
00:17:18,309 --> 00:17:14,480
um a lot of randomness in it um

527
00:17:20,710 --> 00:17:18,319
you you just i mean i think what's the

528
00:17:22,470 --> 00:17:20,720
creative process like it's sort of like

529
00:17:24,309 --> 00:17:22,480
um you know imagine you're on one of

530
00:17:26,470 --> 00:17:24,319
these huge

531
00:17:28,069 --> 00:17:26,480
um garbage dumps that you you know you

532
00:17:29,909 --> 00:17:28,079
sometimes see in countries there are

533
00:17:31,990 --> 00:17:29,919
these garbage dumps of people

534
00:17:33,909 --> 00:17:32,000
picking over them looking for something

535
00:17:34,870 --> 00:17:33,919
interesting and research is a bit like

536
00:17:37,750 --> 00:17:34,880
that you're

537
00:17:38,470 --> 00:17:37,760
wandering around this area looking out

538
00:17:39,909 --> 00:17:38,480
for

539
00:17:42,310 --> 00:17:39,919
something that somebody else has

540
00:17:43,750 --> 00:17:42,320
overlooked and

541
00:17:45,750 --> 00:17:43,760
nearly all the time you don't find

542
00:17:46,630 --> 00:17:45,760
anything because most areas in math

543
00:17:50,150 --> 00:17:46,640
research have been

544
00:17:53,750 --> 00:17:50,160
pretty well picked over by everybody so

545
00:17:56,870 --> 00:17:53,760
you're continually trying out new things

546
00:17:57,990 --> 00:17:56,880
and 99 of the time the new thing you've

547
00:18:01,029 --> 00:17:58,000
tried out

548
00:18:02,390 --> 00:18:01,039
either doesn't work or if you work on it

549
00:18:03,270 --> 00:18:02,400
and discover that someone's already

550
00:18:05,830 --> 00:18:03,280
thought of it

551
00:18:07,590 --> 00:18:05,840
creative process is just trying to

552
00:18:09,669 --> 00:18:07,600
generate enormous numbers of

553
00:18:11,510 --> 00:18:09,679
ideas and throwing nearly all of them

554
00:18:13,350 --> 00:18:11,520
away

555
00:18:15,350 --> 00:18:13,360
actually i've heard the same something

556
00:18:17,669 --> 00:18:15,360
like this is actually supposedly true in

557
00:18:20,310 --> 00:18:17,679
business that i think um

558
00:18:21,750 --> 00:18:20,320
what is it the guy who does the gilbert

559
00:18:22,470 --> 00:18:21,760
cartoons was saying somewhere you know

560
00:18:25,990 --> 00:18:22,480
he had tried

561
00:18:26,390 --> 00:18:26,000
30 ideas for making money and and 27 of

562
00:18:28,310 --> 00:18:26,400
them

563
00:18:29,430 --> 00:18:28,320
failed or something like that right

564
00:18:31,990 --> 00:18:29,440
scott adams

565
00:18:33,750 --> 00:18:32,000
yeah so he you just keep on generating

566
00:18:34,630 --> 00:18:33,760
new ideas and discard the ones that

567
00:18:36,230 --> 00:18:34,640
don't work

568
00:18:38,070 --> 00:18:36,240
do you find you think more geometrically

569
00:18:40,070 --> 00:18:38,080
or algebraically or you think in words

570
00:18:42,549 --> 00:18:40,080
or are you thinking concepts

571
00:18:44,230 --> 00:18:42,559
uh i i tried to wonder about that and

572
00:18:45,830 --> 00:18:44,240
it's amazingly difficult to actually

573
00:18:46,630 --> 00:18:45,840
figure out what's going on in your own

574
00:18:49,909 --> 00:18:46,640
brain

575
00:18:51,190 --> 00:18:49,919
um um it's

576
00:18:53,990 --> 00:18:51,200
it's something that's very difficult to

577
00:18:55,909 --> 00:18:54,000
describe i seem to have sort of

578
00:18:57,510 --> 00:18:55,919
some sort of algorithms built into the

579
00:18:58,549 --> 00:18:57,520
brain and i sort of know how they're

580
00:19:00,870 --> 00:18:58,559
going to work

581
00:19:01,669 --> 00:19:00,880
and i just don't know how to describe

582
00:19:05,110 --> 00:19:01,679
this i mean

583
00:19:08,470 --> 00:19:05,120
there's a bit of geometric

584
00:19:11,190 --> 00:19:08,480
um imagination going on in there

585
00:19:12,549 --> 00:19:11,200
and there's a bit of algebraic

586
00:19:14,470 --> 00:19:12,559
manipulation but i don't know how the

587
00:19:17,110 --> 00:19:14,480
algebraic manipulation works because i'm

588
00:19:18,789 --> 00:19:17,120
doing things with formulas that are

589
00:19:20,390 --> 00:19:18,799
far too complicated for me to actually

590
00:19:22,310 --> 00:19:20,400
visualize i mean i

591
00:19:24,390 --> 00:19:22,320
i can't visualize the formula itself in

592
00:19:26,310 --> 00:19:24,400
my mind but somehow

593
00:19:29,990 --> 00:19:26,320
i still know what it's doing and i've

594
00:19:32,230 --> 00:19:30,000
i've no idea how this works

595
00:19:33,430 --> 00:19:32,240
um actually the mathematician jacques

596
00:19:35,270 --> 00:19:33,440
adamar once

597
00:19:38,230 --> 00:19:35,280
wrote for a lot of mathematicians asking

598
00:19:40,310 --> 00:19:38,240
them to describe how they thought um

599
00:19:41,830 --> 00:19:40,320
and i the problem is it's so long ago

600
00:19:43,510 --> 00:19:41,840
since i looked at this that i can't

601
00:19:45,029 --> 00:19:43,520
remember what he what conclusions he

602
00:19:46,870 --> 00:19:45,039
came to but

603
00:19:49,270 --> 00:19:46,880
um there have been some attempts by

604
00:19:51,669 --> 00:19:49,280
mathematicians to research this question

605
00:19:53,270 --> 00:19:51,679
i was reading penrose's emperor's new

606
00:19:55,510 --> 00:19:53,280
mind and

607
00:19:56,950 --> 00:19:55,520
for anybody who is a mathematician or

608
00:19:58,310 --> 00:19:56,960
physicist that wants to read that book

609
00:20:01,909 --> 00:19:58,320
just read the last third

610
00:20:03,510 --> 00:20:01,919
it was a slug to get through it was

611
00:20:05,190 --> 00:20:03,520
quite an ordeal to get through the first

612
00:20:06,870 --> 00:20:05,200
bit because it's so much

613
00:20:07,909 --> 00:20:06,880
retreading of similar ground and the

614
00:20:08,470 --> 00:20:07,919
last third is actually where it's

615
00:20:10,710 --> 00:20:08,480
interesting

616
00:20:11,990 --> 00:20:10,720
but in the last third he talks about

617
00:20:13,909 --> 00:20:12,000
when he was in high school

618
00:20:15,510 --> 00:20:13,919
he's noticed that he thought differently

619
00:20:17,430 --> 00:20:15,520
than his peers and then

620
00:20:18,549 --> 00:20:17,440
when he got to university he thought

621
00:20:19,990 --> 00:20:18,559
okay great i'll be around other

622
00:20:21,669 --> 00:20:20,000
mathematicians and physicists so

623
00:20:23,750 --> 00:20:21,679
we'll think alike but then he found that

624
00:20:26,070 --> 00:20:23,760
there is even more a diversity in the

625
00:20:26,789 --> 00:20:26,080
in terms of how people think what i'm

626
00:20:29,190 --> 00:20:26,799
wondering is

627
00:20:30,470 --> 00:20:29,200
have you encountered that yeah i i

628
00:20:32,950 --> 00:20:30,480
noticed this too that

629
00:20:33,990 --> 00:20:32,960
that has sort of gradually dawned on me

630
00:20:35,590 --> 00:20:34,000
that lots of people

631
00:20:38,390 --> 00:20:35,600
learn or think in completely different

632
00:20:39,430 --> 00:20:38,400
ways i mean one example is lectures i

633
00:20:41,750 --> 00:20:39,440
mean i i've always found

634
00:20:43,590 --> 00:20:41,760
lectures if i go to a lecture i fall

635
00:20:45,270 --> 00:20:43,600
asleep after 10 minutes i just can't

636
00:20:46,310 --> 00:20:45,280
stay awake and i do all my learning from

637
00:20:48,230 --> 00:20:46,320
books and

638
00:20:49,430 --> 00:20:48,240
i sort of assumed everyone was like this

639
00:20:50,710 --> 00:20:49,440
but no an

640
00:20:53,350 --> 00:20:50,720
awful lot of people do most their

641
00:20:55,750 --> 00:20:53,360
learning from lectures and just

642
00:20:57,830 --> 00:20:55,760
hardly open the textbook so so there are

643
00:21:00,870 --> 00:20:57,840
very different styles

644
00:21:04,549 --> 00:21:00,880
and again some people obviously

645
00:21:07,029 --> 00:21:04,559
very powerful geometric intuition

646
00:21:08,710 --> 00:21:07,039
and other people have some sort of very

647
00:21:09,029 --> 00:21:08,720
good intuition about something abstract

648
00:21:11,110 --> 00:21:09,039
like

649
00:21:12,470 --> 00:21:11,120
set theory and a very little geometric

650
00:21:14,390 --> 00:21:12,480
intuition and so on

651
00:21:16,870 --> 00:21:14,400
when you work do you have to have

652
00:21:18,950 --> 00:21:16,880
uninterrupted bouts of

653
00:21:20,149 --> 00:21:18,960
time exclusive to yourself so what i

654
00:21:21,909 --> 00:21:20,159
mean is

655
00:21:23,350 --> 00:21:21,919
there's this concept called deep work

656
00:21:24,870 --> 00:21:23,360
and i'm wondering if you

657
00:21:26,470 --> 00:21:24,880
instituted that where you tell i don't

658
00:21:27,830 --> 00:21:26,480
know if you're married are you married

659
00:21:29,830 --> 00:21:27,840
first of all yeah

660
00:21:31,590 --> 00:21:29,840
okay so dude tell your wife don't bother

661
00:21:33,750 --> 00:21:31,600
me for four hours because i am

662
00:21:35,029 --> 00:21:33,760
working or do you just you start working

663
00:21:36,310 --> 00:21:35,039
and then she interrupts you that's okay

664
00:21:38,870 --> 00:21:36,320
because that's your process

665
00:21:41,029 --> 00:21:38,880
well yeah i mean if i get interrupted

666
00:21:44,230 --> 00:21:41,039
which happens quite regularly i just

667
00:21:46,549 --> 00:21:44,240
pick it up later um

668
00:21:48,390 --> 00:21:46,559
it just varies i mean i think uh you

669
00:21:49,590 --> 00:21:48,400
have to be a bit like jane austen i just

670
00:21:51,909 --> 00:21:49,600
sort of remember she

671
00:21:53,909 --> 00:21:51,919
she wrote her novels in you know

672
00:21:55,669 --> 00:21:53,919
whenever she could snatch 15 minutes

673
00:21:57,270 --> 00:21:55,679
from her social life or something like

674
00:22:00,149 --> 00:21:57,280
that so you

675
00:22:01,830 --> 00:22:00,159
you you you get so you can work in

676
00:22:04,390 --> 00:22:01,840
whatever spare time you have

677
00:22:06,310 --> 00:22:04,400
do you read any non-mathematical books

678
00:22:06,630 --> 00:22:06,320
yeah i read plenty of novels and things

679
00:22:13,830 --> 00:22:06,640
and

680
00:22:14,630 --> 00:22:13,840
example of one that you particularly

681
00:22:17,830 --> 00:22:14,640
liked besides

682
00:22:22,070 --> 00:22:17,840
lord of the rings well there's

683
00:22:25,190 --> 00:22:22,080
i don't know game of thrones and um

684
00:22:33,270 --> 00:22:28,789
fairly eclectic reading i mean i like

685
00:22:35,190 --> 00:22:33,280
agatha christie novels or um

686
00:22:36,310 --> 00:22:35,200
my mind is blanking out or terry

687
00:22:38,470 --> 00:22:36,320
pratchett or

688
00:22:39,990 --> 00:22:38,480
any any light reading i mean i don't go

689
00:22:41,909 --> 00:22:40,000
around reading sort of

690
00:22:44,149 --> 00:22:41,919
the sort of deep literature that people

691
00:22:45,270 --> 00:22:44,159
in in english literature classes write

692
00:22:47,270 --> 00:22:45,280
essays about

693
00:22:48,549 --> 00:22:47,280
and i've got a copy of finnegan's wake

694
00:22:50,390 --> 00:22:48,559
up stairs and

695
00:22:53,510 --> 00:22:50,400
you know you can open it random page and

696
00:22:55,110 --> 00:22:53,520
i can't understand a single sentence

697
00:22:56,630 --> 00:22:55,120
mandalore here wants to know if you've

698
00:22:58,390 --> 00:22:56,640
read or heard of jordan peterson and

699
00:23:00,390 --> 00:22:58,400
what you think of him or his work jordan

700
00:23:01,350 --> 00:23:00,400
peterson yeah i i've got one of his

701
00:23:03,430 --> 00:23:01,360
books about

702
00:23:04,630 --> 00:23:03,440
um had the word 12 in it i seem to

703
00:23:07,029 --> 00:23:04,640
remember

704
00:23:07,990 --> 00:23:07,039
um the most important part just that

705
00:23:10,549 --> 00:23:08,000
number yeah yeah

706
00:23:12,149 --> 00:23:10,559
and i i sort of read it but must admit i

707
00:23:13,909 --> 00:23:12,159
can't remember an awful lot about it

708
00:23:16,070 --> 00:23:13,919
anymore

709
00:23:17,830 --> 00:23:16,080
do you find that you read slow when it's

710
00:23:19,270 --> 00:23:17,840
a non-mathematical book or even when

711
00:23:22,390 --> 00:23:19,280
it's a mathematical book

712
00:23:23,590 --> 00:23:22,400
uh i read math books slowly other books

713
00:23:26,950 --> 00:23:23,600
fairly fast

714
00:23:28,950 --> 00:23:26,960
i mean math books very slowly

715
00:23:30,789 --> 00:23:28,960
and it takes a long time to absorb

716
00:23:32,230 --> 00:23:30,799
what's in it if it's anything new

717
00:23:34,390 --> 00:23:32,240
okay i'm going to take a question from

718
00:23:36,390 --> 00:23:34,400
the audience here oh okay

719
00:23:38,070 --> 00:23:36,400
prime time durkheim says has he

720
00:23:40,149 --> 00:23:38,080
experienced any sort of moments of

721
00:23:41,909 --> 00:23:40,159
madness or psychological aberration

722
00:23:45,190 --> 00:23:41,919
being someone who has a lifelong habit

723
00:23:47,269 --> 00:23:45,200
of working in high math in isolation

724
00:23:48,549 --> 00:23:47,279
nothing that i've noticed but i mean if

725
00:23:50,630 --> 00:23:48,559
maybe i'm mad and

726
00:23:53,190 --> 00:23:50,640
so mad that i don't notice i'm mad who

727
00:23:57,990 --> 00:23:55,750
maybe doing mathematics obsessively is

728
00:24:01,590 --> 00:23:58,000
is itself a mad thing to do

729
00:24:04,070 --> 00:24:01,600
socolo is stan 96 says

730
00:24:05,669 --> 00:24:04,080
he said he avoids anything that is mind

731
00:24:06,310 --> 00:24:05,679
altering so do you also avoid certain

732
00:24:08,470 --> 00:24:06,320
foods

733
00:24:11,190 --> 00:24:08,480
or do you optimize your diet in general

734
00:24:13,590 --> 00:24:11,200
do you do intermittent fasting

735
00:24:17,590 --> 00:24:13,600
um i tried intermittent fasting for

736
00:24:24,549 --> 00:24:20,870
i don't think that counts yeah well

737
00:24:25,990 --> 00:24:24,559
um yeah that's infinitesimal fasting

738
00:24:27,669 --> 00:24:26,000
well yeah i mean i think i tried it for

739
00:24:29,029 --> 00:24:27,679
a day or two and it didn't seem to make

740
00:24:31,269 --> 00:24:29,039
much difference i gave up

741
00:24:34,070 --> 00:24:31,279
no i i i don't have any particular food

742
00:24:38,710 --> 00:24:36,630
and it's mostly vegetarian partly for

743
00:24:41,110 --> 00:24:38,720
health reasons but other than that

744
00:24:41,750 --> 00:24:41,120
nothing interesting how is it that you

745
00:24:44,070 --> 00:24:41,760
go about

746
00:24:45,029 --> 00:24:44,080
learning a new math and either learning

747
00:24:47,909 --> 00:24:45,039
from a new field or

748
00:24:49,029 --> 00:24:47,919
learning math in general it's very slow

749
00:24:51,269 --> 00:24:49,039
you have to

750
00:24:52,149 --> 00:24:51,279
i mean as i said i i learned by reading

751
00:24:54,870 --> 00:24:52,159
so

752
00:24:57,269 --> 00:24:54,880
what you have to do is to well i learned

753
00:24:59,430 --> 00:24:57,279
by reading and by calculating examples

754
00:25:01,190 --> 00:24:59,440
and it's a very long slow process

755
00:25:04,870 --> 00:25:01,200
learning anything i mean

756
00:25:06,390 --> 00:25:04,880
um generally you know try reading about

757
00:25:08,710 --> 00:25:06,400
it in a dozen different books

758
00:25:09,510 --> 00:25:08,720
working out lots of examples and you

759
00:25:11,350 --> 00:25:09,520
know the first

760
00:25:12,830 --> 00:25:11,360
half dozen times i try and learn it i

761
00:25:17,190 --> 00:25:12,840
just forget it again

762
00:25:18,630 --> 00:25:17,200
um i mean i i i suspect there are a lot

763
00:25:20,710 --> 00:25:18,640
of other good mathematicians who are

764
00:25:22,070 --> 00:25:20,720
much more efficient at learning things i

765
00:25:23,510 --> 00:25:22,080
mean i i get the impression there are

766
00:25:25,350 --> 00:25:23,520
some people who can learn things just by

767
00:25:27,750 --> 00:25:25,360
reading about it once but

768
00:25:28,950 --> 00:25:27,760
i've never been able to do that it's

769
00:25:30,630 --> 00:25:28,960
kind of like learning

770
00:25:33,430 --> 00:25:30,640
you know the way people learn languages

771
00:25:35,190 --> 00:25:33,440
you you learn a language by

772
00:25:37,269 --> 00:25:35,200
you you have to do a lot of repetition

773
00:25:40,230 --> 00:25:37,279
of basic stuff before it sinks in

774
00:25:41,430 --> 00:25:40,240
at least for most people and again there

775
00:25:41,990 --> 00:25:41,440
are some people who seem to be able to

776
00:25:44,950 --> 00:25:42,000
learn 10

777
00:25:45,590 --> 00:25:44,960
or 20 languages i've no idea how they do

778
00:25:47,430 --> 00:25:45,600
it

779
00:25:48,870 --> 00:25:47,440
in one of your q as you mentioned when

780
00:25:50,230 --> 00:25:48,880
someone asks you about setbacks and

781
00:25:51,269 --> 00:25:50,240
difficulties what do you do about them

782
00:25:52,710 --> 00:25:51,279
you said

783
00:25:54,950 --> 00:25:52,720
often you just ignore them because

784
00:25:57,510 --> 00:25:54,960
you'll be surprised how many problems

785
00:25:59,750 --> 00:25:57,520
disappear yeah yeah yeah this is my

786
00:26:02,549 --> 00:25:59,760
fundamental problem solving technique

787
00:26:04,630 --> 00:26:02,559
um especially when when someone else

788
00:26:06,070 --> 00:26:04,640
comes up with a problem for me to do i

789
00:26:07,430 --> 00:26:06,080
sort of figure well if it was really

790
00:26:08,789 --> 00:26:07,440
important they would have done it so i

791
00:26:10,870 --> 00:26:08,799
can just ignore it

792
00:26:12,230 --> 00:26:10,880
do you mind giving a specific example of

793
00:26:13,830 --> 00:26:12,240
a problem you ignored and then it was

794
00:26:15,990 --> 00:26:13,840
solved

795
00:26:18,710 --> 00:26:16,000
um or that you'd realize you didn't even

796
00:26:21,830 --> 00:26:18,720
have to solve it to begin with

797
00:26:25,350 --> 00:26:23,750
i actually find that's that's sort of

798
00:26:28,230 --> 00:26:25,360
true of a surprising number of problems

799
00:26:30,230 --> 00:26:28,240
actually in math research if i if i

800
00:26:31,830 --> 00:26:30,240
don't try and understand a problem and

801
00:26:33,350 --> 00:26:31,840
just sort of

802
00:26:35,350 --> 00:26:33,360
don't try and work hard in it and just

803
00:26:38,710 --> 00:26:35,360
sort of put it aside

804
00:26:39,669 --> 00:26:38,720
that then you find a month or two later

805
00:26:41,350 --> 00:26:39,679
you suddenly

806
00:26:42,789 --> 00:26:41,360
realize it's kind of obvious what you

807
00:26:45,990 --> 00:26:42,799
ought to be doing i mean

808
00:26:47,430 --> 00:26:46,000
maybe it's just my subconscious is

809
00:26:48,149 --> 00:26:47,440
working on it or something i don't

810
00:26:50,470 --> 00:26:48,159
really know

811
00:26:53,029 --> 00:26:50,480
i mean since it's subconscious i don't

812
00:26:55,990 --> 00:26:53,039
know what's going on in there

813
00:26:57,590 --> 00:26:56,000
akash says what advice does he have for

814
00:26:58,230 --> 00:26:57,600
someone in their mid-20s to learn math

815
00:26:59,990 --> 00:26:58,240
and physics

816
00:27:01,269 --> 00:27:00,000
i work in law and i'm interested in

817
00:27:03,029 --> 00:27:01,279
physics i would like to get

818
00:27:05,110 --> 00:27:03,039
a better understanding of physics now i

819
00:27:05,669 --> 00:27:05,120
know fermat and kaylee i believe were

820
00:27:06,950 --> 00:27:05,679
lawyers

821
00:27:08,710 --> 00:27:06,960
in their mid-20s when they started

822
00:27:12,230 --> 00:27:08,720
physics sorry yeah and they started

823
00:27:14,310 --> 00:27:12,240
math i mean yeah sure as you point out

824
00:27:17,029 --> 00:27:14,320
though that there are a couple of

825
00:27:19,590 --> 00:27:17,039
rather prominent examples of lawyers who

826
00:27:23,029 --> 00:27:19,600
end up being really rather good at math

827
00:27:24,710 --> 00:27:23,039
um advice i'd just say follow whatever

828
00:27:29,269 --> 00:27:24,720
you're interested in

829
00:27:31,110 --> 00:27:29,279
um i mean and what one thing

830
00:27:32,470 --> 00:27:31,120
you can do for example is you just go

831
00:27:34,950 --> 00:27:32,480
into a math library and just

832
00:27:36,630 --> 00:27:34,960
browse at random you know you can pick

833
00:27:39,590 --> 00:27:36,640
out books at random look at the first

834
00:27:41,269 --> 00:27:39,600
few pages see if it's interesting and

835
00:27:42,630 --> 00:27:41,279
if it's interesting you could go deeper

836
00:27:45,510 --> 00:27:42,640
into it um

837
00:27:46,149 --> 00:27:45,520
so i think this is an example of what i

838
00:27:48,470 --> 00:27:46,159
was saying of

839
00:27:49,190 --> 00:27:48,480
generating random ideas how do you do it

840
00:27:51,590 --> 00:27:49,200
well

841
00:27:53,269 --> 00:27:51,600
one way is just to pick out books at

842
00:27:54,230 --> 00:27:53,279
random in a math library and see what

843
00:27:57,590 --> 00:27:54,240
they say

844
00:27:58,870 --> 00:27:57,600
and again you know 90 or 99

845
00:28:00,310 --> 00:27:58,880
of the time there won't be anything

846
00:28:00,789 --> 00:28:00,320
interesting there but every now and then

847
00:28:05,350 --> 00:28:00,799
you

848
00:28:07,110 --> 00:28:05,360
really good

849
00:28:09,590 --> 00:28:07,120
what is it about infinity categories

850
00:28:12,149 --> 00:28:09,600
that you find confounding or troublesome

851
00:28:15,110 --> 00:28:12,159
the definition to start off with i mean

852
00:28:17,350 --> 00:28:15,120
it's it's one of these definitions

853
00:28:18,870 --> 00:28:17,360
i i must have read it half a dozen times

854
00:28:20,630 --> 00:28:18,880
and

855
00:28:21,909 --> 00:28:20,640
half an hour later i just totally forgot

856
00:28:24,149 --> 00:28:21,919
what the definition is

857
00:28:26,230 --> 00:28:24,159
it just it just doesn't seem to stick in

858
00:28:29,110 --> 00:28:26,240
my mind at all i mean

859
00:28:30,950 --> 00:28:29,120
most things you know i have to read them

860
00:28:33,269 --> 00:28:30,960
you know half a dozen times before they

861
00:28:34,870 --> 00:28:33,279
stick infinity categories

862
00:28:36,789 --> 00:28:34,880
i i don't know half a dozen times

863
00:28:39,029 --> 00:28:36,799
there's nowhere near enough

864
00:28:40,310 --> 00:28:39,039
have you read any of emily riehl's work

865
00:28:45,990 --> 00:28:40,320
on infinity categories

866
00:28:50,549 --> 00:28:47,990
does he somehow systematically order his

867
00:28:52,789 --> 00:28:50,559
knowledge mathematical or other

868
00:28:54,870 --> 00:28:52,799
in something like a tree of knowledge

869
00:28:55,350 --> 00:28:54,880
does he explicitly memorize theorems or

870
00:28:57,750 --> 00:28:55,360
proof

871
00:28:59,430 --> 00:28:57,760
to make use of them more easily

872
00:29:02,630 --> 00:28:59,440
absolutely not i i'm

873
00:29:05,029 --> 00:29:02,640
as i said i'm really disorganized um

874
00:29:07,029 --> 00:29:05,039
i'd i've never bothered trying to learn

875
00:29:07,669 --> 00:29:07,039
the proof of a theorem or memorize the

876
00:29:10,870 --> 00:29:07,679
theorem

877
00:29:13,350 --> 00:29:10,880
um i just sort of

878
00:29:15,110 --> 00:29:13,360
re-read them several times so i probably

879
00:29:16,789 --> 00:29:15,120
eventually do sort of know the proofs

880
00:29:18,710 --> 00:29:16,799
but i never made a conscious effort to

881
00:29:21,830 --> 00:29:18,720
memorize the proofs

882
00:29:23,510 --> 00:29:21,840
um what i do try and do is instead of

883
00:29:25,269 --> 00:29:23,520
memorizing a proof so i can write it out

884
00:29:27,590 --> 00:29:25,279
word for word

885
00:29:28,870 --> 00:29:27,600
um which is useless i mean a photocopier

886
00:29:31,830 --> 00:29:28,880
can do that

887
00:29:33,669 --> 00:29:31,840
um you somehow want to internalize the

888
00:29:36,710 --> 00:29:33,679
ideas behind

889
00:29:38,230 --> 00:29:36,720
the essential ideas in a proof and

890
00:29:40,149 --> 00:29:38,240
it's sort of very hard to explain

891
00:29:41,990 --> 00:29:40,159
exactly what this is i mean you somehow

892
00:29:43,430 --> 00:29:42,000
want to

893
00:29:45,350 --> 00:29:43,440
know the theorem well enough that you

894
00:29:47,510 --> 00:29:45,360
can actually use the ideas for something

895
00:29:49,590 --> 00:29:47,520
else which of course a photocopier can't

896
00:29:52,149 --> 00:29:49,600
do

897
00:29:55,830 --> 00:29:52,159
and what's going on in my mind when this

898
00:29:57,190 --> 00:29:55,840
is going on i just no idea

899
00:29:58,950 --> 00:29:57,200
do you find that you're happy with your

900
00:30:00,950 --> 00:29:58,960
life yeah sure

901
00:30:02,630 --> 00:30:00,960
um maybe i'm just too dumb to notice i

902
00:30:03,750 --> 00:30:02,640
shouldn't be happy but yeah yeah i'm

903
00:30:05,830 --> 00:30:03,760
generally happy

904
00:30:10,630 --> 00:30:05,840
are you increasingly sol that is with

905
00:30:15,909 --> 00:30:13,190
about the same not something i pay a lot

906
00:30:17,510 --> 00:30:15,919
of attention to but

907
00:30:21,350 --> 00:30:17,520
what are the most meaningful aspects of

908
00:30:24,710 --> 00:30:21,360
your life doing math mainly

909
00:30:29,269 --> 00:30:24,720
relationships well i've

910
00:30:30,950 --> 00:30:29,279
i've got two kids and i'm married yeah

911
00:30:32,230 --> 00:30:30,960
do you find the relationship with your

912
00:30:34,310 --> 00:30:32,240
kids to be more meaningful than the

913
00:30:37,590 --> 00:30:34,320
mathematics

914
00:30:39,669 --> 00:30:37,600
it's different i mean and i'm not sure

915
00:30:42,870 --> 00:30:39,679
you can really compare them they're

916
00:30:45,110 --> 00:30:42,880
quite different sorts of relationships

917
00:30:46,470 --> 00:30:45,120
okay how about this all the major math

918
00:30:49,590 --> 00:30:46,480
theorems that you want

919
00:30:51,029 --> 00:30:49,600
solved are solved and you have

920
00:30:54,310 --> 00:30:51,039
as much money as you like what do you do

921
00:30:58,070 --> 00:30:54,320
with your time sleep i don't know

922
00:31:00,070 --> 00:30:58,080
um i've no idea um

923
00:31:01,830 --> 00:31:00,080
i mean i spent all my life basically my

924
00:31:03,669 --> 00:31:01,840
spare time has been spent thinking about

925
00:31:04,630 --> 00:31:03,679
mathematics if there was no mathematics

926
00:31:07,669 --> 00:31:04,640
left to do i

927
00:31:10,950 --> 00:31:07,679
really don't know um

928
00:31:14,230 --> 00:31:12,630
maybe just read math for fun or

929
00:31:16,789 --> 00:31:14,240
something i mean it's it's

930
00:31:18,389 --> 00:31:16,799
still quite i mean even if you're not

931
00:31:20,310 --> 00:31:18,399
actually doing research it's still quite

932
00:31:22,389 --> 00:31:20,320
interesting just reading other people's

933
00:31:24,230 --> 00:31:22,399
theorems and their research

934
00:31:25,669 --> 00:31:24,240
so it would be a bit like me asking a

935
00:31:27,669 --> 00:31:25,679
dolphin what if you weren't a dolphin

936
00:31:31,029 --> 00:31:27,679
anymore and it can't conceptualize it

937
00:31:32,950 --> 00:31:31,039
yeah yeah i mean it's it's just

938
00:31:34,789 --> 00:31:32,960
the question doesn't actually mean very

939
00:31:36,149 --> 00:31:34,799
much what was it like to win the fields

940
00:31:40,950 --> 00:31:36,159
medal

941
00:31:45,590 --> 00:31:41,610
yeah um

942
00:31:50,470 --> 00:31:48,549
i mean it didn't really mean very much i

943
00:31:53,190 --> 00:31:50,480
mean it was just a sort of

944
00:31:55,509 --> 00:31:53,200
rather embarrassing ceremony where where

945
00:31:56,230 --> 00:31:55,519
i when i sort of froze as far as i

946
00:32:00,389 --> 00:31:56,240
remember

947
00:32:02,070 --> 00:32:00,399
and they they you know actually proving

948
00:32:03,750 --> 00:32:02,080
proving the theorems is fun you feel

949
00:32:05,750 --> 00:32:03,760
very excited when you've done that

950
00:32:08,710 --> 00:32:05,760
but but you know getting a medal or

951
00:32:10,950 --> 00:32:08,720
something for it is just

952
00:32:11,909 --> 00:32:10,960
just sort of nothing the the only

953
00:32:15,750 --> 00:32:11,919
advantage of it

954
00:32:17,110 --> 00:32:15,760
is is as you stop is you stop worrying

955
00:32:18,549 --> 00:32:17,120
about getting these

956
00:32:20,470 --> 00:32:18,559
these things when you realize how

957
00:32:21,830 --> 00:32:20,480
unimportant they are

958
00:32:23,350 --> 00:32:21,840
when you talked about math you mentioned

959
00:32:24,870 --> 00:32:23,360
that it was it's meaningful to you maybe

960
00:32:26,310 --> 00:32:24,880
one of the most meaningful if not the

961
00:32:27,029 --> 00:32:26,320
most meaningful aspect of your life so

962
00:32:29,269 --> 00:32:27,039
what is it

963
00:32:31,990 --> 00:32:29,279
particularly about math that you find

964
00:32:36,870 --> 00:32:34,470
it's understanding it's part of

965
00:32:38,149 --> 00:32:36,880
understanding how the universe

966
00:32:40,230 --> 00:32:38,159
works you know there are all these

967
00:32:41,830 --> 00:32:40,240
fundamental questions like why does the

968
00:32:43,590 --> 00:32:41,840
universe exist and what are the

969
00:32:47,269 --> 00:32:43,600
fundamental laws of physics

970
00:32:50,389 --> 00:32:47,279
and mathematics is part of that um

971
00:32:51,430 --> 00:32:50,399
so um whenever you're doing mathematics

972
00:32:53,990 --> 00:32:51,440
you sort of

973
00:32:55,830 --> 00:32:54,000
it every piece of mathematics is helping

974
00:32:58,070 --> 00:32:55,840
you a little bit to understand how the

975
00:33:01,029 --> 00:32:58,080
universe works maybe not very much

976
00:33:01,830 --> 00:33:01,039
but um you know the universe as far as

977
00:33:04,070 --> 00:33:01,840
we can tell from

978
00:33:05,909 --> 00:33:04,080
physics the universe is running mainly

979
00:33:09,110 --> 00:33:05,919
on mathematics although we

980
00:33:10,310 --> 00:33:09,120
haven't yet quite figured out the exact

981
00:33:12,470 --> 00:33:10,320
mathematics behind

982
00:33:13,750 --> 00:33:12,480
it does that mean that you have the

983
00:33:16,310 --> 00:33:13,760
sense that when you're

984
00:33:18,549 --> 00:33:16,320
performing math you're engaged in an act

985
00:33:21,430 --> 00:33:18,559
of discovery rather than invention

986
00:33:21,830 --> 00:33:21,440
oh very much so um mathematics is yeah

987
00:33:26,630 --> 00:33:21,840
the

988
00:33:29,430 --> 00:33:26,640
invent or discover math and i'd say it's

989
00:33:31,269 --> 00:33:29,440
entirely discovered not invented well

990
00:33:33,190 --> 00:33:31,279
there are one or two areas i won't

991
00:33:34,470 --> 00:33:33,200
mention where i would say it's invented

992
00:33:36,549 --> 00:33:34,480
and

993
00:33:37,590 --> 00:33:36,559
totally useless but but almost all

994
00:33:38,789 --> 00:33:37,600
mathematics it's

995
00:33:41,669 --> 00:33:38,799
you're discovering something that's

996
00:33:43,350 --> 00:33:41,679
already there so a classical example of

997
00:33:46,310 --> 00:33:43,360
this is the

998
00:33:47,990 --> 00:33:46,320
monster sporadic simple group and this

999
00:33:50,630 --> 00:33:48,000
this has always

1000
00:33:51,990 --> 00:33:50,640
really amazed me because you know the

1001
00:33:54,310 --> 00:33:52,000
axioms for a finite simple

1002
00:33:55,990 --> 00:33:54,320
group are so trivial you you can write

1003
00:33:57,750 --> 00:33:56,000
them out in one line and they're very

1004
00:33:59,029 --> 00:33:57,760
true they're natural and then the

1005
00:34:01,909 --> 00:33:59,039
monster simple group is

1006
00:34:03,430 --> 00:34:01,919
somehow hidden in this single line so

1007
00:34:05,509 --> 00:34:03,440
we've got this monster simple group with

1008
00:34:07,990 --> 00:34:05,519
what 10 to the 54 elements and this

1009
00:34:11,030 --> 00:34:08,000
fantastically intricate structure

1010
00:34:12,629 --> 00:34:11,040
somehow hiding in this trivial one-line

1011
00:34:14,470 --> 00:34:12,639
definition

1012
00:34:15,750 --> 00:34:14,480
and a lot of the best mathematics is

1013
00:34:18,869 --> 00:34:15,760
like that you

1014
00:34:20,869 --> 00:34:18,879
you you know you you

1015
00:34:22,550 --> 00:34:20,879
you've got some sort of box that looks

1016
00:34:26,149 --> 00:34:22,560
just like a plain small

1017
00:34:28,389 --> 00:34:26,159
box without anything figuring it out and

1018
00:34:31,589 --> 00:34:28,399
you open it up and somehow there's this

1019
00:34:33,190 --> 00:34:31,599
massive diamond inside it with no

1020
00:34:34,310 --> 00:34:33,200
indication on the outside of the box

1021
00:34:37,190 --> 00:34:34,320
there's anything

1022
00:34:38,069 --> 00:34:37,200
like that in it what is it about the

1023
00:34:39,589 --> 00:34:38,079
monster group

1024
00:34:41,909 --> 00:34:39,599
or the monster the sporadic monster

1025
00:34:43,909 --> 00:34:41,919
group that you find fascinating because

1026
00:34:45,109 --> 00:34:43,919
to an outsider so let's say someone

1027
00:34:46,790 --> 00:34:45,119
who's not interested in math

1028
00:34:48,710 --> 00:34:46,800
to say that it's interesting is almost

1029
00:34:50,790 --> 00:34:48,720
as arbitrary as saying

1030
00:34:53,270 --> 00:34:50,800
why are there six platonic solids or why

1031
00:34:56,629 --> 00:34:53,280
does the number 1740 exist

1032
00:34:57,829 --> 00:34:56,639
yeah um because we don't understand why

1033
00:35:00,390 --> 00:34:57,839
the monster exists

1034
00:35:02,470 --> 00:35:00,400
i mean you know so there's this

1035
00:35:03,030 --> 00:35:02,480
classification of the finite simple

1036
00:35:05,190 --> 00:35:03,040
groups

1037
00:35:06,630 --> 00:35:05,200
and the classification says well there

1038
00:35:09,510 --> 00:35:06,640
are these infinite families

1039
00:35:10,950 --> 00:35:09,520
and okay infinite families of things are

1040
00:35:13,510 --> 00:35:10,960
kind of uninteresting and

1041
00:35:14,870 --> 00:35:13,520
well okay they're not uninteresting but

1042
00:35:16,390 --> 00:35:14,880
most mathematicians find them very

1043
00:35:19,670 --> 00:35:16,400
interesting but

1044
00:35:21,270 --> 00:35:19,680
um finding an infinite family of things

1045
00:35:22,790 --> 00:35:21,280
isn't too surprising but but the

1046
00:35:24,310 --> 00:35:22,800
classification says there are these

1047
00:35:25,109 --> 00:35:24,320
infinite families like alternating

1048
00:35:28,630 --> 00:35:25,119
groups and then there

1049
00:35:29,990 --> 00:35:28,640
are 26 others left over which

1050
00:35:32,550 --> 00:35:30,000
there's no obvious reason why they

1051
00:35:34,150 --> 00:35:32,560
should exist and the infinite families

1052
00:35:35,829 --> 00:35:34,160
you can sort of think of a reason why

1053
00:35:36,710 --> 00:35:35,839
they exist i mean you know they're

1054
00:35:38,310 --> 00:35:36,720
they're

1055
00:35:39,990 --> 00:35:38,320
general linear groups and they exist

1056
00:35:41,510 --> 00:35:40,000
because they're symmetries of vector

1057
00:35:43,829 --> 00:35:41,520
spaces

1058
00:35:45,510 --> 00:35:43,839
it's a very natural explanation and then

1059
00:35:47,910 --> 00:35:45,520
you have these sporadic simple groups

1060
00:35:50,150 --> 00:35:47,920
exist and they exist because

1061
00:35:51,270 --> 00:35:50,160
well nobody really has any idea why they

1062
00:35:53,829 --> 00:35:51,280
exist there's

1063
00:35:54,950 --> 00:35:53,839
there's no explanation for them beyond

1064
00:35:56,829 --> 00:35:54,960
going through

1065
00:35:59,030 --> 00:35:56,839
you know 10 000 pages of the

1066
00:36:01,510 --> 00:35:59,040
classification

1067
00:36:03,990 --> 00:36:01,520
um so this this may be one of these

1068
00:36:05,430 --> 00:36:04,000
unanswerable questions like you know

1069
00:36:07,990 --> 00:36:05,440
what i mentioned is why does the

1070
00:36:09,829 --> 00:36:08,000
universe exist um

1071
00:36:11,030 --> 00:36:09,839
i mean maybe it just doesn't have an

1072
00:36:15,510 --> 00:36:11,040
answer

1073
00:36:17,349 --> 00:36:15,520
the problem i just cannot imagine

1074
00:36:19,349 --> 00:36:17,359
how you could even answer the question

1075
00:36:20,950 --> 00:36:19,359
why does the universe exist i mean

1076
00:36:22,710 --> 00:36:20,960
imagine an answer that would satisfy you

1077
00:36:24,950 --> 00:36:22,720
as to why the monster group exists what

1078
00:36:28,870 --> 00:36:24,960
would that even look like

1079
00:36:30,870 --> 00:36:28,880
um one one thing might be that

1080
00:36:32,950 --> 00:36:30,880
you know that there's some very natural

1081
00:36:36,470 --> 00:36:32,960
class of geometric objects

1082
00:36:38,790 --> 00:36:36,480
whose symmetries are the

1083
00:36:40,630 --> 00:36:38,800
um sporadic simple groups and people

1084
00:36:43,270 --> 00:36:40,640
have been searching for this for

1085
00:36:45,670 --> 00:36:43,280
decades and no one has ever found any

1086
00:36:49,030 --> 00:36:45,680
plausible candidates

1087
00:36:50,310 --> 00:36:49,040
so um

1088
00:36:51,910 --> 00:36:50,320
i mean for instance the infinite

1089
00:36:53,030 --> 00:36:51,920
families of groups there is a sort of

1090
00:36:56,870 --> 00:36:53,040
natural answer they

1091
00:36:59,190 --> 00:36:56,880
that they all act that the the they

1092
00:37:00,310 --> 00:36:59,200
all have these structures called bn

1093
00:37:02,550 --> 00:37:00,320
pairs

1094
00:37:03,349 --> 00:37:02,560
and this sort of gives an explanation of

1095
00:37:05,670 --> 00:37:03,359
them

1096
00:37:07,270 --> 00:37:05,680
that there's a uniform construction of

1097
00:37:10,710 --> 00:37:07,280
all the

1098
00:37:12,310 --> 00:37:10,720
that aren't sporadic you know there's

1099
00:37:13,750 --> 00:37:12,320
sort of one construction that works for

1100
00:37:16,150 --> 00:37:13,760
all of them you just

1101
00:37:17,829 --> 00:37:16,160
twiddle a few parameters and you you get

1102
00:37:19,750 --> 00:37:17,839
out all of them but for the spreadings

1103
00:37:21,270 --> 00:37:19,760
there's nothing like that

1104
00:37:23,750 --> 00:37:21,280
what is it about quantum field theory

1105
00:37:26,069 --> 00:37:23,760
that you find difficult

1106
00:37:27,670 --> 00:37:26,079
um in our email exchange you mentioned

1107
00:37:31,109 --> 00:37:27,680
that it gives you a headache

1108
00:37:33,190 --> 00:37:31,119
yeah i think the problem is that

1109
00:37:34,870 --> 00:37:33,200
mathematicians are trained that

1110
00:37:35,670 --> 00:37:34,880
everything should be really precisely

1111
00:37:37,670 --> 00:37:35,680
defined

1112
00:37:39,510 --> 00:37:37,680
and you you shouldn't go into the next

1113
00:37:41,349 --> 00:37:39,520
step before you've completely understood

1114
00:37:43,270 --> 00:37:41,359
all the previous steps

1115
00:37:44,870 --> 00:37:43,280
and quantum field theory just isn't like

1116
00:37:48,150 --> 00:37:44,880
that things just

1117
00:37:50,790 --> 00:37:48,160
aren't precisely defined and if you try

1118
00:37:52,550 --> 00:37:50,800
and really find out what the definition

1119
00:37:54,630 --> 00:37:52,560
is you find there's nothing there and it

1120
00:37:57,910 --> 00:37:54,640
just doesn't make sense

1121
00:38:00,230 --> 00:37:57,920
um so do you mind giving an example yeah

1122
00:38:01,910 --> 00:38:00,240
sure if if you look at fiment diagrams

1123
00:38:03,670 --> 00:38:01,920
for example there are

1124
00:38:05,910 --> 00:38:03,680
um that they give you a sort of

1125
00:38:08,630 --> 00:38:05,920
asymptotic expansion of something like a

1126
00:38:11,030 --> 00:38:08,640
scattering coefficient or whatever

1127
00:38:11,990 --> 00:38:11,040
so it's a well-defined asymptotic

1128
00:38:13,990 --> 00:38:12,000
expansion

1129
00:38:17,670 --> 00:38:14,000
you can sort of make sense of that and

1130
00:38:20,470 --> 00:38:17,680
it's an asymptotic expansion of

1131
00:38:21,430 --> 00:38:20,480
and at that point you suddenly get stuck

1132
00:38:22,790 --> 00:38:21,440
um

1133
00:38:25,030 --> 00:38:22,800
no one has actually figured out what

1134
00:38:27,910 --> 00:38:25,040
it's an asymptotic expansion of

1135
00:38:28,950 --> 00:38:27,920
so in some sense it doesn't really make

1136
00:38:31,510 --> 00:38:28,960
sense

1137
00:38:33,510 --> 00:38:31,520
and what is even more annoying is it i

1138
00:38:34,790 --> 00:38:33,520
mean if it didn't make sense i could

1139
00:38:36,710 --> 00:38:34,800
cope with that

1140
00:38:38,870 --> 00:38:36,720
the trouble is that it doesn't make

1141
00:38:40,790 --> 00:38:38,880
sense and it gives answers that you can

1142
00:38:43,510 --> 00:38:40,800
check in experiments and this is

1143
00:38:45,109 --> 00:38:43,520
really annoying because you know

1144
00:38:46,950 --> 00:38:45,119
theoretically it doesn't make sense but

1145
00:38:48,470 --> 00:38:46,960
experimentally it does so there's this

1146
00:38:51,750 --> 00:38:48,480
horrible conflict

1147
00:38:54,870 --> 00:38:51,760
um um so

1148
00:38:56,230 --> 00:38:54,880
and so so i mean in some sense the

1149
00:38:57,670 --> 00:38:56,240
fundamental problem of

1150
00:38:59,510 --> 00:38:57,680
quantum field theory is to give a

1151
00:39:00,710 --> 00:38:59,520
rigorous definition of it there still

1152
00:39:02,150 --> 00:39:00,720
isn't one

1153
00:39:05,190 --> 00:39:02,160
well people have given rigorous

1154
00:39:07,430 --> 00:39:05,200
definitions the trouble is

1155
00:39:08,870 --> 00:39:07,440
the the the quantum field theories that

1156
00:39:11,670 --> 00:39:08,880
people actually use

1157
00:39:13,510 --> 00:39:11,680
in the standard model don't fit these

1158
00:39:16,390 --> 00:39:13,520
rigorous definitions or at least no one

1159
00:39:19,510 --> 00:39:16,400
has managed to prove that they do

1160
00:39:22,470 --> 00:39:19,520
and so this has been an open problem for

1161
00:39:24,390 --> 00:39:22,480
maybe 90 years or so do you have any

1162
00:39:26,150 --> 00:39:24,400
thoughts on the existence of free will

1163
00:39:28,390 --> 00:39:26,160
do you think you have free will and if

1164
00:39:30,230 --> 00:39:28,400
not then why not if so why so

1165
00:39:31,589 --> 00:39:30,240
how are you defining it i thought about

1166
00:39:32,950 --> 00:39:31,599
this a bit and what i

1167
00:39:34,870 --> 00:39:32,960
eventually came to the conclusion was

1168
00:39:35,829 --> 00:39:34,880
that i didn't even know how to define

1169
00:39:39,510 --> 00:39:35,839
what free will

1170
00:39:41,030 --> 00:39:39,520
was so if you can't define something

1171
00:39:41,750 --> 00:39:41,040
precisely it makes it very hard to

1172
00:39:45,030 --> 00:39:41,760
discuss

1173
00:39:47,349 --> 00:39:45,040
in fact this this is a big problem with

1174
00:39:48,950 --> 00:39:47,359
an awful lot of philosophical questions

1175
00:39:51,030 --> 00:39:48,960
if you look at them close enough you

1176
00:39:53,589 --> 00:39:51,040
discover the terms in them are simply

1177
00:39:56,710 --> 00:39:53,599
not well defined enough to talk about

1178
00:39:59,109 --> 00:39:56,720
so can you even define free will can you

1179
00:40:02,069 --> 00:39:59,119
talk about it not as a mathematician but

1180
00:40:02,950 --> 00:40:02,079
let's say as a regular person about what

1181
00:40:05,910 --> 00:40:02,960
free will

1182
00:40:06,710 --> 00:40:05,920
is that there's the slippery definition

1183
00:40:08,950 --> 00:40:06,720
but so

1184
00:40:10,470 --> 00:40:08,960
there is also a slippery definition as

1185
00:40:13,190 --> 00:40:10,480
to what constitutes a chair

1186
00:40:14,470 --> 00:40:13,200
or i or you and presumably you've used

1187
00:40:16,470 --> 00:40:14,480
those in sentences before

1188
00:40:18,790 --> 00:40:16,480
with facility well that so can you do

1189
00:40:20,870 --> 00:40:18,800
this yeah i i can sort of

1190
00:40:22,790 --> 00:40:20,880
vaguely define a chair in some way that

1191
00:40:23,190 --> 00:40:22,800
i can most the time recognize a chair

1192
00:40:27,270 --> 00:40:23,200
i've

1193
00:40:28,870 --> 00:40:27,280
just cannot come up with a definition i

1194
00:40:30,470 --> 00:40:28,880
poached around a bit as far as i can

1195
00:40:33,750 --> 00:40:30,480
figure out nobody else has come up with

1196
00:40:35,670 --> 00:40:33,760
a convincing definition either

1197
00:40:37,589 --> 00:40:35,680
i mean you certainly have this feeling

1198
00:40:40,950 --> 00:40:37,599
in inside yourself

1199
00:40:43,109 --> 00:40:40,960
that you can choose what to do but

1200
00:40:44,069 --> 00:40:43,119
um you know maybe this feeling is an

1201
00:40:47,910 --> 00:40:44,079
illusion

1202
00:40:50,230 --> 00:40:47,920
and everything we do is determined by

1203
00:40:51,990 --> 00:40:50,240
some laws of physics and we just have

1204
00:40:53,750 --> 00:40:52,000
this illusion that

1205
00:40:56,150 --> 00:40:53,760
we're choosing what these laws of

1206
00:40:58,230 --> 00:40:56,160
physics do

1207
00:41:00,309 --> 00:40:58,240
but i don't know i mean i i can't even

1208
00:41:02,870 --> 00:41:00,319
define what is meant by

1209
00:41:03,910 --> 00:41:02,880
having a feeling that we we can choose

1210
00:41:07,030 --> 00:41:03,920
what to do

1211
00:41:08,790 --> 00:41:07,040
so you're agnostic on the issue i'm

1212
00:41:10,870 --> 00:41:08,800
i think it's even worse than being

1213
00:41:12,470 --> 00:41:10,880
agnostic i i'd say i i don't

1214
00:41:14,150 --> 00:41:12,480
i'm not saying i don't know what the

1215
00:41:15,670 --> 00:41:14,160
answer to the question is i'm saying i

1216
00:41:17,829 --> 00:41:15,680
i don't even know what the question

1217
00:41:19,349 --> 00:41:17,839
means and i not at all sure it even

1218
00:41:22,230 --> 00:41:19,359
makes sense

1219
00:41:23,030 --> 00:41:22,240
what about god do you believe in god and

1220
00:41:24,790 --> 00:41:23,040
the same problem

1221
00:41:26,470 --> 00:41:24,800
uh before we start discussing god i

1222
00:41:27,190 --> 00:41:26,480
would like you to define what you mean

1223
00:41:29,589 --> 00:41:27,200
by the term

1224
00:41:31,109 --> 00:41:29,599
god because there are so many different

1225
00:41:33,030 --> 00:41:31,119
definitions

1226
00:41:35,190 --> 00:41:33,040
um so you could have a god of your

1227
00:41:37,109 --> 00:41:35,200
favorite religion saying it's this

1228
00:41:39,190 --> 00:41:37,119
guy who maybe zaps people with

1229
00:41:41,750 --> 00:41:39,200
thunderbolts or whatever

1230
00:41:42,230 --> 00:41:41,760
or you could say you know god is just a

1231
00:41:44,150 --> 00:41:42,240
name

1232
00:41:45,670 --> 00:41:44,160
for the underlying essence of the

1233
00:41:48,710 --> 00:41:45,680
universe which is sort of

1234
00:41:51,109 --> 00:41:48,720
maybe meaningless but you could say in

1235
00:41:52,710 --> 00:41:51,119
in that sense god exists because it's

1236
00:41:54,710 --> 00:41:52,720
god is just a name for whatever the

1237
00:41:55,670 --> 00:41:54,720
explanation of the universe is so there

1238
00:41:57,589 --> 00:41:55,680
are

1239
00:41:59,190 --> 00:41:57,599
all these different possible definitions

1240
00:42:02,309 --> 00:41:59,200
of god and

1241
00:42:04,069 --> 00:42:02,319
some of them that you

1242
00:42:05,670 --> 00:42:04,079
you could recently say they do exist

1243
00:42:06,950 --> 00:42:05,680
some of them you could say

1244
00:42:08,790 --> 00:42:06,960
there seems to be very little evidence

1245
00:42:10,630 --> 00:42:08,800
for it and others it's just not clear

1246
00:42:12,309 --> 00:42:10,640
what the question means so

1247
00:42:13,670 --> 00:42:12,319
before discussing this philosophical

1248
00:42:15,990 --> 00:42:13,680
question let's first have some

1249
00:42:17,670 --> 00:42:16,000
precise definitions you mentioned one

1250
00:42:18,390 --> 00:42:17,680
that god is the universe in some way

1251
00:42:21,270 --> 00:42:18,400
shape or form

1252
00:42:22,309 --> 00:42:21,280
now why is that meaningless well it

1253
00:42:23,910 --> 00:42:22,319
because

1254
00:42:25,670 --> 00:42:23,920
it's just words it doesn't actually tell

1255
00:42:27,349 --> 00:42:25,680
you anything more about the universe

1256
00:42:29,109 --> 00:42:27,359
that you didn't already know

1257
00:42:30,630 --> 00:42:29,119
um so that there's a whole lot of

1258
00:42:31,270 --> 00:42:30,640
questions like this you could say you

1259
00:42:34,390 --> 00:42:31,280
know the

1260
00:42:38,630 --> 00:42:34,400
the universe is really a simulation or

1261
00:42:40,710 --> 00:42:38,640
the universe is um a cellular automaton

1262
00:42:41,750 --> 00:42:40,720
or maybe there are lots of parallel

1263
00:42:44,710 --> 00:42:41,760
universes

1264
00:42:46,230 --> 00:42:44,720
and none of these actually say anything

1265
00:42:47,190 --> 00:42:46,240
whatsoever about the universe i mean

1266
00:42:49,270 --> 00:42:47,200
that they're all

1267
00:42:51,670 --> 00:42:49,280
great plots for comic book stories or

1268
00:42:52,790 --> 00:42:51,680
whatever but

1269
00:42:54,390 --> 00:42:52,800
you know what what's the difference

1270
00:42:55,910 --> 00:42:54,400
between the universe being a cellular

1271
00:42:58,230 --> 00:42:55,920
automaton the universe not being a

1272
00:42:59,589 --> 00:42:58,240
cellular automaton well i've

1273
00:43:02,550 --> 00:42:59,599
there just doesn't seem to be any

1274
00:43:03,589 --> 00:43:02,560
difference or what what's the universe

1275
00:43:05,910 --> 00:43:03,599
what's the difference between there

1276
00:43:07,430 --> 00:43:05,920
being a sort of pantheistic god

1277
00:43:09,510 --> 00:43:07,440
underlying everything or they're not

1278
00:43:12,470 --> 00:43:09,520
being a pantheistic god well

1279
00:43:13,430 --> 00:43:12,480
i've no idea it it just seems to be a

1280
00:43:16,550 --> 00:43:13,440
content-free

1281
00:43:18,550 --> 00:43:16,560
sentence in your psychology and your

1282
00:43:19,990 --> 00:43:18,560
mindset nothing would be changed if you

1283
00:43:21,190 --> 00:43:20,000
found out that you were the only

1284
00:43:24,550 --> 00:43:21,200
conscious person

1285
00:43:25,829 --> 00:43:24,560
or that you were living in a dream i i

1286
00:43:27,190 --> 00:43:25,839
don't know how i could tell the

1287
00:43:28,950 --> 00:43:27,200
difference between being the only

1288
00:43:30,150 --> 00:43:28,960
conscious person or not being the only

1289
00:43:32,230 --> 00:43:30,160
conscious person

1290
00:43:34,550 --> 00:43:32,240
i mean i assume other people are

1291
00:43:35,829 --> 00:43:34,560
conscious just by analogy with myself

1292
00:43:37,910 --> 00:43:35,839
but i

1293
00:43:39,589 --> 00:43:37,920
i can't imagine any experiment that

1294
00:43:41,349 --> 00:43:39,599
could actually prove beyond doubt that

1295
00:43:42,470 --> 00:43:41,359
someone else was really conscious rather

1296
00:43:47,030 --> 00:43:42,480
than just a

1297
00:43:48,870 --> 00:43:47,040
running inside someone's brain

1298
00:43:50,390 --> 00:43:48,880
okay again it's this problem of what is

1299
00:43:52,470 --> 00:43:50,400
free will i

1300
00:43:53,990 --> 00:43:52,480
i can't think of any experiment that can

1301
00:43:57,270 --> 00:43:54,000
tell the difference between having free

1302
00:44:00,390 --> 00:43:57,280
will and not having free will okay

1303
00:44:01,270 --> 00:44:00,400
how about this i imagine that there is

1304
00:44:03,829 --> 00:44:01,280
no

1305
00:44:05,910 --> 00:44:03,839
experiment that can test whether you

1306
00:44:07,670 --> 00:44:05,920
love your wife or your wife loves you

1307
00:44:09,430 --> 00:44:07,680
yet i imagine also that the answer to

1308
00:44:11,109 --> 00:44:09,440
that matters to you

1309
00:44:13,349 --> 00:44:11,119
so in a similar well does it first of

1310
00:44:15,030 --> 00:44:13,359
all well it's it's a it's another these

1311
00:44:18,790 --> 00:44:15,040
terms it's really hard to

1312
00:44:20,550 --> 00:44:18,800
define i mean i'm i think this is this

1313
00:44:22,550 --> 00:44:20,560
is another question about my internal

1314
00:44:24,710 --> 00:44:22,560
state of mind which as i've noticed in

1315
00:44:26,470 --> 00:44:24,720
several of your other questions i a very

1316
00:44:28,550 --> 00:44:26,480
hard time figuring out what my internal

1317
00:44:33,510 --> 00:44:28,560
state of mind actually is

1318
00:44:36,470 --> 00:44:35,109
do you tend to think about yourself or

1319
00:44:37,750 --> 00:44:36,480
do you just tend to think outside

1320
00:44:40,069 --> 00:44:37,760
yourself

1321
00:44:41,750 --> 00:44:40,079
i i do sometimes think about myself and

1322
00:44:43,670 --> 00:44:41,760
the conclusion i tend to come to is that

1323
00:44:44,630 --> 00:44:43,680
i have absolutely no idea what is going

1324
00:44:46,790 --> 00:44:44,640
on i mean it's

1325
00:44:49,030 --> 00:44:46,800
it's it's a problem that i've that

1326
00:44:50,710 --> 00:44:49,040
completely baffles me

1327
00:44:52,390 --> 00:44:50,720
i mean i have no idea what is going on

1328
00:44:54,470 --> 00:44:52,400
in my own mind let alone what is going

1329
00:44:55,910 --> 00:44:54,480
on in other people's minds

1330
00:44:57,750 --> 00:44:55,920
so do you have any thoughts about

1331
00:45:01,190 --> 00:44:57,760
equivocal questions about the

1332
00:45:02,710 --> 00:45:01,200
hard problem of consciousness um

1333
00:45:04,950 --> 00:45:02,720
you have to remind me which which is the

1334
00:45:07,030 --> 00:45:04,960
hard problem i vaguely remember penrose

1335
00:45:08,550 --> 00:45:07,040
talking about this but i've

1336
00:45:10,470 --> 00:45:08,560
forgotten which is the easy problem

1337
00:45:12,069 --> 00:45:10,480
which is the hard problem the easy

1338
00:45:14,309 --> 00:45:12,079
problem are the correlates so for

1339
00:45:15,589 --> 00:45:14,319
example anger is associated with so and

1340
00:45:17,589 --> 00:45:15,599
so part of the brain

1341
00:45:19,190 --> 00:45:17,599
and a certain circuit the heart problem

1342
00:45:20,870 --> 00:45:19,200
is how is it at all that

1343
00:45:24,230 --> 00:45:20,880
consciousness that is experienced can

1344
00:45:27,670 --> 00:45:24,240
arise from material only

1345
00:45:29,270 --> 00:45:27,680
um yeah this th this is like all these

1346
00:45:32,630 --> 00:45:29,280
questions in

1347
00:45:33,829 --> 00:45:32,640
douglas hof starters books and again i

1348
00:45:35,829 --> 00:45:33,839
have no idea

1349
00:45:38,470 --> 00:45:35,839
we have all these experiments like like

1350
00:45:39,109 --> 00:45:38,480
suppose you simulate the brain by taking

1351
00:45:51,430 --> 00:45:39,119
a

1352
00:45:53,109 --> 00:45:51,440
conscious

1353
00:45:54,470 --> 00:45:53,119
and then you could go a step further and

1354
00:45:56,870 --> 00:45:54,480
you could

1355
00:45:58,309 --> 00:45:56,880
write a complete description of the

1356
00:46:00,470 --> 00:45:58,319
human brain and what it's doing on a

1357
00:46:03,670 --> 00:46:00,480
very big piece of paper

1358
00:46:06,309 --> 00:46:03,680
and is that piece of paper conscious and

1359
00:46:08,150 --> 00:46:06,319
you know if if you you know erase bits

1360
00:46:09,670 --> 00:46:08,160
of this piece of paper according to

1361
00:46:10,710 --> 00:46:09,680
certain rules they're simulating the

1362
00:46:13,270 --> 00:46:10,720
action of the brain

1363
00:46:14,950 --> 00:46:13,280
are is you know is is that piece of

1364
00:46:17,030 --> 00:46:14,960
paper with all these

1365
00:46:18,790 --> 00:46:17,040
things being erased repeatedly conscious

1366
00:46:21,190 --> 00:46:18,800
because it's you know in some sense it's

1367
00:46:23,589 --> 00:46:21,200
indistinguishable from a human brain

1368
00:46:25,670 --> 00:46:23,599
and on the other hand it seems utterly

1369
00:46:28,550 --> 00:46:25,680
ridiculous to claim it's conscious

1370
00:46:29,349 --> 00:46:28,560
i i have no idea how to resolve this

1371
00:46:30,230 --> 00:46:29,359
problem

1372
00:46:32,390 --> 00:46:30,240
what are some of your favorite

1373
00:46:35,910 --> 00:46:32,400
mathematicians and physicists

1374
00:46:37,910 --> 00:46:35,920
alive alive oh um

1375
00:46:39,190 --> 00:46:37,920
well i think the the one i like reading

1376
00:46:41,510 --> 00:46:39,200
most is probably jp

1377
00:46:43,589 --> 00:46:41,520
ser i mean i i don't work in his area

1378
00:46:45,990 --> 00:46:43,599
but he's so good at writing that

1379
00:46:47,430 --> 00:46:46,000
that i read almost you know i try and

1380
00:46:48,150 --> 00:46:47,440
read almost everything he's written

1381
00:46:50,230 --> 00:46:48,160
because he's saying

1382
00:46:51,670 --> 00:46:50,240
the number theorists explaining well

1383
00:46:52,790 --> 00:46:51,680
he's he's one of these really great

1384
00:46:56,150 --> 00:46:52,800
mathematicians who

1385
00:46:57,829 --> 00:46:56,160
moves around so he's a number theorist

1386
00:47:01,030 --> 00:46:57,839
he's also an algebraic geometry he's

1387
00:47:03,349 --> 00:47:01,040
also an algebraic apologist and he's

1388
00:47:04,790 --> 00:47:03,359
also done quite a few other things i

1389
00:47:06,550 --> 00:47:04,800
mean he's he's sort of one of the

1390
00:47:09,190 --> 00:47:06,560
closest things we have to a universal

1391
00:47:12,630 --> 00:47:09,200
mathematician what about terry tau

1392
00:47:13,670 --> 00:47:12,640
um yeah again um um i've been collecting

1393
00:47:15,910 --> 00:47:13,680
his books and

1394
00:47:17,430 --> 00:47:15,920
and and they're on my big pile of books

1395
00:47:18,150 --> 00:47:17,440
i really ought to get around to reading

1396
00:47:21,670 --> 00:47:18,160
some day

1397
00:47:23,190 --> 00:47:21,680
um and yeah he's

1398
00:47:24,950 --> 00:47:23,200
that that's interesting because he

1399
00:47:26,630 --> 00:47:24,960
thinks in such a different way from what

1400
00:47:30,549 --> 00:47:26,640
i do i mean he's an analyst

1401
00:47:32,150 --> 00:47:30,559
and um well again he's not just an

1402
00:47:33,990 --> 00:47:32,160
analyst he also does lots of things in

1403
00:47:35,910 --> 00:47:34,000
number theory and and so on but

1404
00:47:37,829 --> 00:47:35,920
and he's obviously thinking much more in

1405
00:47:39,670 --> 00:47:37,839
terms of inequalities and error

1406
00:47:43,030 --> 00:47:39,680
estimates and all the other things that

1407
00:47:45,109 --> 00:47:43,040
analysts do than i do and so i'm i'd say

1408
00:47:46,150 --> 00:47:45,119
much more towards the algebraic side

1409
00:47:48,390 --> 00:47:46,160
where i

1410
00:47:49,349 --> 00:47:48,400
do equalities and then sort of get a bit

1411
00:47:52,630 --> 00:47:49,359
nervous whenever

1412
00:47:55,190 --> 00:47:52,640
anybody writes down an inequality sign

1413
00:47:57,030 --> 00:47:55,200
what about physicists now uh i don't

1414
00:48:00,390 --> 00:47:57,040
really have favorite physicists

1415
00:48:01,910 --> 00:48:00,400
um i mean i i enjoy reading richard

1416
00:48:03,990 --> 00:48:01,920
feynman but that's

1417
00:48:05,829 --> 00:48:04,000
that's that's largely because of his

1418
00:48:09,630 --> 00:48:05,839
popular books rather than because of his

1419
00:48:15,190 --> 00:48:12,390
[Music]

1420
00:48:17,270 --> 00:48:15,200
who else i read you know stephen

1421
00:48:18,630 --> 00:48:17,280
weinberg has some rather nice books on

1422
00:48:22,470 --> 00:48:18,640
quantum field theory

1423
00:48:24,150 --> 00:48:22,480
and yeah i i i don't spend so much time

1424
00:48:25,430 --> 00:48:24,160
on physics really

1425
00:48:26,870 --> 00:48:25,440
what are your thoughts on ed whitten

1426
00:48:27,349 --> 00:48:26,880
have you collaborated with him or met

1427
00:48:31,750 --> 00:48:27,359
him

1428
00:48:34,069 --> 00:48:31,760
terrifying he he produced these you know

1429
00:48:36,309 --> 00:48:34,079
fantastically brilliant papers about one

1430
00:48:38,470 --> 00:48:36,319
a month or something and i

1431
00:48:39,910 --> 00:48:38,480
i don't know i have no idea how he has

1432
00:48:43,349 --> 00:48:39,920
the energy to do this

1433
00:48:45,589 --> 00:48:43,359
and you know it's a stream of endless

1434
00:48:49,030 --> 00:48:45,599
good ideas that he comes up with i mean

1435
00:48:51,190 --> 00:48:49,040
he i mean he he he came up with these

1436
00:48:53,430 --> 00:48:51,200
cyborg written in vance and they they

1437
00:48:55,750 --> 00:48:53,440
were almost a sort of minor side effect

1438
00:48:57,589 --> 00:48:55,760
of something else he was thinking on and

1439
00:49:00,069 --> 00:48:57,599
you know they revolutionized some area

1440
00:49:03,270 --> 00:49:00,079
in mathematics that

1441
00:49:05,190 --> 00:49:03,280
you know he he really

1442
00:49:07,670 --> 00:49:05,200
had almost had nothing to do with before

1443
00:49:09,670 --> 00:49:07,680
that's you know he was just sort of

1444
00:49:11,910 --> 00:49:09,680
revolutionizing the area of mathematics

1445
00:49:13,270 --> 00:49:11,920
just as a casual side effect of

1446
00:49:14,710 --> 00:49:13,280
something else he was doing

1447
00:49:16,309 --> 00:49:14,720
let's get to the monster group what are

1448
00:49:16,710 --> 00:49:16,319
some of the applications of the monster

1449
00:49:20,150 --> 00:49:16,720
group

1450
00:49:23,829 --> 00:49:20,160
to physics they're all intended

1451
00:49:25,910 --> 00:49:23,839
are there conjectures um well

1452
00:49:27,270 --> 00:49:25,920
there there are some there's been some

1453
00:49:30,870 --> 00:49:27,280
speculation i mean

1454
00:49:32,710 --> 00:49:30,880
ed whitton for example has some

1455
00:49:34,069 --> 00:49:32,720
um speculation about a connection

1456
00:49:35,670 --> 00:49:34,079
between the monster and some sort of

1457
00:49:37,349 --> 00:49:35,680
gravity theory

1458
00:49:39,510 --> 00:49:37,359
and that the mathematics behind the

1459
00:49:41,349 --> 00:49:39,520
monsters is quite similar to a lot of

1460
00:49:44,790 --> 00:49:41,359
mathematics that turns up in string

1461
00:49:47,910 --> 00:49:44,800
theory so you can speculate that there's

1462
00:49:49,910 --> 00:49:47,920
a connection but no one has ever found

1463
00:49:51,349 --> 00:49:49,920
any sign that the monsters anything to

1464
00:49:53,430 --> 00:49:51,359
do with you know real

1465
00:49:55,109 --> 00:49:53,440
everyday four-dimensional physics there

1466
00:49:56,309 --> 00:49:55,119
are some people who try to build physics

1467
00:49:58,470 --> 00:49:56,319
off of the e8

1468
00:49:59,670 --> 00:49:58,480
and what has a dimension in eight has an

1469
00:50:02,150 --> 00:49:59,680
echo in 24

1470
00:50:03,030 --> 00:50:02,160
and then 24 is somehow associated with a

1471
00:50:05,430 --> 00:50:03,040
monster

1472
00:50:07,829 --> 00:50:05,440
so yeah i'm wondering can one base

1473
00:50:12,150 --> 00:50:07,839
physics off of the monster group

1474
00:50:14,390 --> 00:50:12,160
um i wouldn't

1475
00:50:15,510 --> 00:50:14,400
um i would write that off as a really

1476
00:50:16,790 --> 00:50:15,520
crazy idea

1477
00:50:18,790 --> 00:50:16,800
i'm not saying it's wrong i'm just

1478
00:50:20,309 --> 00:50:18,800
saying it's really crazy

1479
00:50:21,990 --> 00:50:20,319
um i mean it'd be really nice if the

1480
00:50:23,670 --> 00:50:22,000
monster group did turn up in physics

1481
00:50:24,630 --> 00:50:23,680
somewhere but as i said there's there's

1482
00:50:26,870 --> 00:50:24,640
no

1483
00:50:28,950 --> 00:50:26,880
realistic sign of this yet apart from

1484
00:50:32,870 --> 00:50:28,960
the fact that both the monster and

1485
00:50:33,910 --> 00:50:32,880
string theory use that you use similar

1486
00:50:35,670 --> 00:50:33,920
ideas

1487
00:50:37,990 --> 00:50:35,680
for people watching just so you know

1488
00:50:41,270 --> 00:50:38,000
professor portraits has a

1489
00:50:42,710 --> 00:50:41,280
great youtube series on teaching

1490
00:50:44,309 --> 00:50:42,720
graduate level mathematics and i

1491
00:50:45,829 --> 00:50:44,319
recommend you check that out do you

1492
00:50:48,390 --> 00:50:45,839
enjoy teaching

1493
00:50:50,230 --> 00:50:48,400
is it just your connotation it's fun

1494
00:50:53,349 --> 00:50:50,240
making these videos except it's

1495
00:50:56,309 --> 00:50:53,359
it's also kind of stressful because

1496
00:50:56,710 --> 00:50:56,319
i mean it's i hadn't realized just how

1497
00:50:59,829 --> 00:50:56,720
many

1498
00:51:01,030 --> 00:50:59,839
errors i made in lectures um you know

1499
00:51:03,349 --> 00:51:01,040
you're lecturing and

1500
00:51:04,150 --> 00:51:03,359
you don't notice anything wrong and then

1501
00:51:05,750 --> 00:51:04,160
suddenly

1502
00:51:07,589 --> 00:51:05,760
when you put the youtube up people

1503
00:51:08,150 --> 00:51:07,599
pointing out all these embarrassingly

1504
00:51:11,750 --> 00:51:08,160
stupid

1505
00:51:13,829 --> 00:51:11,760
misprints you made and

1506
00:51:15,430 --> 00:51:13,839
you know i i i guess i should just feel

1507
00:51:16,950 --> 00:51:15,440
relieved that i'm not a you know i

1508
00:51:18,950 --> 00:51:16,960
sometimes think well it's

1509
00:51:20,309 --> 00:51:18,960
thank goodness i'm not a doctor or a cop

1510
00:51:22,150 --> 00:51:20,319
or something because you know if a

1511
00:51:23,910 --> 00:51:22,160
doctor or a cop makes a mistake

1512
00:51:26,390 --> 00:51:23,920
you know there's someone dead and there

1513
00:51:26,870 --> 00:51:26,400
are headlines and committees of inquiry

1514
00:51:28,710 --> 00:51:26,880
and

1515
00:51:30,710 --> 00:51:28,720
when i make an embarrassing mistake i

1516
00:51:31,589 --> 00:51:30,720
get this polite note from a youtube

1517
00:51:33,109 --> 00:51:31,599
comment so i

1518
00:51:34,790 --> 00:51:33,119
maybe i shouldn't complain too much

1519
00:51:36,630 --> 00:51:34,800
about it you mentioned

1520
00:51:38,150 --> 00:51:36,640
that innovations coming from outside the

1521
00:51:41,030 --> 00:51:38,160
field of academia

1522
00:51:43,030 --> 00:51:41,040
for math in particular is rare unlike

1523
00:51:44,470 --> 00:51:43,040
the past which was

1524
00:51:46,630 --> 00:51:44,480
you gave some examples for matt and

1525
00:51:48,549 --> 00:51:46,640
kaylee who were lawyers

1526
00:51:50,470 --> 00:51:48,559
and i'm wondering is this still true

1527
00:51:51,829 --> 00:51:50,480
today as far as i know

1528
00:51:53,349 --> 00:51:51,839
you mentioned one of the reasons is that

1529
00:51:54,069 --> 00:51:53,359
it's easier to get a position in

1530
00:51:57,109 --> 00:51:54,079
academia

1531
00:51:59,270 --> 00:51:57,119
but i don't know if that's true today

1532
00:52:01,349 --> 00:51:59,280
well unless you're a postdoc it's very

1533
00:52:02,710 --> 00:52:01,359
much true compared to now compared to a

1534
00:52:04,309 --> 00:52:02,720
few hundred years ago when there

1535
00:52:06,069 --> 00:52:04,319
basically weren't any positions for

1536
00:52:09,190 --> 00:52:06,079
mathematicians in academia

1537
00:52:10,870 --> 00:52:09,200
maybe one or two in the world the the

1538
00:52:12,710 --> 00:52:10,880
other big problem is

1539
00:52:15,109 --> 00:52:12,720
all the easy stuff in mathematics and

1540
00:52:18,309 --> 00:52:15,119
physics has been done

1541
00:52:20,710 --> 00:52:18,319
so people like firma when they started

1542
00:52:24,470 --> 00:52:20,720
doing mathematics said that there were

1543
00:52:26,710 --> 00:52:24,480
whole loads of things they could do

1544
00:52:28,549 --> 00:52:26,720
which well that they were difficult for

1545
00:52:29,910 --> 00:52:28,559
the time but nowadays they count as easy

1546
00:52:31,910 --> 00:52:29,920
whereas

1547
00:52:33,190 --> 00:52:31,920
if someone was starting from outside

1548
00:52:35,109 --> 00:52:33,200
trying to do mathematics now it'd be

1549
00:52:37,990 --> 00:52:35,119
incredibly difficult because

1550
00:52:40,470 --> 00:52:38,000
anything you can think of in less than

1551
00:52:44,309 --> 00:52:40,480
several years study someone has already

1552
00:52:45,589 --> 00:52:44,319
thought of it so it's it's partly that

1553
00:52:48,470 --> 00:52:45,599
there are

1554
00:52:50,150 --> 00:52:48,480
i mean i mean people coming from outside

1555
00:52:51,270 --> 00:52:50,160
doing something big in mathematics has

1556
00:52:53,270 --> 00:52:51,280
become

1557
00:52:54,870 --> 00:52:53,280
very rare because it's so difficult to

1558
00:52:58,870 --> 00:52:54,880
find

1559
00:53:00,549 --> 00:52:58,880
any problem that an outsider can do

1560
00:53:02,549 --> 00:53:00,559
what advice do you have for outsiders

1561
00:53:04,710 --> 00:53:02,559
who want to contribute to math or at

1562
00:53:05,990 --> 00:53:04,720
least study it at the graduate phd level

1563
00:53:08,549 --> 00:53:06,000
but they're on their own it's the

1564
00:53:10,230 --> 00:53:08,559
pandemic they don't have peers

1565
00:53:12,150 --> 00:53:10,240
much like yourself you don't collaborate

1566
00:53:13,910 --> 00:53:12,160
so what advice do you have for them

1567
00:53:15,349 --> 00:53:13,920
if you really want to contribute

1568
00:53:16,390 --> 00:53:15,359
something new you need to find a

1569
00:53:19,430 --> 00:53:16,400
relatively new

1570
00:53:21,349 --> 00:53:19,440
area in mathematics um

1571
00:53:23,349 --> 00:53:21,359
so i mean every now and then that

1572
00:53:24,230 --> 00:53:23,359
someone has a new idea that breaks open

1573
00:53:26,630 --> 00:53:24,240
a new area

1574
00:53:28,549 --> 00:53:26,640
and then you know it's it's like you

1575
00:53:31,670 --> 00:53:28,559
know there's this

1576
00:53:32,870 --> 00:53:31,680
um dead whale theory you know if you're

1577
00:53:34,390 --> 00:53:32,880
at the bottom of an ocean there's

1578
00:53:36,390 --> 00:53:34,400
usually nothing to eat but every now and

1579
00:53:38,230 --> 00:53:36,400
then there's a dead whale comes down and

1580
00:53:40,390 --> 00:53:38,240
everybody goes frantic eating it

1581
00:53:42,230 --> 00:53:40,400
and every now and then there's a really

1582
00:53:44,150 --> 00:53:42,240
new area in mathematics and if you can

1583
00:53:45,670 --> 00:53:44,160
spot one of those and get in on it then

1584
00:53:48,950 --> 00:53:45,680
there's a lot to do

1585
00:53:49,670 --> 00:53:48,960
a typical example a few years ago with

1586
00:53:51,829 --> 00:53:49,680
things like

1587
00:53:55,589 --> 00:53:51,839
fractals and chaos became really big

1588
00:54:01,750 --> 00:53:59,109
it's very hard to suggest new areas

1589
00:54:03,430 --> 00:54:01,760
because if i knew about them then

1590
00:54:06,069 --> 00:54:03,440
i'd probably already be working in it or

1591
00:54:08,309 --> 00:54:06,079
something um

1592
00:54:09,349 --> 00:54:08,319
yeah there's one thing i was thinking of

1593
00:54:14,470 --> 00:54:09,359
that

1594
00:54:16,230 --> 00:54:14,480
none people are not mathematicians might

1595
00:54:19,270 --> 00:54:16,240
be able to contribute to and that's

1596
00:54:22,470 --> 00:54:19,280
um artificial intelligence

1597
00:54:24,870 --> 00:54:22,480
doing mathematics i mean you know

1598
00:54:26,309 --> 00:54:24,880
um so google came up with this

1599
00:54:27,510 --> 00:54:26,319
artificial intelligence program that

1600
00:54:29,510 --> 00:54:27,520
could play go or chess

1601
00:54:31,190 --> 00:54:29,520
very well and i'm pretty sure the people

1602
00:54:32,950 --> 00:54:31,200
at google programming this were not

1603
00:54:34,630 --> 00:54:32,960
expert go or chess players

1604
00:54:36,230 --> 00:54:34,640
they they were what they were really

1605
00:54:38,870 --> 00:54:36,240
good at was building an artificial

1606
00:54:41,510 --> 00:54:38,880
intelligence system and

1607
00:54:42,870 --> 00:54:41,520
sooner or later artificial intelligence

1608
00:54:45,349 --> 00:54:42,880
is probably going to get good enough to

1609
00:54:49,109 --> 00:54:45,359
do serious mathematics

1610
00:54:52,470 --> 00:54:49,119
um so that might be one thing to look at

1611
00:54:54,630 --> 00:54:52,480
if you're an outsider um you know

1612
00:54:56,470 --> 00:54:54,640
get into artificial intelligence doing

1613
00:54:57,430 --> 00:54:56,480
mathematics i think there are not so

1614
00:54:59,670 --> 00:54:57,440
many

1615
00:55:00,950 --> 00:54:59,680
pure mathematicians looking at that now

1616
00:55:03,030 --> 00:55:00,960
and

1617
00:55:05,349 --> 00:55:03,040
in a few years it might take off quite

1618
00:55:06,950 --> 00:55:05,359
suddenly so in some sense

1619
00:55:08,470 --> 00:55:06,960
let's say 30 40 years from now the

1620
00:55:09,829 --> 00:55:08,480
computers will be better than us at

1621
00:55:11,829 --> 00:55:09,839
doing mathematics so why don't you be

1622
00:55:13,910 --> 00:55:11,839
the puppet master behind the computer

1623
00:55:14,950 --> 00:55:13,920
if you want to help the innovation yeah

1624
00:55:16,230 --> 00:55:14,960
yeah exactly

1625
00:55:18,230 --> 00:55:16,240
at some point did you ever feel like

1626
00:55:20,230 --> 00:55:18,240
math and physics wasn't for you either

1627
00:55:21,990 --> 00:55:20,240
because of its difficulty or for some

1628
00:55:25,829 --> 00:55:22,000
other reason

1629
00:55:29,430 --> 00:55:25,839
um no not really

1630
00:55:30,950 --> 00:55:29,440
um it sort of never never seriously

1631
00:55:32,069 --> 00:55:30,960
occurred to me to do anything other than

1632
00:55:34,309 --> 00:55:32,079
mathematics i mean

1633
00:55:35,589 --> 00:55:34,319
maybe when i was six i you know thought

1634
00:55:37,349 --> 00:55:35,599
it'd be fun to be a

1635
00:55:40,390 --> 00:55:37,359
fighter pilot or something but apart

1636
00:55:41,750 --> 00:55:40,400
from that it's

1637
00:55:44,069 --> 00:55:41,760
never seriously considered anything

1638
00:55:47,270 --> 00:55:44,079
other than mathematics or possibly

1639
00:55:48,390 --> 00:55:47,280
computing as an emergency backup

1640
00:55:51,589 --> 00:55:48,400
what are your thoughts on the many

1641
00:55:55,349 --> 00:55:54,549
well like i said it's you have all these

1642
00:55:57,510 --> 00:55:55,359
phrases

1643
00:55:59,030 --> 00:55:57,520
like you know maybe the maybe there are

1644
00:56:02,230 --> 00:55:59,040
many worlds maybe there's a

1645
00:56:05,910 --> 00:56:02,240
we're a computer simulation maybe we're

1646
00:56:08,950 --> 00:56:05,920
uh cellular automaton that

1647
00:56:10,309 --> 00:56:08,960
they don't seem to mean anything um so

1648
00:56:12,150 --> 00:56:10,319
what's the difference between a many

1649
00:56:13,910 --> 00:56:12,160
worlds interpretation and a non-many

1650
00:56:16,630 --> 00:56:13,920
worlds interpretation well there doesn't

1651
00:56:18,390 --> 00:56:16,640
seem to be any difference

1652
00:56:19,750 --> 00:56:18,400
okay i'm gonna get to some audience

1653
00:56:22,390 --> 00:56:19,760
questions from

1654
00:56:24,150 --> 00:56:22,400
reddit i think that modern geometry is

1655
00:56:25,589 --> 00:56:24,160
overly complicated as in

1656
00:56:27,829 --> 00:56:25,599
if you look at john lee's introduction

1657
00:56:28,470 --> 00:56:27,839
to smooth manifolds you'll find that it

1658
00:56:29,990 --> 00:56:28,480
has

1659
00:56:32,309 --> 00:56:30,000
plenty of little lemmas and theorem

1660
00:56:33,829 --> 00:56:32,319
theorems that say very little

1661
00:56:35,430 --> 00:56:33,839
the content is little but they're

1662
00:56:37,670 --> 00:56:35,440
elaborate proofs

1663
00:56:39,589 --> 00:56:37,680
and i'm wondering if this inadequacy is

1664
00:56:40,549 --> 00:56:39,599
due to basing the foundations of math on

1665
00:56:42,870 --> 00:56:40,559
set theory

1666
00:56:44,150 --> 00:56:42,880
leading to very cumbersome frameworks

1667
00:56:45,750 --> 00:56:44,160
for geometry

1668
00:56:48,069 --> 00:56:45,760
do you sometimes feel that there should

1669
00:56:50,870 --> 00:56:48,079
be a way to base mathematics

1670
00:56:54,549 --> 00:56:50,880
off of some alternate framework some

1671
00:56:57,349 --> 00:56:54,559
topological geometric consideration

1672
00:56:58,069 --> 00:56:57,359
that's less cumbersome well there have

1673
00:57:00,549 --> 00:56:58,079
been

1674
00:57:01,910 --> 00:57:00,559
endless attempts to do this i mean what

1675
00:57:04,549 --> 00:57:01,920
you have to remember is that

1676
00:57:06,230 --> 00:57:04,559
set theory didn't become the well

1677
00:57:08,390 --> 00:57:06,240
practical foundations and mathematics

1678
00:57:09,990 --> 00:57:08,400
just because someone decreed it

1679
00:57:11,670 --> 00:57:10,000
um what happened early in the 20th

1680
00:57:13,670 --> 00:57:11,680
century people were trying

1681
00:57:15,670 --> 00:57:13,680
dozens and dozens and dozens of

1682
00:57:16,789 --> 00:57:15,680
different attempts to have foundations

1683
00:57:18,710 --> 00:57:16,799
and mathematics i mean

1684
00:57:19,910 --> 00:57:18,720
the principia mathematica of russell and

1685
00:57:22,950 --> 00:57:19,920
white's head

1686
00:57:26,230 --> 00:57:22,960
lambda calculus um

1687
00:57:27,430 --> 00:57:26,240
and um quine or however you pronounce

1688
00:57:29,829 --> 00:57:27,440
his name came up with

1689
00:57:31,510 --> 00:57:29,839
another foundation of mathematics and

1690
00:57:34,069 --> 00:57:31,520
the reason we use set theory because it

1691
00:57:34,950 --> 00:57:34,079
was one out as being the most convenient

1692
00:57:36,470 --> 00:57:34,960
one and

1693
00:57:38,309 --> 00:57:36,480
people are trying all sorts of things

1694
00:57:40,069 --> 00:57:38,319
these days based on type theory or

1695
00:57:43,829 --> 00:57:40,079
category theory

1696
00:57:45,510 --> 00:57:43,839
and again none of them have really taken

1697
00:57:48,870 --> 00:57:45,520
over from set theory so

1698
00:57:50,470 --> 00:57:48,880
so set theory as sort of one by sort of

1699
00:57:53,030 --> 00:57:50,480
evolutionary process

1700
00:57:54,950 --> 00:57:53,040
people keep trying to modify things and

1701
00:57:57,270 --> 00:57:54,960
taking the fittest one that

1702
00:57:59,030 --> 00:57:57,280
that survives best and set theory is the

1703
00:58:02,630 --> 00:57:59,040
one that has won out

1704
00:58:05,829 --> 00:58:02,640
so when you say set theory is clumsy and

1705
00:58:07,510 --> 00:58:05,839
lots of problems to it yes that's true

1706
00:58:10,390 --> 00:58:07,520
but the trouble is everything else is

1707
00:58:13,270 --> 00:58:10,400
even worse problems

1708
00:58:14,230 --> 00:58:13,280
um i figure that when computers start

1709
00:58:16,150 --> 00:58:14,240
doing mathematics

1710
00:58:17,670 --> 00:58:16,160
that it may be that they won't use set

1711
00:58:19,990 --> 00:58:17,680
theory because

1712
00:58:21,829 --> 00:58:20,000
some forms of type theory or something a

1713
00:58:23,270 --> 00:58:21,839
little bit more computational and set

1714
00:58:26,309 --> 00:58:23,280
theory maybe a bit better

1715
00:58:28,309 --> 00:58:26,319
um and in fact there there are

1716
00:58:29,910 --> 00:58:28,319
about a dozen or so different attempts

1717
00:58:32,309 --> 00:58:29,920
to

1718
00:58:34,950 --> 00:58:32,319
find a good foundation for computers

1719
00:58:37,349 --> 00:58:34,960
doing mathematics and most of them

1720
00:58:39,190 --> 00:58:37,359
um don't seem to use set theory directly

1721
00:58:41,030 --> 00:58:39,200
but again what we're seeing is an

1722
00:58:42,309 --> 00:58:41,040
evolutionary process people are going to

1723
00:58:45,270 --> 00:58:42,319
try out

1724
00:58:46,870 --> 00:58:45,280
all these different approaches and

1725
00:58:49,270 --> 00:58:46,880
probably one of them will turn out to be

1726
00:58:50,870 --> 00:58:49,280
better than the others and take over

1727
00:58:52,870 --> 00:58:50,880
i find that when i talk to category

1728
00:58:54,069 --> 00:58:52,880
theorists they say the foundation should

1729
00:58:56,710 --> 00:58:54,079
be category

1730
00:58:58,710 --> 00:58:56,720
oh that's nonsense category theory is a

1731
00:59:00,230 --> 00:58:58,720
useful bookkeeping device but the idea

1732
00:59:00,549 --> 00:59:00,240
that it's the ultimate foundation is

1733
00:59:02,789 --> 00:59:00,559
just

1734
00:59:03,910 --> 00:59:02,799
silly i mean it's like you know finite

1735
00:59:05,510 --> 00:59:03,920
simple group theorists saying the

1736
00:59:07,670 --> 00:59:05,520
ultimate foundation should be finite

1737
00:59:10,069 --> 00:59:07,680
simple group theory or whatever

1738
00:59:11,990 --> 00:59:10,079
um the problem is category is just not a

1739
00:59:13,910 --> 00:59:12,000
primitive concept

1740
00:59:15,750 --> 00:59:13,920
um you can write down axioms for a

1741
00:59:17,670 --> 00:59:15,760
category but there's

1742
00:59:19,430 --> 00:59:17,680
you know it's you know i mean maybe you

1743
00:59:21,589 --> 00:59:19,440
want to base mathematics on say an

1744
00:59:22,870 --> 00:59:21,599
elementary topos which is a special sort

1745
00:59:24,950 --> 00:59:22,880
of category

1746
00:59:27,109 --> 00:59:24,960
well fine you can develop mathematics

1747
00:59:27,910 --> 00:59:27,119
inside an elementary topos that's no

1748
00:59:29,670 --> 00:59:27,920
problem

1749
00:59:30,950 --> 00:59:29,680
the trouble is this gives you no

1750
00:59:32,630 --> 00:59:30,960
explanation for why

1751
00:59:34,549 --> 00:59:32,640
the actions for an elementary topper

1752
00:59:36,950 --> 00:59:34,559
should be consistent

1753
00:59:38,950 --> 00:59:36,960
um set theory at least makes a sort of

1754
00:59:41,030 --> 00:59:38,960
gesture about trying to explain why the

1755
00:59:41,829 --> 00:59:41,040
axioms of set theory are consistent i

1756
00:59:43,510 --> 00:59:41,839
mean

1757
00:59:45,030 --> 00:59:43,520
i don't think it's a very successful

1758
00:59:46,470 --> 00:59:45,040
explanation but at least they sort of

1759
00:59:51,190 --> 00:59:46,480
make a

1760
00:59:54,150 --> 00:59:51,200
token attempt

1761
00:59:55,829 --> 00:59:54,160
um trying to claim the foundations of

1762
00:59:58,630 --> 00:59:55,839
mathematics a category theory there's

1763
01:00:01,589 --> 00:59:58,640
there's just no attempt to explain why

1764
01:00:03,589 --> 01:00:01,599
the axiom should be true or consistent

1765
01:00:06,630 --> 01:00:03,599
or whatever

1766
01:00:08,069 --> 01:00:06,640
this is a similar question i have always

1767
01:00:09,510 --> 01:00:08,079
been interested in seeing whether we

1768
01:00:11,510 --> 01:00:09,520
could develop an all-encompassing

1769
01:00:12,870 --> 01:00:11,520
framework despite decades of seeing a

1770
01:00:14,870 --> 01:00:12,880
proliferation of different set

1771
01:00:17,030 --> 01:00:14,880
theories with all sorts of independent

1772
01:00:19,670 --> 01:00:17,040
results i know hugh woodland

1773
01:00:20,630 --> 01:00:19,680
or hugh wooden has been working on

1774
01:00:25,430 --> 01:00:20,640
ultimate l

1775
01:00:28,789 --> 01:00:25,440
others say pluralism is here to stay

1776
01:00:30,950 --> 01:00:28,799
people like joel david hampkins

1777
01:00:32,870 --> 01:00:30,960
who is a mathematical platonist what are

1778
01:00:34,870 --> 01:00:32,880
your thoughts on this subject

1779
01:00:35,910 --> 01:00:34,880
do you think mathematicians like hugh

1780
01:00:38,230 --> 01:00:35,920
wooden and

1781
01:00:40,069 --> 01:00:38,240
peter culner may find success in

1782
01:00:41,109 --> 01:00:40,079
developing an ultimate canonical model

1783
01:00:43,109 --> 01:00:41,119
of set theory

1784
01:00:44,549 --> 01:00:43,119
or would you more closely align yourself

1785
01:00:46,390 --> 01:00:44,559
with the multiverse view

1786
01:00:48,150 --> 01:00:46,400
of set theory that hampkins advocates

1787
01:00:50,390 --> 01:00:48,160
for i think

1788
01:00:51,910 --> 01:00:50,400
well my views on this change every month

1789
01:00:55,910 --> 01:00:51,920
or every year or so so

1790
01:00:56,150 --> 01:00:55,920
the current views is that my impression

1791
01:00:59,349 --> 01:00:56,160
is

1792
01:01:00,069 --> 01:00:59,359
different models of set theory and

1793
01:01:02,950 --> 01:01:00,079
there's no

1794
01:01:05,030 --> 01:01:02,960
ultimate model um in in some sense as a

1795
01:01:05,829 --> 01:01:05,040
consequence of godel's incompleteness

1796
01:01:07,829 --> 01:01:05,839
sim there's no

1797
01:01:09,349 --> 01:01:07,839
ultimate model of all sets that the best

1798
01:01:12,710 --> 01:01:09,359
we can do is have a

1799
01:01:14,870 --> 01:01:12,720
hierarchy of increasingly powerful

1800
01:01:17,910 --> 01:01:14,880
models or systems of set theory

1801
01:01:20,870 --> 01:01:17,920
so you know you can start off with say

1802
01:01:22,390 --> 01:01:20,880
zermlow set theory might be you know

1803
01:01:24,150 --> 01:01:22,400
somewhere near the bottom and then

1804
01:01:25,829 --> 01:01:24,160
above that you can have zermalo frenkel

1805
01:01:26,710 --> 01:01:25,839
set there which is a more powerful model

1806
01:01:30,069 --> 01:01:26,720
and then you can

1807
01:01:33,589 --> 01:01:30,079
start adding in your favorite um

1808
01:01:35,589 --> 01:01:33,599
your your favorite large cardinal axioms

1809
01:01:37,190 --> 01:01:35,599
and it just doesn't seem to be an

1810
01:01:39,030 --> 01:01:37,200
ultimate model

1811
01:01:40,390 --> 01:01:39,040
um and i think it's unlikely that it

1812
01:01:43,109 --> 01:01:40,400
will be in fact if there was an

1813
01:01:43,510 --> 01:01:43,119
ultimate model then you could just you

1814
01:01:45,270 --> 01:01:43,520
know

1815
01:01:46,870 --> 01:01:45,280
hit it with gerdell's theorem and point

1816
01:01:48,789 --> 01:01:46,880
out there's an even bigger model that

1817
01:01:51,109 --> 01:01:48,799
proves the consistency of your so-called

1818
01:01:54,549 --> 01:01:51,119
ultimate model

1819
01:01:57,670 --> 01:01:54,559
um you you may be able to find a sort of

1820
01:02:00,309 --> 01:01:57,680
ultimate convenient model that can do

1821
01:02:01,029 --> 01:02:00,319
everything we can think of at the moment

1822
01:02:02,789 --> 01:02:01,039
um

1823
01:02:05,349 --> 01:02:02,799
but i mean in some sense that's what

1824
01:02:07,270 --> 01:02:05,359
zermelo frankel set theory is it's

1825
01:02:08,789 --> 01:02:07,280
it's i don't think anybody claims that

1826
01:02:10,309 --> 01:02:08,799
zermelo franco's set theory is an

1827
01:02:12,390 --> 01:02:10,319
ultimate model but it's

1828
01:02:13,990 --> 01:02:12,400
it's enough to do almost everything we

1829
01:02:15,910 --> 01:02:14,000
need to in mathematics so it's a very

1830
01:02:17,430 --> 01:02:15,920
convenient one

1831
01:02:19,270 --> 01:02:17,440
you said that your views on this change

1832
01:02:20,950 --> 01:02:19,280
month by month or year by year

1833
01:02:22,470 --> 01:02:20,960
so what was it before and why did you

1834
01:02:24,150 --> 01:02:22,480
change it i don't know i sometimes

1835
01:02:26,630 --> 01:02:24,160
thought that

1836
01:02:27,750 --> 01:02:26,640
you know you can it can oscillate

1837
01:02:29,910 --> 01:02:27,760
between

1838
01:02:31,430 --> 01:02:29,920
finitis mathematics where you deny

1839
01:02:33,349 --> 01:02:31,440
everything that can't be expressed in

1840
01:02:35,270 --> 01:02:33,359
terms of computation and

1841
01:02:36,789 --> 01:02:35,280
you can go from there all the way to

1842
01:02:38,950 --> 01:02:36,799
platonism where you

1843
01:02:40,470 --> 01:02:38,960
claim that there is a single ultimate

1844
01:02:42,630 --> 01:02:40,480
universe of all sets

1845
01:02:44,309 --> 01:02:42,640
and there are all sorts of intermediate

1846
01:02:45,910 --> 01:02:44,319
points and i sort of float up and down

1847
01:02:47,510 --> 01:02:45,920
this depending on

1848
01:02:49,910 --> 01:02:47,520
i don't know depending on my mood or

1849
01:02:51,430 --> 01:02:49,920
what i've been thinking about recently

1850
01:02:53,670 --> 01:02:51,440
so recently or currently what do you

1851
01:02:54,630 --> 01:02:53,680
think of finite you called it finite

1852
01:02:56,230 --> 01:02:54,640
as far as i know it's called

1853
01:02:57,109 --> 01:02:56,240
intuitionist logic the computational

1854
01:03:00,470 --> 01:02:57,119
model

1855
01:03:03,510 --> 01:03:00,480
um that that has a lot going

1856
01:03:05,109 --> 01:03:03,520
for it um basically it's especially if

1857
01:03:07,029 --> 01:03:05,119
you're trying to do mathematics on a

1858
01:03:09,510 --> 01:03:07,039
computer because of course

1859
01:03:11,190 --> 01:03:09,520
a computational based foundations of

1860
01:03:12,230 --> 01:03:11,200
mathematics are particularly convenient

1861
01:03:13,990 --> 01:03:12,240
if you're actually trying to do

1862
01:03:17,349 --> 01:03:14,000
computations

1863
01:03:19,430 --> 01:03:17,359
um i mean you know computers can't

1864
01:03:20,950 --> 01:03:19,440
directly manipulate sets in the way that

1865
01:03:24,549 --> 01:03:20,960
they can directly manipulate

1866
01:03:26,789 --> 01:03:24,559
integers um the only trouble with the

1867
01:03:28,870 --> 01:03:26,799
finitistic foundations and mathematics

1868
01:03:31,190 --> 01:03:28,880
is they're very restrictive and it's

1869
01:03:33,109 --> 01:03:31,200
it's really hard to do most mathematics

1870
01:03:36,390 --> 01:03:33,119
in them i mean

1871
01:03:37,750 --> 01:03:36,400
it's sort of what the analogy is like um

1872
01:03:39,430 --> 01:03:37,760
you know it's one of these religious

1873
01:03:41,190 --> 01:03:39,440
sets i think someone once said it's a

1874
01:03:43,510 --> 01:03:41,200
bit like the shakers who

1875
01:03:45,430 --> 01:03:43,520
who built really sturdy barns but didn't

1876
01:03:47,029 --> 01:03:45,440
have offspring and and fine artist

1877
01:03:50,069 --> 01:03:47,039
mathematics is like that it's

1878
01:03:52,150 --> 01:03:50,079
it's really solid and

1879
01:03:53,829 --> 01:03:52,160
absolutely solid foundation but there's

1880
01:03:57,510 --> 01:03:53,839
it's it's difficult to do anything

1881
01:04:02,630 --> 01:04:00,150
i mean i mean if if you look at any

1882
01:04:05,029 --> 01:04:02,640
almost any piece of

1883
01:04:06,150 --> 01:04:05,039
mathematics for instance if you look at

1884
01:04:07,750 --> 01:04:06,160
say

1885
01:04:10,470 --> 01:04:07,760
why is this proof of firma's last

1886
01:04:12,309 --> 01:04:10,480
theorem okay fermi's last theorem makes

1887
01:04:15,349 --> 01:04:12,319
perfect good sense to a constructive

1888
01:04:18,549 --> 01:04:15,359
fine artist mathematician but

1889
01:04:20,870 --> 01:04:18,559
trying to encode wires as proof in

1890
01:04:22,549 --> 01:04:20,880
finitis terms well it would probably be

1891
01:04:25,029 --> 01:04:22,559
possible but it would be a real

1892
01:04:27,270 --> 01:04:25,039
nightmare to do i mean it would it would

1893
01:04:29,349 --> 01:04:27,280
take years and years of really boring

1894
01:04:30,549 --> 01:04:29,359
tedious work even if you could actually

1895
01:04:34,069 --> 01:04:30,559
do it

1896
01:04:35,990 --> 01:04:34,079
ariane raj asks can people after 40s

1897
01:04:37,109 --> 01:04:36,000
learn mathematics up to an advanced

1898
01:04:38,950 --> 01:04:37,119
level now let's

1899
01:04:40,470 --> 01:04:38,960
break that down i don't believe he's

1900
01:04:41,670 --> 01:04:40,480
asking can they research can they

1901
01:04:43,589 --> 01:04:41,680
contribute to research

1902
01:04:45,430 --> 01:04:43,599
i think this person wants to know can i

1903
01:04:47,029 --> 01:04:45,440
learn enough that i can

1904
01:04:49,670 --> 01:04:47,039
let's say understand one of your papers

1905
01:04:51,589 --> 01:04:49,680
if i'm starting at 40

1906
01:04:53,430 --> 01:04:51,599
i'm sure you could if you if you're

1907
01:04:54,710 --> 01:04:53,440
willing to spend enough time on it so

1908
01:04:57,109 --> 01:04:54,720
you have to remember that when people in

1909
01:04:58,630 --> 01:04:57,119
their 20s learning mathematics

1910
01:05:01,589 --> 01:04:58,640
as grad students whatever they're

1911
01:05:04,150 --> 01:05:01,599
spending you know 8 or 12 hours a day

1912
01:05:05,750 --> 01:05:04,160
every day for years learning it and if

1913
01:05:07,990 --> 01:05:05,760
you're prepared to put that amount of

1914
01:05:10,870 --> 01:05:08,000
time into it in your 40s

1915
01:05:12,230 --> 01:05:10,880
my guess would be you probably could the

1916
01:05:13,990 --> 01:05:12,240
problem is you know by the time people

1917
01:05:15,349 --> 01:05:14,000
are in their 40s they tend to have jobs

1918
01:05:17,270 --> 01:05:15,359
and kids and all sorts of other

1919
01:05:19,510 --> 01:05:17,280
distractions so

1920
01:05:21,990 --> 01:05:19,520
it's very much harder to put in the

1921
01:05:24,069 --> 01:05:22,000
amount of time necessary

1922
01:05:26,230 --> 01:05:24,079
boris costello wants to know your take

1923
01:05:28,710 --> 01:05:26,240
on the unreasonable effectiveness

1924
01:05:29,270 --> 01:05:28,720
of mathematics in the natural sciences

1925
01:05:32,470 --> 01:05:29,280
this has

1926
01:05:33,270 --> 01:05:32,480
really baffled me i mean that what was

1927
01:05:35,829 --> 01:05:33,280
my take on it

1928
01:05:36,549 --> 01:05:35,839
well that just sums it i mean so the

1929
01:05:38,230 --> 01:05:36,559
problem is there's

1930
01:05:39,990 --> 01:05:38,240
there seems to be no reason at all why

1931
01:05:41,190 --> 01:05:40,000
the universe should make any sense i

1932
01:05:43,029 --> 01:05:41,200
mean

1933
01:05:44,549 --> 01:05:43,039
you you imagine what people thought

1934
01:05:46,230 --> 01:05:44,559
about the way the universe works

1935
01:05:48,069 --> 01:05:46,240
you know two or three thousand years ago

1936
01:05:49,990 --> 01:05:48,079
you know things just happened for no

1937
01:05:50,710 --> 01:05:50,000
reason trees just grew because that's

1938
01:05:53,109 --> 01:05:50,720
what trees

1939
01:05:54,470 --> 01:05:53,119
did or maybe there was some god making

1940
01:05:56,309 --> 01:05:54,480
them grow or something and

1941
01:05:57,829 --> 01:05:56,319
we've discovered since then that nearly

1942
01:06:01,109 --> 01:05:57,839
everything seems to be

1943
01:06:04,470 --> 01:06:01,119
ultimately controlled by mathematics

1944
01:06:05,829 --> 01:06:04,480
and i've no idea why or no idea why this

1945
01:06:08,630 --> 01:06:05,839
should be true

1946
01:06:09,750 --> 01:06:08,640
um you know it's possible you could have

1947
01:06:11,910 --> 01:06:09,760
a universe that

1948
01:06:13,990 --> 01:06:11,920
that just sort of was like a universe

1949
01:06:16,150 --> 01:06:14,000
that sprang from the mind of a fantasy

1950
01:06:18,470 --> 01:06:16,160
author where things just worked by magic

1951
01:06:20,230 --> 01:06:18,480
for no particular reason but

1952
01:06:21,910 --> 01:06:20,240
we seem to be in one where it runs on

1953
01:06:24,069 --> 01:06:21,920
mathematics

1954
01:06:26,230 --> 01:06:24,079
rajesh v wants to know are you puzzled

1955
01:06:26,950 --> 01:06:26,240
by most people's inability to understand

1956
01:06:29,910 --> 01:06:26,960
math

1957
01:06:31,750 --> 01:06:29,920
or do you see a reason behind it i'm not

1958
01:06:33,670 --> 01:06:31,760
puzzled by most people's inability to

1959
01:06:35,510 --> 01:06:33,680
understand math what really puzzles me

1960
01:06:36,789 --> 01:06:35,520
is the fact that anyone can understand

1961
01:06:39,349 --> 01:06:36,799
math at all

1962
01:06:41,670 --> 01:06:39,359
i mean from a point of view if you're an

1963
01:06:44,630 --> 01:06:41,680
evolutionary psychologist

1964
01:06:46,230 --> 01:06:44,640
you can pretty much prove that no human

1965
01:06:47,990 --> 01:06:46,240
could possibly do mathematics because

1966
01:06:48,549 --> 01:06:48,000
you know think about where we evolved we

1967
01:06:50,470 --> 01:06:48,559
were

1968
01:06:51,670 --> 01:06:50,480
running around on the probably the

1969
01:06:53,349 --> 01:06:51,680
african plains being

1970
01:06:55,029 --> 01:06:53,359
chased by leopards or tigers or

1971
01:06:57,430 --> 01:06:55,039
something and if you get someone who

1972
01:06:58,630 --> 01:06:57,440
you know stops to wander about large

1973
01:07:00,069 --> 01:06:58,640
cardinals well

1974
01:07:01,670 --> 01:07:00,079
you know 10 minutes later they're going

1975
01:07:03,829 --> 01:07:01,680
to be passing through the digestive

1976
01:07:05,990 --> 01:07:03,839
system of some large carnivore

1977
01:07:08,390 --> 01:07:06,000
i mean the the mathematics gene should

1978
01:07:12,069 --> 01:07:08,400
have been wiped out by

1979
01:07:15,510 --> 01:07:12,079
um a high evolutionary pressure

1980
01:07:17,510 --> 01:07:15,520
so you know what why why do humans get

1981
01:07:19,990 --> 01:07:17,520
get interested in mathematics it's

1982
01:07:21,430 --> 01:07:20,000
this is what's difficult to explain

1983
01:07:22,710 --> 01:07:21,440
what's the longest time you've thought

1984
01:07:26,829 --> 01:07:22,720
about a problem before finding a

1985
01:07:34,549 --> 01:07:29,430
uh

1986
01:07:37,589 --> 01:07:36,630
i think let me see moonshine conjectures

1987
01:07:40,549 --> 01:07:37,599
were probably about

1988
01:07:42,390 --> 01:07:40,559
10 years um i might be able to give you

1989
01:07:44,150 --> 01:07:42,400
about 40 years and i don't know whether

1990
01:07:45,750 --> 01:07:44,160
i've actually solved the problem yet so

1991
01:07:47,029 --> 01:07:45,760
somewhere between 10 and 40 years

1992
01:07:48,710 --> 01:07:47,039
depending on whether the

1993
01:07:50,549 --> 01:07:48,720
problem i'm currently working on works

1994
01:07:52,789 --> 01:07:50,559
out or not is the problem you're

1995
01:07:54,309 --> 01:07:52,799
currently working on a monumentous one

1996
01:07:58,870 --> 01:07:54,319
is it one that people would recognize if

1997
01:08:02,069 --> 01:08:00,309
if i know that you stated my name

1998
01:08:03,829 --> 01:08:02,079
everyone would think i'd gone completely

1999
01:08:07,750 --> 01:08:03,839
mad so i'm not going to say anything

2000
01:08:11,349 --> 01:08:07,760
more about it it's about god isn't it

2001
01:08:13,190 --> 01:08:11,359
i said mad i didn't say crazy

2002
01:08:15,990 --> 01:08:13,200
what do you think of ramanajan a

2003
01:08:18,870 --> 01:08:16,000
self-taught math genius

2004
01:08:20,870 --> 01:08:18,880
this is just i'm just overwhelmed by it

2005
01:08:22,070 --> 01:08:20,880
because he he did something that

2006
01:08:23,829 --> 01:08:22,080
you know i thought would have been

2007
01:08:25,030 --> 01:08:23,839
almost impossible that's it that he

2008
01:08:27,110 --> 01:08:25,040
managed

2009
01:08:28,390 --> 01:08:27,120
by his own unaided efforts to turn

2010
01:08:30,630 --> 01:08:28,400
himself into one of the

2011
01:08:32,470 --> 01:08:30,640
you know greatest mathematicians i mean

2012
01:08:34,470 --> 01:08:32,480
you you look at what he was

2013
01:08:36,229 --> 01:08:34,480
growing up in he was he was growing up

2014
01:08:39,669 --> 01:08:36,239
in extreme poverty

2015
01:08:40,390 --> 01:08:39,679
and i mean even surviving in those

2016
01:08:42,550 --> 01:08:40,400
conditions

2017
01:08:43,510 --> 01:08:42,560
would have been as much as most people

2018
01:08:46,630 --> 01:08:43,520
could do and to

2019
01:08:50,149 --> 01:08:46,640
to do this phenomenal mathematics i just

2020
01:08:53,669 --> 01:08:50,159
cannot imagine how he did it um

2021
01:08:55,030 --> 01:08:53,679
i mean you know i mean ramanujan himself

2022
01:08:56,709 --> 01:08:55,040
said that you know how did he get his

2023
01:08:58,630 --> 01:08:56,719
mathematical formulas and he said he got

2024
01:08:59,749 --> 01:08:58,640
them in dreams from some goddess or

2025
01:09:01,749 --> 01:08:59,759
something and

2026
01:09:03,030 --> 01:09:01,759
i i can't actually think of it a better

2027
01:09:05,749 --> 01:09:03,040
explanation i mean

2028
01:09:07,510 --> 01:09:05,759
it's it's it's almost miraculous that he

2029
01:09:09,829 --> 01:09:07,520
managed to do this

2030
01:09:10,870 --> 01:09:09,839
right some of the formulas are so arcane

2031
01:09:12,709 --> 01:09:10,880
and so esoteric

2032
01:09:14,870 --> 01:09:12,719
that you wonder how can you come up with

2033
01:09:15,430 --> 01:09:14,880
it without deriving them and he would

2034
01:09:18,630 --> 01:09:15,440
just

2035
01:09:20,709 --> 01:09:18,640
they would turn out to be true well

2036
01:09:25,269 --> 01:09:20,719
i i don't know i i i think i think he

2037
01:09:28,550 --> 01:09:28,149
um i mean you know some mathematicians

2038
01:09:30,630 --> 01:09:28,560
have this

2039
01:09:32,309 --> 01:09:30,640
a bit of a desire to keep their methods

2040
01:09:34,149 --> 01:09:32,319
to themselves a bit and

2041
01:09:35,510 --> 01:09:34,159
maybe romantic was doing that to some

2042
01:09:37,910 --> 01:09:35,520
extent

2043
01:09:39,829 --> 01:09:37,920
um but i i really don't know i mean i've

2044
01:09:42,950 --> 01:09:39,839
looked at his

2045
01:09:44,870 --> 01:09:42,960
some of his papers and books and i just

2046
01:09:46,149 --> 01:09:44,880
i just cannot imagine how he thought of

2047
01:09:48,309 --> 01:09:46,159
them i mean

2048
01:09:50,229 --> 01:09:48,319
some of his formulas you can prove by

2049
01:09:52,950 --> 01:09:50,239
using techniques that ramanujan didn't

2050
01:09:54,950 --> 01:09:52,960
know about i mean it's kind of

2051
01:09:57,189 --> 01:09:54,960
notorious that manager never knew

2052
01:10:00,149 --> 01:09:57,199
complex analysis

2053
01:10:01,430 --> 01:10:00,159
which is a but he know which is a very

2054
01:10:04,070 --> 01:10:01,440
powerful method for

2055
01:10:05,750 --> 01:10:04,080
evaluating integrals but somehow he he

2056
01:10:07,669 --> 01:10:05,760
never seemed to feel the lack of it he

2057
01:10:10,310 --> 01:10:07,679
was able to do by

2058
01:10:12,470 --> 01:10:10,320
real variable methods what most of us

2059
01:10:15,590 --> 01:10:12,480
need complex variable methods to do

2060
01:10:17,270 --> 01:10:15,600
so somehow he just got

2061
01:10:19,430 --> 01:10:17,280
really really really good at real

2062
01:10:23,669 --> 01:10:19,440
variable methods in a way that almost

2063
01:10:26,470 --> 01:10:23,679
nobody since has managed to equal

2064
01:10:28,149 --> 01:10:26,480
bob bobady says thanks for the q a i'm

2065
01:10:30,310 --> 01:10:28,159
just wondering if you plan on continuing

2066
01:10:33,189 --> 01:10:30,320
your number theory series

2067
01:10:34,149 --> 01:10:33,199
yeah um the if you're talking about my

2068
01:10:36,070 --> 01:10:34,159
youtube channel

2069
01:10:37,669 --> 01:10:36,080
um well i i'm not really planning to but

2070
01:10:40,870 --> 01:10:37,679
i'm not planning not to it's

2071
01:10:42,630 --> 01:10:40,880
it's just sort of topics just

2072
01:10:44,070 --> 01:10:42,640
turn up at random depending on what i

2073
01:10:46,310 --> 01:10:44,080
feel like and what people

2074
01:10:47,750 --> 01:10:46,320
vote for and so on so probably if i if i

2075
01:10:49,430 --> 01:10:47,760
keep going number theory will probably

2076
01:10:51,270 --> 01:10:49,440
continue

2077
01:10:53,270 --> 01:10:51,280
i requested to you over email for you to

2078
01:10:56,550 --> 01:10:53,280
start a series on quantum field theory

2079
01:11:00,070 --> 01:10:56,560
what are the chances of that uh

2080
01:11:01,910 --> 01:11:00,080
not all that high because i i had a sort

2081
01:11:04,180 --> 01:11:01,920
of bad experience with it

2082
01:11:05,510 --> 01:11:04,190
like like i tried to understand it and

2083
01:11:07,510 --> 01:11:05,520
[Music]

2084
01:11:09,510 --> 01:11:07,520
you know invested a few years and felt

2085
01:11:13,110 --> 01:11:09,520
i'd really

2086
01:11:15,590 --> 01:11:13,120
it's like really hitting a concrete wall

2087
01:11:16,229 --> 01:11:15,600
when you read quantum field theory books

2088
01:11:18,310 --> 01:11:16,239
virtually

2089
01:11:19,430 --> 01:11:18,320
every one of them tackle the problem

2090
01:11:22,790 --> 01:11:19,440
differently

2091
01:11:23,350 --> 01:11:22,800
unlike mechanics or quantum mechanics

2092
01:11:25,270 --> 01:11:23,360
even

2093
01:11:27,189 --> 01:11:25,280
i would be so curious to see how you

2094
01:11:29,669 --> 01:11:27,199
tackled it

2095
01:11:30,390 --> 01:11:29,679
well that yeah so so when you say

2096
01:11:32,390 --> 01:11:30,400
different or

2097
01:11:33,350 --> 01:11:32,400
differently i think you you presumably

2098
01:11:34,630 --> 01:11:33,360
mean there are lots of different

2099
01:11:36,790 --> 01:11:34,640
approaches like you can do it by

2100
01:11:37,830 --> 01:11:36,800
operator algebras or by perturbation

2101
01:11:39,189 --> 01:11:37,840
theory or by

2102
01:11:41,110 --> 01:11:39,199
trying to make sense of infinite

2103
01:11:43,669 --> 01:11:41,120
dimensional integrals or by

2104
01:11:45,430 --> 01:11:43,679
doing topological quantum field theories

2105
01:11:46,790 --> 01:11:45,440
or whatever so so there are

2106
01:11:48,550 --> 01:11:46,800
all these different approaches and what

2107
01:11:50,229 --> 01:11:48,560
they all have in common is that none of

2108
01:11:53,110 --> 01:11:50,239
them really work

2109
01:11:54,310 --> 01:11:53,120
um so i was looking at all of them and

2110
01:11:56,470 --> 01:11:54,320
couldn't really make pretty much

2111
01:11:59,590 --> 01:11:56,480
progress on any of them

2112
01:12:00,149 --> 01:11:59,600
so i mean the the the one that people

2113
01:12:01,750 --> 01:12:00,159
have

2114
01:12:03,590 --> 01:12:01,760
that's been most successful is the

2115
01:12:06,310 --> 01:12:03,600
perturbation theory approach i mean this

2116
01:12:09,110 --> 01:12:06,320
is sort of what physicists actually use

2117
01:12:09,669 --> 01:12:09,120
to calculate numbers that they check in

2118
01:12:16,310 --> 01:12:09,679
um

2119
01:12:19,590 --> 01:12:16,320
you know perturbation theory produces

2120
01:12:21,350 --> 01:12:19,600
these divergent infinite series

2121
01:12:23,110 --> 01:12:21,360
and to make sense of them you cheat you

2122
01:12:24,950 --> 01:12:23,120
just take the first few terms which

2123
01:12:27,990 --> 01:12:24,960
makes no mathematical sense

2124
01:12:30,149 --> 01:12:28,000
and i was never able to

2125
01:12:31,830 --> 01:12:30,159
figure this out so you see an

2126
01:12:34,830 --> 01:12:31,840
arbitrariness as to when they choose to

2127
01:12:34,840 --> 01:12:38,790
well

2128
01:12:42,310 --> 01:12:40,470
maybe physicists who know more about

2129
01:12:43,990 --> 01:12:42,320
this would say it isn't arbitrary but as

2130
01:12:45,830 --> 01:12:44,000
far as i can figure out

2131
01:12:47,990 --> 01:12:45,840
that there didn't seem to be any very

2132
01:12:49,669 --> 01:12:48,000
good reason for stopping at some point

2133
01:12:52,310 --> 01:12:49,679
rather than another i mean

2134
01:12:54,229 --> 01:12:52,320
i guess you can stop when the terms

2135
01:12:58,270 --> 01:12:54,239
start getting bigger again but that's

2136
01:13:01,750 --> 01:13:00,790
ja524309 that's the username says i'm

2137
01:13:03,430 --> 01:13:01,760
curious

2138
01:13:05,189 --> 01:13:03,440
why you think memorizing proofs is

2139
01:13:06,630 --> 01:13:05,199
useless or less useful than doing

2140
01:13:09,110 --> 01:13:06,640
calculations

2141
01:13:10,550 --> 01:13:09,120
could you elaborate i should say i agree

2142
01:13:13,750 --> 01:13:10,560
with some of your other remarks

2143
01:13:15,910 --> 01:13:13,760
eg they're not being the best proof

2144
01:13:17,270 --> 01:13:15,920
of any particular theorem that was when

2145
01:13:20,149 --> 01:13:17,280
you were asked about

2146
01:13:21,189 --> 01:13:20,159
the book i was watching a talk by barry

2147
01:13:23,270 --> 01:13:21,199
mazur

2148
01:13:24,550 --> 01:13:23,280
the other day and he spoke also how

2149
01:13:26,310 --> 01:13:24,560
different proofs can sort

2150
01:13:28,229 --> 01:13:26,320
of allude to different possible

2151
01:13:29,750 --> 01:13:28,239
generalizations of the same problem

2152
01:13:32,149 --> 01:13:29,760
which may or may not necessarily

2153
01:13:37,350 --> 01:13:32,159
themselves be able which they may not

2154
01:13:40,790 --> 01:13:39,590
sorry that was yeah let me just read the

2155
01:13:42,550 --> 01:13:40,800
first part because i believe the

2156
01:13:43,430 --> 01:13:42,560
question is got confused by having two

2157
01:13:45,990 --> 01:13:43,440
questions right

2158
01:13:46,709 --> 01:13:46,000
oh i'm confused i'm confused reading it

2159
01:13:48,149 --> 01:13:46,719
okay

2160
01:13:49,910 --> 01:13:48,159
i'm curious why you think memorizing

2161
01:13:52,229 --> 01:13:49,920
proofs is less useful than doing okay

2162
01:13:53,669 --> 01:13:52,239
let's do that let's do that part first

2163
01:13:55,270 --> 01:13:53,679
um i think this is one of the things

2164
01:13:56,070 --> 01:13:55,280
that probably varies from person to

2165
01:13:58,870 --> 01:13:56,080
person so

2166
01:14:00,709 --> 01:13:58,880
so people have very different styles for

2167
01:14:02,470 --> 01:14:00,719
learning things and maybe for some

2168
01:14:04,550 --> 01:14:02,480
people memorizing proofs

2169
01:14:05,990 --> 01:14:04,560
is a useful thing i'm just saying for me

2170
01:14:08,390 --> 01:14:06,000
personally

2171
01:14:10,709 --> 01:14:08,400
i i never found memorizing proofs to be

2172
01:14:12,630 --> 01:14:10,719
very useful that's mainly because my

2173
01:14:13,990 --> 01:14:12,640
memory isn't as good as some people's i

2174
01:14:15,750 --> 01:14:14,000
mean i've i've

2175
01:14:17,110 --> 01:14:15,760
noticed that some people have incredible

2176
01:14:18,870 --> 01:14:17,120
memories i i mean

2177
01:14:20,709 --> 01:14:18,880
you know that they can sort of read a

2178
01:14:21,270 --> 01:14:20,719
book and basically recite it back word

2179
01:14:23,669 --> 01:14:21,280
for word

2180
01:14:24,550 --> 01:14:23,679
so so von neumann for example could do

2181
01:14:26,630 --> 01:14:24,560
that and

2182
01:14:27,990 --> 01:14:26,640
maybe for people like that that they can

2183
01:14:31,910 --> 01:14:28,000
memorize proofs but

2184
01:14:33,590 --> 01:14:31,920
for for me at least the i mean i i could

2185
01:14:35,590 --> 01:14:33,600
memorize a proof of i put a lot of

2186
01:14:38,550 --> 01:14:35,600
effort into it but it would be

2187
01:14:40,630 --> 01:14:38,560
you know i mean it's it's there's what

2188
01:14:42,470 --> 01:14:40,640
economists call an opportunity cost

2189
01:14:45,270 --> 01:14:42,480
my time is actually more productively

2190
01:14:47,430 --> 01:14:45,280
spent doing something else because

2191
01:14:48,550 --> 01:14:47,440
i i seem to learn i seem to understand

2192
01:14:51,510 --> 01:14:48,560
things better by actually doing

2193
01:14:55,110 --> 01:14:51,520
calculations with examples so

2194
01:14:56,709 --> 01:14:55,120
um so so i i guess my answer only

2195
01:14:58,790 --> 01:14:56,719
applies to me and doesn't necessarily

2196
01:15:01,669 --> 01:14:58,800
apply to other people

2197
01:15:02,790 --> 01:15:01,679
you mentioned learning styles yeah okay

2198
01:15:04,310 --> 01:15:02,800
so what are some of the different

2199
01:15:05,669 --> 01:15:04,320
learning styles and how does one figure

2200
01:15:08,870 --> 01:15:05,679
out their own

2201
01:15:12,070 --> 01:15:08,880
the one that fits for them well for me

2202
01:15:14,070 --> 01:15:12,080
learning is very very much i have to

2203
01:15:15,830 --> 01:15:14,080
my learning style is i as i said i need

2204
01:15:17,669 --> 01:15:15,840
to do calculations and i need to

2205
01:15:19,270 --> 01:15:17,679
read things over and over again because

2206
01:15:21,189 --> 01:15:19,280
i'm rather bad at

2207
01:15:23,030 --> 01:15:21,199
learning things other people's learning

2208
01:15:26,229 --> 01:15:23,040
styles i

2209
01:15:27,830 --> 01:15:26,239
i don't actually know much about because

2210
01:15:29,430 --> 01:15:27,840
all i can notice is that they're

2211
01:15:31,669 --> 01:15:29,440
obviously different from mine in some

2212
01:15:33,669 --> 01:15:31,679
ways

2213
01:15:35,350 --> 01:15:33,679
a really obvious one is i'm terrible at

2214
01:15:35,910 --> 01:15:35,360
learning languages whereas other people

2215
01:15:37,669 --> 01:15:35,920
can

2216
01:15:40,790 --> 01:15:37,679
learn languages really easily so they

2217
01:15:42,550 --> 01:15:40,800
must be doing something different

2218
01:15:44,950 --> 01:15:42,560
do you have a philosophy of mathematics

2219
01:15:46,550 --> 01:15:44,960
and if so what is it

2220
01:15:48,070 --> 01:15:46,560
philosophy of mathematics well this is

2221
01:15:51,430 --> 01:15:48,080
this is like the question about

2222
01:15:54,470 --> 01:15:51,440
what the right foundation should be and

2223
01:15:55,910 --> 01:15:54,480
as i said my that that there are several

2224
01:15:59,189 --> 01:15:55,920
underlying philosophies

2225
01:16:01,030 --> 01:15:59,199
so there's finitism where you think

2226
01:16:02,870 --> 01:16:01,040
everything should be computation and

2227
01:16:04,390 --> 01:16:02,880
platonism where you think everything

2228
01:16:04,950 --> 01:16:04,400
exists in some mystical realm and

2229
01:16:06,709 --> 01:16:04,960
there's

2230
01:16:08,070 --> 01:16:06,719
formalism where it's just a game you

2231
01:16:11,669 --> 01:16:08,080
play

2232
01:16:14,790 --> 01:16:11,679
with with with rules and

2233
01:16:16,709 --> 01:16:14,800
i'd say i i sort of

2234
01:16:18,709 --> 01:16:16,719
kind of oscillate between them or maybe

2235
01:16:20,950 --> 01:16:18,719
amalgamate them all i mean that

2236
01:16:21,830 --> 01:16:20,960
they all have some good points and some

2237
01:16:24,070 --> 01:16:21,840
bad points

2238
01:16:27,590 --> 01:16:24,080
so i don't really have a single

2239
01:16:31,669 --> 01:16:30,149
um kind of amalgamate all philosophies

2240
01:16:32,950 --> 01:16:31,679
and pick and choose whichever is most

2241
01:16:35,669 --> 01:16:32,960
convenient at the time

2242
01:16:37,270 --> 01:16:35,679
and it seems you know there seems to be

2243
01:16:39,110 --> 01:16:37,280
something a little bit off about this

2244
01:16:40,870 --> 01:16:39,120
it's like trying to belong to several

2245
01:16:43,350 --> 01:16:40,880
different religions all at once

2246
01:16:45,110 --> 01:16:43,360
but but somehow for mathematical

2247
01:16:45,750 --> 01:16:45,120
philosophies maybe you can get away with

2248
01:16:46,950 --> 01:16:45,760
it

2249
01:16:49,030 --> 01:16:46,960
what do you mean you pick and choose

2250
01:16:50,870 --> 01:16:49,040
which one's useful what would be an

2251
01:16:53,430 --> 01:16:50,880
example of one that's useful for you

2252
01:16:54,390 --> 01:16:53,440
um well i mean i think the different

2253
01:16:57,510 --> 01:16:54,400
philosophy

2254
01:16:58,790 --> 01:16:57,520
wouldn't really be useful for actually

2255
01:17:00,470 --> 01:16:58,800
doing math research

2256
01:17:02,149 --> 01:17:00,480
the different philosophies would be

2257
01:17:03,830 --> 01:17:02,159
useful for trying to understand what the

2258
01:17:05,590 --> 01:17:03,840
foundations of mathematics and the

2259
01:17:10,070 --> 01:17:05,600
universe are

2260
01:17:12,790 --> 01:17:10,080
um so if you if you think the universe

2261
01:17:14,790 --> 01:17:12,800
should be based on computation then

2262
01:17:16,709 --> 01:17:14,800
maybe you try working with a

2263
01:17:18,550 --> 01:17:16,719
finitistic computational model of

2264
01:17:21,030 --> 01:17:18,560
mathematics

2265
01:17:21,910 --> 01:17:21,040
um if you if you're trying to understand

2266
01:17:25,510 --> 01:17:21,920
some

2267
01:17:27,350 --> 01:17:25,520
deep complicated theorem then

2268
01:17:29,270 --> 01:17:27,360
it's it's very difficult to prove these

2269
01:17:31,430 --> 01:17:29,280
theorems in a finitistic model so you

2270
01:17:34,310 --> 01:17:31,440
may have to sort of switch to a

2271
01:17:35,110 --> 01:17:34,320
more platonic model where there is you

2272
01:17:37,030 --> 01:17:35,120
know you

2273
01:17:38,870 --> 01:17:37,040
you you assume the existence of very

2274
01:17:40,149 --> 01:17:38,880
strong constructions like the power set

2275
01:17:42,550 --> 01:17:40,159
of a set

2276
01:17:44,550 --> 01:17:42,560
i mean it's very difficult developing

2277
01:17:45,110 --> 01:17:44,560
things like general topology for example

2278
01:17:48,870 --> 01:17:45,120
in the

2279
01:17:50,870 --> 01:17:48,880
in a finitistic universe

2280
01:17:52,229 --> 01:17:50,880
how does one know by the way this

2281
01:17:53,590 --> 01:17:52,239
question is from bag bigger

2282
01:17:55,430 --> 01:17:53,600
how does one know when they're on the

2283
01:17:57,669 --> 01:17:55,440
right path in finding a solution

2284
01:17:59,110 --> 01:17:57,679
i've tried substantial unsolved problems

2285
01:18:00,550 --> 01:17:59,120
and i end up making progress

2286
01:18:03,750 --> 01:18:00,560
but then i feel like i'm chasing my own

2287
01:18:04,709 --> 01:18:03,760
tail this is one of the hardest problems

2288
01:18:07,030 --> 01:18:04,719
in research

2289
01:18:08,470 --> 01:18:07,040
and if you you know if you could solve

2290
01:18:10,229 --> 01:18:08,480
this problem

2291
01:18:12,229 --> 01:18:10,239
you you become the world's greatest

2292
01:18:14,310 --> 01:18:12,239
mathematician it's sort of like asking

2293
01:18:16,390 --> 01:18:14,320
how do you time the stock market

2294
01:18:18,550 --> 01:18:16,400
nobody knows how to do it and if you if

2295
01:18:21,270 --> 01:18:18,560
you could you'd be really rich

2296
01:18:22,550 --> 01:18:21,280
um so so that it's this question of

2297
01:18:26,149 --> 01:18:22,560
knowing

2298
01:18:29,110 --> 01:18:26,159
what the right solution to a problem is

2299
01:18:30,550 --> 01:18:29,120
the right way to solve a problem is and

2300
01:18:32,310 --> 01:18:30,560
you know i mean

2301
01:18:34,229 --> 01:18:32,320
this is in some sense the hardest part

2302
01:18:36,310 --> 01:18:34,239
of research trying to trying to figure

2303
01:18:37,750 --> 01:18:36,320
out whether you're on track or not

2304
01:18:40,709 --> 01:18:37,760
um i heard a story about that there was

2305
01:18:43,030 --> 01:18:40,719
this mathematician called nagata who was

2306
01:18:45,189 --> 01:18:43,040
you know half his work was proving these

2307
01:18:46,950 --> 01:18:45,199
amazing theorems and half his work was

2308
01:18:48,229 --> 01:18:46,960
proven these stunning counter examples

2309
01:18:49,830 --> 01:18:48,239
to theorems and

2310
01:18:51,590 --> 01:18:49,840
the story i heard was that you know

2311
01:18:52,310 --> 01:18:51,600
every morning he would try and prove a

2312
01:18:53,750 --> 01:18:52,320
theorem

2313
01:18:56,149 --> 01:18:53,760
and every afternoon he would try and

2314
01:18:57,830 --> 01:18:56,159
find a counter example so so one or the

2315
01:19:00,709 --> 01:18:57,840
other would work out so so

2316
01:19:02,149 --> 01:19:00,719
so he had both both bases covered in

2317
01:19:04,070 --> 01:19:02,159
some sense he he

2318
01:19:05,590 --> 01:19:04,080
he he didn't need to know when he was on

2319
01:19:08,149 --> 01:19:05,600
the right track because he was trying

2320
01:19:10,149 --> 01:19:08,159
all possible tracks simultaneously

2321
01:19:12,630 --> 01:19:10,159
and and just found out which one worked

2322
01:19:14,630 --> 01:19:12,640
by trying everything

2323
01:19:16,149 --> 01:19:14,640
tahum asks can you explain langlin's

2324
01:19:18,070 --> 01:19:16,159
program and does it have any connection

2325
01:19:22,070 --> 01:19:18,080
to physics

2326
01:19:23,990 --> 01:19:22,080
no yes um langland's program

2327
01:19:25,590 --> 01:19:24,000
if you had to say it in one sentence it

2328
01:19:28,630 --> 01:19:25,600
would say that

2329
01:19:30,390 --> 01:19:28,640
um automorphic forms on groups have

2330
01:19:32,950 --> 01:19:30,400
something to do with

2331
01:19:34,630 --> 01:19:32,960
representations of galway groups which

2332
01:19:38,229 --> 01:19:34,640
sounds like this

2333
01:19:40,950 --> 01:19:38,239
obscure technical stuff

2334
01:19:42,709 --> 01:19:40,960
but um rather amazingly an awful lot of

2335
01:19:45,270 --> 01:19:42,719
problems in mathematics

2336
01:19:47,430 --> 01:19:45,280
turn out if you go very deep into them

2337
01:19:50,310 --> 01:19:47,440
to to be related to the langlens

2338
01:19:51,990 --> 01:19:50,320
program for example um the classic

2339
01:19:54,149 --> 01:19:52,000
example of this is wireless as proof of

2340
01:19:56,070 --> 01:19:54,159
firma's last theorem was was essentially

2341
01:19:57,590 --> 01:19:56,080
using this idea

2342
01:20:00,229 --> 01:19:57,600
um does it have anything to do with

2343
01:20:01,590 --> 01:20:00,239
physics well

2344
01:20:03,910 --> 01:20:01,600
some of the more recent work on

2345
01:20:06,390 --> 01:20:03,920
geometric langlands is using ideas from

2346
01:20:08,229 --> 01:20:06,400
quantum field theory so

2347
01:20:09,430 --> 01:20:08,239
i can give you a definite maybe on that

2348
01:20:12,390 --> 01:20:09,440
one

2349
01:20:14,070 --> 01:20:12,400
um there are certainly some ideas that

2350
01:20:15,590 --> 01:20:14,080
turn up in both langman's program and

2351
01:20:17,510 --> 01:20:15,600
physics whether or not there's any more

2352
01:20:20,070 --> 01:20:17,520
direct connection

2353
01:20:21,750 --> 01:20:20,080
i don't know but it wouldn't surprise me

2354
01:20:22,950 --> 01:20:21,760
langland's program seems to

2355
01:20:24,629 --> 01:20:22,960
it seems to be one of these things that

2356
01:20:27,110 --> 01:20:24,639
turns up almost everywhere if you go

2357
01:20:28,310 --> 01:20:27,120
really deeply into something

2358
01:20:31,030 --> 01:20:28,320
you mentioned that you're extremely

2359
01:20:33,669 --> 01:20:31,040
interested in learning more about it

2360
01:20:35,350 --> 01:20:33,679
i've been so for decades and there's

2361
01:20:38,629 --> 01:20:35,360
there's just so much to learn

2362
01:20:40,629 --> 01:20:38,639
i mean um

2363
01:20:42,629 --> 01:20:40,639
i mean that langland's program seems to

2364
01:20:44,950 --> 01:20:42,639
be the ultimate black hole for what you

2365
01:20:47,350 --> 01:20:44,960
need to learn in order to understand it

2366
01:20:49,669 --> 01:20:47,360
like there are there are several very

2367
01:20:51,189 --> 01:20:49,679
deep subjects like representation theory

2368
01:20:53,750 --> 01:20:51,199
and algebraic geometry which are

2369
01:20:55,430 --> 01:20:53,760
themselves notorious for how

2370
01:20:56,870 --> 01:20:55,440
how much you have to learn to get into

2371
01:20:59,510 --> 01:20:56,880
them and langlen's program

2372
01:21:00,950 --> 01:20:59,520
sort of sub sums all of these you need

2373
01:21:02,629 --> 01:21:00,960
to know algebraic geometry and

2374
01:21:04,629 --> 01:21:02,639
representation theory

2375
01:21:05,990 --> 01:21:04,639
and a lot of hard analysis so it's more

2376
01:21:07,750 --> 01:21:06,000
or less

2377
01:21:10,470 --> 01:21:07,760
it's almost like it's every hard area of

2378
01:21:12,310 --> 01:21:10,480
mathematics all combined into one

2379
01:21:13,590 --> 01:21:12,320
well you do have a course on

2380
01:21:16,950 --> 01:21:13,600
representation theory

2381
01:21:17,590 --> 01:21:16,960
and on algebraic geometry so you should

2382
01:21:19,669 --> 01:21:17,600
have some

2383
01:21:21,750 --> 01:21:19,679
advantage there no these are just

2384
01:21:22,390 --> 01:21:21,760
scratching the surface of what you need

2385
01:21:24,629 --> 01:21:22,400
to know

2386
01:21:25,990 --> 01:21:24,639
the representation theory i've put on is

2387
01:21:28,229 --> 01:21:26,000
just finite

2388
01:21:30,390 --> 01:21:28,239
groups in characteristic zero which is

2389
01:21:32,470 --> 01:21:30,400
the

2390
01:21:34,310 --> 01:21:32,480
easiest example it's not quite trivial

2391
01:21:37,189 --> 01:21:34,320
but it's it's the really easy part of

2392
01:21:40,709 --> 01:21:37,199
representation theory langland's program

2393
01:21:43,910 --> 01:21:42,470
infinite groups the representations

2394
01:21:45,830 --> 01:21:43,920
become infinite dimensional

2395
01:21:47,910 --> 01:21:45,840
everything becomes far far more

2396
01:21:51,110 --> 01:21:47,920
complicated

2397
01:21:52,790 --> 01:21:51,120
just us perths asks how can a person

2398
01:21:53,510 --> 01:21:52,800
who's self-studying deal with gaps in

2399
01:21:56,149 --> 01:21:53,520
knowledge

2400
01:21:57,270 --> 01:21:56,159
when i get stuck on a new concept i'm

2401
01:21:58,790 --> 01:21:57,280
often unsure

2402
01:22:00,870 --> 01:21:58,800
exactly what it is that's preventing me

2403
01:22:02,550 --> 01:22:00,880
from understanding it and i

2404
01:22:04,070 --> 01:22:02,560
in other words i don't know what i don't

2405
01:22:06,149 --> 01:22:04,080
know well one

2406
01:22:07,990 --> 01:22:06,159
one thing you can do these days is is

2407
01:22:09,669 --> 01:22:08,000
there are lots of math discussion groups

2408
01:22:09,990 --> 01:22:09,679
on things like reddit and you can just

2409
01:22:12,310 --> 01:22:10,000
try

2410
01:22:14,149 --> 01:22:12,320
asking i mean you may have to poke

2411
01:22:16,310 --> 01:22:14,159
around a bit to find the right sort of

2412
01:22:18,390 --> 01:22:16,320
math discussion group to answer whatever

2413
01:22:22,149 --> 01:22:18,400
level of question you're asking

2414
01:22:25,430 --> 01:22:22,159
um some groups i think there's a

2415
01:22:29,350 --> 01:22:25,440
there's if you search for math overflow

2416
01:22:31,189 --> 01:22:29,360
and math stack exchange these

2417
01:22:32,470 --> 01:22:31,199
uh where you can ask questions and

2418
01:22:34,790 --> 01:22:32,480
you'll quite often get

2419
01:22:35,910 --> 01:22:34,800
serious answers from from mathematicians

2420
01:22:38,790 --> 01:22:35,920
about them

2421
01:22:40,709 --> 01:22:38,800
okay for the people watching please ask

2422
01:22:42,470 --> 01:22:40,719
any further questions because i'm gonna

2423
01:22:43,990 --> 01:22:42,480
end this at some point soon but make

2424
01:22:45,910 --> 01:22:44,000
sure your question is asked in such a

2425
01:22:47,270 --> 01:22:45,920
way that if i read it verbatim it makes

2426
01:22:48,310 --> 01:22:47,280
sense because i don't like having to

2427
01:22:50,790 --> 01:22:48,320
parse them

2428
01:22:52,550 --> 01:22:50,800
in real time just one question at a time

2429
01:22:54,550 --> 01:22:52,560
because my short-term memory seems to

2430
01:22:56,870 --> 01:22:54,560
getting worse and worse yes just

2431
01:22:58,550 --> 01:22:56,880
keep it at the length of one sentence

2432
01:23:02,070 --> 01:22:58,560
one short one

2433
01:23:03,110 --> 01:23:02,080
14-word sentence okay what have you been

2434
01:23:11,350 --> 01:23:03,120
reading recently

2435
01:23:15,189 --> 01:23:13,030
my mind is for some reason completely

2436
01:23:19,189 --> 01:23:15,199
blanking out on this

2437
01:23:24,149 --> 01:23:22,149
um i mean i can give a boring answer of

2438
01:23:26,480 --> 01:23:24,159
all the books i was reading for my

2439
01:23:27,830 --> 01:23:26,490
youtube videos um

2440
01:23:29,750 --> 01:23:27,840
[Music]

2441
01:23:31,270 --> 01:23:29,760
and you tend to look at older books at

2442
01:23:32,550 --> 01:23:31,280
least you reference them plenty for

2443
01:23:33,590 --> 01:23:32,560
example you referenced a book that was

2444
01:23:35,430 --> 01:23:33,600
100 years old

2445
01:23:36,790 --> 01:23:35,440
where the calculation where the graphics

2446
01:23:40,149 --> 01:23:36,800
look like it's modern graphic

2447
01:23:43,270 --> 01:23:40,159
but it was oh yeah yeah

2448
01:23:45,270 --> 01:23:43,280
that yeah that's that's that that book

2449
01:23:46,870 --> 01:23:45,280
is absolutely fantastic because it's

2450
01:23:48,709 --> 01:23:46,880
it's got all

2451
01:23:50,950 --> 01:23:48,719
you know it's written in the days before

2452
01:23:52,870 --> 01:23:50,960
computers and the graphics there just

2453
01:23:55,590 --> 01:23:52,880
blow away most of the graphics people

2454
01:23:57,590 --> 01:23:55,600
produce by computer these days somehow

2455
01:23:59,590 --> 01:23:57,600
their pictures have a sort of soul in

2456
01:24:01,110 --> 01:23:59,600
them whereas if you if you just get a

2457
01:24:04,950 --> 01:24:01,120
computer to draw a graph of

2458
01:24:08,229 --> 01:24:04,960
function it's just you know the is

2459
01:24:09,270 --> 01:24:08,239
it's just not there yeah yeah the heart

2460
01:24:12,470 --> 01:24:09,280
isn't in it

2461
01:24:12,709 --> 01:24:12,480
exactly i mean that the you know known

2462
01:24:16,310 --> 01:24:12,719
as

2463
01:24:19,030 --> 01:24:16,320
and you're just not interested

2464
01:24:19,990 --> 01:24:19,040
and i can't imagine how they did it i

2465
01:24:23,030 --> 01:24:20,000
mean that they're just

2466
01:24:24,950 --> 01:24:23,040
pages and pages of numerical data they

2467
01:24:25,830 --> 01:24:24,960
must have all done by hand and that

2468
01:24:27,669 --> 01:24:25,840
there are

2469
01:24:30,790 --> 01:24:27,679
pages and pages of graphs that must have

2470
01:24:32,310 --> 01:24:30,800
been painstakingly drawn and calculated

2471
01:24:35,030 --> 01:24:32,320
i mean that the amount of effort they

2472
01:24:37,030 --> 01:24:35,040
put into that is just extraordinary

2473
01:24:38,629 --> 01:24:37,040
how are you finding youtube by the way i

2474
01:24:41,110 --> 01:24:38,639
imagine it's new for you

2475
01:24:42,149 --> 01:24:41,120
um it's it's interesting and very

2476
01:24:45,030 --> 01:24:42,159
stressful as

2477
01:24:47,189 --> 01:24:45,040
i said i get really really bugged out by

2478
01:24:50,550 --> 01:24:47,199
making mistakes on my videos

2479
01:24:52,950 --> 01:24:50,560
it's it's just it's just so embarrassing

2480
01:24:56,390 --> 01:24:52,960
having these

2481
01:24:57,990 --> 01:24:56,400
well um what i was thinking is um

2482
01:25:00,070 --> 01:24:58,000
what it reminds me of you you know you

2483
01:25:01,830 --> 01:25:00,080
get these books um written

2484
01:25:03,830 --> 01:25:01,840
you know that the million stupidest

2485
01:25:06,310 --> 01:25:03,840
things ever said by professor watts

2486
01:25:07,430 --> 01:25:06,320
by by president watts's name and things

2487
01:25:09,189 --> 01:25:07,440
like that

2488
01:25:11,270 --> 01:25:09,199
i suddenly have an awful lot more

2489
01:25:13,110 --> 01:25:11,280
sympathy for president watts's name who

2490
01:25:14,629 --> 01:25:13,120
who blurts out something stupid whenever

2491
01:25:16,790 --> 01:25:14,639
he opens his mouth because i've noticed

2492
01:25:20,229 --> 01:25:16,800
in my youtube videos i'm continually

2493
01:25:22,470 --> 01:25:20,239
making really really dumb mistakes

2494
01:25:23,669 --> 01:25:22,480
i mean it seems to be almost impossible

2495
01:25:25,910 --> 01:25:23,679
not to you

2496
01:25:27,270 --> 01:25:25,920
you can prepare and check everything and

2497
01:25:28,229 --> 01:25:27,280
it doesn't matter when you're actually

2498
01:25:31,750 --> 01:25:28,239
talking the stress

2499
01:25:32,950 --> 01:25:31,760
causes you to say really dumb things

2500
01:25:35,750 --> 01:25:32,960
you get stressed out when you're making

2501
01:25:37,830 --> 01:25:35,760
your youtube videos it's somehow very

2502
01:25:39,910 --> 01:25:37,840
yeah yeah it's it's very stressful and

2503
01:25:41,510 --> 01:25:39,920
when you're stressed your mind just

2504
01:25:44,310 --> 01:25:41,520
closes down and you

2505
01:25:46,470 --> 01:25:44,320
you make the dumbest mistakes and you

2506
01:25:47,990 --> 01:25:46,480
get to the end of the video and you

2507
01:25:50,470 --> 01:25:48,000
wonder how you could have said something

2508
01:25:51,910 --> 01:25:50,480
so stupid what is it about it that you

2509
01:25:52,950 --> 01:25:51,920
like so you just mentioned a negative

2510
01:25:55,350 --> 01:25:52,960
aspect

2511
01:25:56,709 --> 01:25:55,360
well it gives me something to do i mean

2512
01:25:58,149 --> 01:25:56,719
as i said research

2513
01:25:59,830 --> 01:25:58,159
consists most of the time of getting

2514
01:26:01,669 --> 01:25:59,840
nowhere and if you're making youtube

2515
01:26:02,709 --> 01:26:01,679
videos you're at least doing something

2516
01:26:04,390 --> 01:26:02,719
and

2517
01:26:06,470 --> 01:26:04,400
um i was rather surprised people

2518
01:26:09,189 --> 01:26:06,480
actually seem to like watching

2519
01:26:10,870 --> 01:26:09,199
math lectures on youtube i mean yeah i

2520
01:26:12,709 --> 01:26:10,880
mean i i started putting these videos

2521
01:26:14,470 --> 01:26:12,719
because they were my

2522
01:26:15,910 --> 01:26:14,480
you know lectures for courses i supposed

2523
01:26:18,950 --> 01:26:15,920
to be teaching and i had to

2524
01:26:21,189 --> 01:26:18,960
make some videos for them and

2525
01:26:22,550 --> 01:26:21,199
i i sort of didn't really occur to me

2526
01:26:25,030 --> 01:26:22,560
that people would actually watch them

2527
01:26:25,990 --> 01:26:25,040
for fun because i i can't stand watching

2528
01:26:28,149 --> 01:26:26,000
lectures

2529
01:26:29,669 --> 01:26:28,159
um so but other people obviously learn

2530
01:26:31,350 --> 01:26:29,679
differently

2531
01:26:33,590 --> 01:26:31,360
how much time do you spend thinking

2532
01:26:35,669 --> 01:26:33,600
about your own particular background on

2533
01:26:37,030 --> 01:26:35,679
knowledge and skills and relating it to

2534
01:26:39,510 --> 01:26:37,040
previous knowledge

2535
01:26:41,990 --> 01:26:39,520
versus spending time thinking without

2536
01:26:46,070 --> 01:26:42,000
relating

2537
01:26:48,830 --> 01:26:46,080
uh gosh that's a abstract question i'm

2538
01:26:51,830 --> 01:26:48,840
not quite sure

2539
01:26:53,990 --> 01:26:51,840
um i i would

2540
01:26:55,990 --> 01:26:54,000
say i'll try and answer it i would say

2541
01:26:57,669 --> 01:26:56,000
that nearly everything i do i'm trying

2542
01:27:00,790 --> 01:26:57,679
to relate it to other things

2543
01:27:03,270 --> 01:27:00,800
other things i know i mean a lot of

2544
01:27:04,070 --> 01:27:03,280
what research consists of is making

2545
01:27:06,229 --> 01:27:04,080
unexpected

2546
01:27:07,350 --> 01:27:06,239
connections between things so so if

2547
01:27:10,870 --> 01:27:07,360
you're

2548
01:27:11,910 --> 01:27:10,880
that has no connections to anything you

2549
01:27:13,750 --> 01:27:11,920
know in the past

2550
01:27:15,110 --> 01:27:13,760
it's going to be really really difficult

2551
01:27:17,510 --> 01:27:15,120
because it's going to take a lot of time

2552
01:27:19,030 --> 01:27:17,520
to build up

2553
01:27:21,590 --> 01:27:19,040
enough knowledge to start making

2554
01:27:23,990 --> 01:27:21,600
connections so so you really want to be

2555
01:27:25,430 --> 01:27:24,000
relating everything you do to

2556
01:27:28,229 --> 01:27:25,440
hopefully to something you've done

2557
01:27:32,310 --> 01:27:30,149
i mean you you're trying to build up a

2558
01:27:34,790 --> 01:27:32,320
big in connected web not have a lot of

2559
01:27:36,709 --> 01:27:34,800
series of discrete

2560
01:27:38,390 --> 01:27:36,719
domains of information that have nothing

2561
01:27:41,030 --> 01:27:38,400
to do with each other

2562
01:27:42,070 --> 01:27:41,040
neon dagger asks math people often talk

2563
01:27:44,470 --> 01:27:42,080
about being drawn

2564
01:27:45,669 --> 01:27:44,480
in by a wow subject that is hidden from

2565
01:27:47,830 --> 01:27:45,679
them earlier on

2566
01:27:50,790 --> 01:27:47,840
is it important to wow students to draw

2567
01:27:54,629 --> 01:27:52,870
um if you're trying to encourage people

2568
01:27:55,430 --> 01:27:54,639
to do mathematics this would be one way

2569
01:27:57,910 --> 01:27:55,440
of doing it

2570
01:27:59,030 --> 01:27:57,920
but it's again one of these things where

2571
01:28:01,030 --> 01:27:59,040
different people have different

2572
01:28:02,149 --> 01:28:01,040
approaches that some people are drawn in

2573
01:28:04,070 --> 01:28:02,159
by this

2574
01:28:05,750 --> 01:28:04,080
wow thing and others have drawn in

2575
01:28:09,030 --> 01:28:05,760
because they

2576
01:28:12,830 --> 01:28:09,040
the the they're just in they

2577
01:28:14,070 --> 01:28:12,840
they're just like working steadily for

2578
01:28:16,310 --> 01:28:14,080
um

2579
01:28:17,830 --> 01:28:16,320
your your hang on your your screen has

2580
01:28:19,910 --> 01:28:17,840
gone very weird

2581
01:28:22,149 --> 01:28:19,920
oh okay one second where we go there we

2582
01:28:24,629 --> 01:28:22,159
go there we go

2583
01:28:26,550 --> 01:28:24,639
do you remember what you were saying as

2584
01:28:29,189 --> 01:28:26,560
i said i'm under stress which makes my

2585
01:28:31,590 --> 01:28:29,199
short term memory even worse than usual

2586
01:28:32,870 --> 01:28:31,600
do you feel stressed being interviewed

2587
01:28:35,830 --> 01:28:32,880
right now

2588
01:28:36,870 --> 01:28:35,840
very much so i mean i i've noticed i've

2589
01:28:39,270 --> 01:28:36,880
noticed this that

2590
01:28:40,310 --> 01:28:39,280
i'm having great difficulty thinking

2591
01:28:42,310 --> 01:28:40,320
about

2592
01:28:43,990 --> 01:28:42,320
questions that people ask um i have the

2593
01:28:45,830 --> 01:28:44,000
same phenomenon in lectures people ask

2594
01:28:47,510 --> 01:28:45,840
me a question in a lecture and i've

2595
01:28:48,950 --> 01:28:47,520
no idea what the answer is and then i

2596
01:28:52,149 --> 01:28:48,960
get out of the lecture and it's

2597
01:28:53,910 --> 01:28:52,159
it's completely obvious so somehow

2598
01:28:55,350 --> 01:28:53,920
yeah yeah being interviewed or talking

2599
01:28:57,590 --> 01:28:55,360
whatever the

2600
01:28:58,470 --> 01:28:57,600
the high parts of my brain simply close

2601
01:29:04,709 --> 01:28:58,480
down

2602
01:29:04,719 --> 01:29:08,149
i think well

2603
01:29:11,910 --> 01:29:10,950
not not very um i mean there's seen here

2604
01:29:13,910 --> 01:29:11,920
one or two people

2605
01:29:15,590 --> 01:29:13,920
asking me for you know their

2606
01:29:16,950 --> 01:29:15,600
undergraduates doing projects where they

2607
01:29:19,030 --> 01:29:16,960
have to interview a professor or

2608
01:29:21,270 --> 01:29:19,040
something so

2609
01:29:22,629 --> 01:29:21,280
i've had maybe two or three um

2610
01:29:25,270 --> 01:29:22,639
interviews yours

2611
01:29:27,030 --> 01:29:25,280
your screen has gone weird again okay

2612
01:29:27,669 --> 01:29:27,040
okay let me just switch cameras then

2613
01:29:31,270 --> 01:29:27,679
completely

2614
01:29:32,950 --> 01:29:31,280
i have a feeling it's just overheating

2615
01:29:35,030 --> 01:29:32,960
yeah i was looking just so you know i

2616
01:29:36,709 --> 01:29:35,040
was looking for interviews of you

2617
01:29:42,310 --> 01:29:36,719
other people doing podcasts with you and

2618
01:29:48,149 --> 01:29:44,390
okay what's up with goldbach's

2619
01:29:52,149 --> 01:29:50,149
i don't really know why it's hard to

2620
01:29:54,790 --> 01:29:52,159
crack um

2621
01:29:56,229 --> 01:29:54,800
it's people have got very close i think

2622
01:30:00,470 --> 01:29:56,239
there was a

2623
01:30:02,229 --> 01:30:00,480
um i think

2624
01:30:03,910 --> 01:30:02,239
this isn't my area so i may have

2625
01:30:04,950 --> 01:30:03,920
misremembered i think there's a chinese

2626
01:30:07,030 --> 01:30:04,960
mathematician maybe

2627
01:30:08,950 --> 01:30:07,040
chen or something who who managed to get

2628
01:30:10,070 --> 01:30:08,960
very close so so goldback's conjecture

2629
01:30:13,430 --> 01:30:10,080
says that

2630
01:30:17,110 --> 01:30:13,440
um um every uh

2631
01:30:20,149 --> 01:30:17,120
which every even number is the sum of

2632
01:30:21,270 --> 01:30:20,159
two primes and you can get quite close

2633
01:30:22,709 --> 01:30:21,280
to that that

2634
01:30:24,470 --> 01:30:22,719
with a lot of work you can prove that

2635
01:30:27,350 --> 01:30:24,480
every even number is the sum of a prime

2636
01:30:29,189 --> 01:30:27,360
and a product of two primes

2637
01:30:31,110 --> 01:30:29,199
and for some reason there's some

2638
01:30:32,550 --> 01:30:31,120
horrible obstruction to going any

2639
01:30:33,990 --> 01:30:32,560
further than that

2640
01:30:36,629 --> 01:30:34,000
and i've never managed to understand

2641
01:30:37,350 --> 01:30:36,639
what the instruction is um i think terry

2642
01:30:39,350 --> 01:30:37,360
tau

2643
01:30:40,709 --> 01:30:39,360
who you mentioned i i once saw a

2644
01:30:41,990 --> 01:30:40,719
discussion by him of what this

2645
01:30:45,270 --> 01:30:42,000
obstruction is so

2646
01:30:46,470 --> 01:30:45,280
he might be the better person to ask um

2647
01:30:49,510 --> 01:30:46,480
and again

2648
01:30:51,510 --> 01:30:49,520
you can we we can prove that every odd

2649
01:30:53,350 --> 01:30:51,520
number is the sum of three primes

2650
01:30:55,750 --> 01:30:53,360
so we've got three primes instead of two

2651
01:30:57,510 --> 01:30:55,760
primes so we've got very close to it but

2652
01:30:59,990 --> 01:30:57,520
again there seems to be this weird

2653
01:31:03,270 --> 01:31:00,000
obstruction to pushing that last little

2654
01:31:06,709 --> 01:31:03,280
little step um

2655
01:31:08,390 --> 01:31:06,719
so as i said it's not my area so i don't

2656
01:31:11,669 --> 01:31:08,400
know exactly what this obstruction

2657
01:31:14,390 --> 01:31:11,679
is elham romanti

2658
01:31:16,390 --> 01:31:14,400
or rahami asks what advice do you have

2659
01:31:18,229 --> 01:31:16,400
for someone in their 20s trying to learn

2660
01:31:19,910 --> 01:31:18,239
math

2661
01:31:21,270 --> 01:31:19,920
um i know variations on this question

2662
01:31:23,510 --> 01:31:21,280
i've been asked before already

2663
01:31:25,510 --> 01:31:23,520
well go for it i mean i mean it it

2664
01:31:27,189 --> 01:31:25,520
depends very much on how much time you

2665
01:31:29,510 --> 01:31:27,199
can spare to put into it i mean people

2666
01:31:31,270 --> 01:31:29,520
in their 20s are quite often trying to

2667
01:31:34,070 --> 01:31:31,280
have their career starting up so may not

2668
01:31:37,590 --> 01:31:34,080
actually have a whole lot of spare time

2669
01:31:39,270 --> 01:31:37,600
um um

2670
01:31:40,870 --> 01:31:39,280
so i'm probably just repeating the

2671
01:31:42,310 --> 01:31:40,880
answer i gave earlier but

2672
01:31:45,350 --> 01:31:42,320
my advice would be to find something

2673
01:31:47,030 --> 01:31:45,360
you're really interested in and

2674
01:31:49,910 --> 01:31:47,040
my usual suggestion for that is

2675
01:31:52,470 --> 01:31:49,920
something like modular forms which is

2676
01:31:54,470 --> 01:31:52,480
the but that that's the area i found

2677
01:31:56,149 --> 01:31:54,480
particularly striking

2678
01:31:57,510 --> 01:31:56,159
i just wanted to conclude by saying

2679
01:31:58,790 --> 01:31:57,520
thank you i appreciate you being

2680
01:32:01,110 --> 01:31:58,800
generous with your time

2681
01:32:02,310 --> 01:32:01,120
i watch your videos i gain from them and

2682
01:32:04,070 --> 01:32:02,320
i'm pretty sure

2683
01:32:05,669 --> 01:32:04,080
plenty of the audience from this channel

2684
01:32:08,950 --> 01:32:05,679
will gain from it as well

2685
01:32:11,270 --> 01:32:08,960
yeah well i i i'm sort of

2686
01:32:14,149 --> 01:32:11,280
i i think having interviews like this is

2687
01:32:17,110 --> 01:32:14,159
really good practice for me since i'm

2688
01:32:19,110 --> 01:32:17,120
as you know as i show you observed i'm

2689
01:32:21,750 --> 01:32:19,120
rather nervous not very good at them

2690
01:32:23,430 --> 01:32:21,760
so well just so you know i'm extremely

2691
01:32:24,870 --> 01:32:23,440
nervous as well and partly one of the

2692
01:32:28,390 --> 01:32:24,880
reasons i have to go urinate is because

2693
01:32:31,750 --> 01:32:30,310
yeah i'm thinking how cut how calm and

2694
01:32:32,229 --> 01:32:31,760
professional you looked no i'm

2695
01:32:34,950 --> 01:32:32,239
absolutely

2696
01:32:36,790 --> 01:32:34,960
professional i appreciate that you would

2697
01:32:39,990 --> 01:32:36,800
even give me a modicum of that

2698
01:32:41,510 --> 01:32:40,000
i'm more i i'm much

2699
01:32:44,070 --> 01:32:41,520
i'm extremely introverted and i have

2700
01:32:45,830 --> 01:32:44,080
social anxiety it's just that i've

2701
01:32:47,830 --> 01:32:45,840
had to trade myself to overcome it to

2702
01:32:49,430 --> 01:32:47,840
some degree is everybody

2703
01:32:51,110 --> 01:32:49,440
faking it or there's some people who are

2704
01:32:52,310 --> 01:32:51,120
really extroverts

2705
01:32:54,149 --> 01:32:52,320
oh there are plenty of people who are

2706
01:32:56,070 --> 01:32:54,159
extroverts just so you know it was

2707
01:32:59,830 --> 01:32:56,080
somewhat ill-advised on my part to

2708
01:33:03,350 --> 01:32:59,840
speak to you because usually

2709
01:33:03,990 --> 01:33:03,360
i have i ask a professor can i speak

2710
01:33:05,590 --> 01:33:04,000
with you

2711
01:33:07,270 --> 01:33:05,600
six to eight weeks from now and then

2712
01:33:08,950 --> 01:33:07,280
they'll say yes or no and then i have

2713
01:33:11,910 --> 01:33:08,960
six to eight weeks to look up

2714
01:33:13,350 --> 01:33:11,920
their corpus of work and make notes and

2715
01:33:14,790 --> 01:33:13,360
and ask them somewhat

2716
01:33:17,270 --> 01:33:14,800
challenging questions or technical

2717
01:33:18,709 --> 01:33:17,280
questions for

2718
01:33:20,070 --> 01:33:18,719
furthering my understanding basically

2719
01:33:21,030 --> 01:33:20,080
trying to get in their head not trying

2720
01:33:22,790 --> 01:33:21,040
to disprove or

2721
01:33:24,149 --> 01:33:22,800
have a contentious interview at all just

2722
01:33:26,470 --> 01:33:24,159
trying to understand

2723
01:33:28,550 --> 01:33:26,480
and for this one i had i messaged you on

2724
01:33:31,750 --> 01:33:28,560
monday i believe you said yes on tuesday

2725
01:33:32,229 --> 01:33:31,760
and then i had one full day only this

2726
01:33:34,390 --> 01:33:32,239
week

2727
01:33:37,830 --> 01:33:34,400
to go through your entire work and i

2728
01:33:39,669 --> 01:33:37,840
could barely get through the

2729
01:33:41,510 --> 01:33:39,679
i can barely get through the overview of

2730
01:33:43,590 --> 01:33:41,520
the proof for the monstrous moonshine

2731
01:33:45,590 --> 01:33:43,600
conjecture i think you're way ahead of

2732
01:33:47,270 --> 01:33:45,600
most people on that

2733
01:33:49,189 --> 01:33:47,280
the surprise is not that it's hard to

2734
01:33:50,470 --> 01:33:49,199
understand the surprises that we can

2735
01:33:52,070 --> 01:33:50,480
understand it at all

2736
01:33:53,830 --> 01:33:52,080
i'm much more algebraic far more

2737
01:33:54,950 --> 01:33:53,840
algebraic than i am geometric and i

2738
01:33:57,270 --> 01:33:54,960
dislike when people

2739
01:33:58,870 --> 01:33:57,280
show group theory at first with the

2740
01:34:00,070 --> 01:33:58,880
rubik's cuber with the triangle

2741
01:34:01,830 --> 01:34:00,080
because to me i'm just thinking there

2742
01:34:02,229 --> 01:34:01,840
are far more symmetries than what you've

2743
01:34:03,669 --> 01:34:02,239
just

2744
01:34:05,910 --> 01:34:03,679
shown so someone will say the triangle

2745
01:34:06,870 --> 01:34:05,920
has six it may not may have eight i

2746
01:34:08,149 --> 01:34:06,880
don't know but whatever then i'm

2747
01:34:09,270 --> 01:34:08,159
thinking yeah but isn't there also the

2748
01:34:10,709 --> 01:34:09,280
symmetry of

2749
01:34:12,390 --> 01:34:10,719
let's say you invert the thickness of

2750
01:34:13,669 --> 01:34:12,400
the line and then bring it back so is

2751
01:34:15,110 --> 01:34:13,679
that not a symmetry

2752
01:34:16,629 --> 01:34:15,120
or is there not a symmetry of inverting

2753
01:34:17,510 --> 01:34:16,639
the colors and then bringing that like

2754
01:34:18,870 --> 01:34:17,520
why are you choosing

2755
01:34:20,790 --> 01:34:18,880
just just show me the axioms

2756
01:34:24,070 --> 01:34:20,800
algebraically i understand that

2757
01:34:27,430 --> 01:34:24,080
yeah well yeah

2758
01:34:30,229 --> 01:34:27,440
um yeah but i think i think that

2759
01:34:32,310 --> 01:34:30,239
it's a usual problem that you you can't

2760
01:34:34,149 --> 01:34:32,320
give a presentation of group theory that

2761
01:34:35,750 --> 01:34:34,159
satisfies everybody because people's

2762
01:34:37,669 --> 01:34:35,760
learning styles are so different some

2763
01:34:40,550 --> 01:34:37,679
want to see the axioms

2764
01:34:42,790 --> 01:34:40,560
some want to see examples and so on were

2765
01:34:46,709 --> 01:34:42,800
the questions okay

2766
01:34:48,390 --> 01:34:46,719
yeah except the ones where i

2767
01:34:50,149 --> 01:34:48,400
when i kind of got stressed out and

2768
01:34:52,470 --> 01:34:50,159
couldn't think what to say i mean

2769
01:34:54,390 --> 01:34:52,480
you know sometimes my i think there's

2770
01:34:55,910 --> 01:34:54,400
one weird one you're asking what what i

2771
01:34:58,149 --> 01:34:55,920
had been reading recently my brain just

2772
01:35:01,030 --> 01:34:58,159
completely froze

2773
01:35:01,430 --> 01:35:01,040
um yeah i find that happens for me as

2774
01:35:03,510 --> 01:35:01,440
well

2775
01:35:04,550 --> 01:35:03,520
you know no no no i think it i was

2776
01:35:06,629 --> 01:35:04,560
actually thinking about that

2777
01:35:08,229 --> 01:35:06,639
i'd read somewhere where where you know

2778
01:35:09,910 --> 01:35:08,239
someone was saying well that they'd ask

2779
01:35:10,709 --> 01:35:09,920
people what they're reading been reading

2780
01:35:12,310 --> 01:35:10,719
recently and

2781
01:35:14,070 --> 01:35:12,320
and some people were unable to answer

2782
01:35:16,070 --> 01:35:14,080
with a single book

2783
01:35:18,229 --> 01:35:16,080
as an example of how illiterate people

2784
01:35:19,910 --> 01:35:18,239
weren't i think to myself well

2785
01:35:21,270 --> 01:35:19,920
exactly the same is happening with me i

2786
01:35:22,790 --> 01:35:21,280
just can't think of anything i've

2787
01:35:23,830 --> 01:35:22,800
written in the part anything i've read

2788
01:35:27,270 --> 01:35:23,840
in the past day

2789
01:35:29,750 --> 01:35:27,280
i just couldn't think of anything at all

2790
01:35:31,189 --> 01:35:29,760
even though i've looked at several books

2791
01:35:32,229 --> 01:35:31,199
you know just hoping i didn't say

2792
01:35:34,229 --> 01:35:32,239
anything that's going to get me

2793
01:35:36,709 --> 01:35:34,239
condemned on the internet you know there

2794
01:35:38,229 --> 01:35:36,719
seem to be

2795
01:35:40,229 --> 01:35:38,239
too many cases of people who

2796
01:35:41,990 --> 01:35:40,239
inadvertently say something harmless

2797
01:35:44,229 --> 01:35:42,000
which turns out to be a code word for

2798
01:35:46,709 --> 01:35:44,239
some horrible crime see many

2799
01:35:48,149 --> 01:35:46,719
mathematicians physicists too

2800
01:35:49,910 --> 01:35:48,159
they have a difficult time with

2801
01:35:52,870 --> 01:35:49,920
answering questions that have to do with

2802
01:35:56,790 --> 01:35:52,880
that are ambiguous and yeah well me too

2803
01:35:58,470 --> 01:35:56,800
i mean you know whenever there was a

2804
01:36:01,030 --> 01:35:58,480
freezing up every now and then with uh

2805
01:36:03,830 --> 01:36:01,040
with with one of these

2806
01:36:04,790 --> 01:36:03,840
more more general questions right and i

2807
01:36:07,750 --> 01:36:04,800
would freeze up too

2808
01:36:08,790 --> 01:36:07,760
but the difference between me is that i

2809
01:36:10,310 --> 01:36:08,800
first

2810
01:36:11,750 --> 01:36:10,320
i have an artistic side that's the

2811
01:36:12,629 --> 01:36:11,760
filmmaking side that's the stand-up

2812
01:36:14,390 --> 01:36:12,639
comedy side

2813
01:36:17,350 --> 01:36:14,400
so in a sense that's almost like you're

2814
01:36:20,550 --> 01:36:17,360
you deal with ambiguity

2815
01:36:22,229 --> 01:36:20,560
as your regular male you so for me

2816
01:36:25,910 --> 01:36:22,239
i don't have too much of a problem with

2817
01:36:27,109 --> 01:36:25,920
it and it and i find that much of the

2818
01:36:29,270 --> 01:36:27,119
i don't know if you'll agree with this

2819
01:36:31,350 --> 01:36:29,280
but i've heard this said that much of

2820
01:36:33,669 --> 01:36:31,360
the pr much of the solution comes from

2821
01:36:37,109 --> 01:36:33,679
specifying the problem

2822
01:36:38,629 --> 01:36:37,119
and so i wonder how much of let's say

2823
01:36:40,149 --> 01:36:38,639
is an ant conscious or what is

2824
01:36:43,430 --> 01:36:40,159
consciousness and so on so on

2825
01:36:45,270 --> 01:36:43,440
how much of it is the solution

2826
01:36:46,550 --> 01:36:45,280
is just well how do we define it

2827
01:36:48,950 --> 01:36:46,560
properly

2828
01:36:50,950 --> 01:36:48,960
yeah well and this this seems to be the

2829
01:36:52,390 --> 01:36:50,960
cause of half the problems in philosophy

2830
01:36:55,830 --> 01:36:52,400
there they're arguing about something

2831
01:36:58,550 --> 01:36:55,840
that simply hasn't been properly defined

2832
01:36:59,270 --> 01:36:58,560
um possibly you could say the same about

2833
01:37:02,709 --> 01:36:59,280
religion

2834
01:37:05,990 --> 01:37:04,149
yeah and then some will even say that

2835
01:37:07,590 --> 01:37:06,000
par actually it's the opposite

2836
01:37:09,669 --> 01:37:07,600
the problem in religion is that people

2837
01:37:10,149 --> 01:37:09,679
are trying to define it and it should be

2838
01:37:14,709 --> 01:37:10,159
left

2839
01:37:18,310 --> 01:37:17,590
it's like me backing out of your

2840
01:37:19,990 --> 01:37:18,320
question about

2841
01:37:23,109 --> 01:37:20,000
god by saying i didn't know how it was

2842
01:37:26,950 --> 01:37:25,669
that's everyone that's every well that's

2843
01:37:29,189 --> 01:37:26,960
not everyone but that's most

2844
01:37:30,709 --> 01:37:29,199
mathematicians most physicists

2845
01:37:32,310 --> 01:37:30,719
and that would be me prior to two years

2846
01:37:35,030 --> 01:37:32,320
ago yeah so

2847
01:37:36,790 --> 01:37:35,040
well mathematicians actually trained to

2848
01:37:39,750 --> 01:37:36,800
have things well defined before you

2849
01:37:43,750 --> 01:37:39,760
start discussing them of course

2850
01:37:48,310 --> 01:37:46,070
sorry i wanted to speculate around that

2851
01:37:49,910 --> 01:37:48,320
because i wonder how much of it is

2852
01:37:51,669 --> 01:37:49,920
it's not that they don't like that it's

2853
01:37:54,149 --> 01:37:51,679
somewhat meaningless quote unquote

2854
01:37:55,590 --> 01:37:54,159
but that because it's meaningless

2855
01:37:56,950 --> 01:37:55,600
they're afraid that what they will say

2856
01:37:59,350 --> 01:37:56,960
will then be used against them

2857
01:38:00,870 --> 01:37:59,360
in some fool like oh you're imbecilic

2858
01:38:03,189 --> 01:38:00,880
for saying so and so

2859
01:38:04,070 --> 01:38:03,199
and it's more about the fear of

2860
01:38:07,189 --> 01:38:04,080
commenting

2861
01:38:09,270 --> 01:38:07,199
on what's vague and saying something

2862
01:38:11,270 --> 01:38:09,280
foolish than it is about commenting on

2863
01:38:12,870 --> 01:38:11,280
it at all and the reason why i say that

2864
01:38:14,629 --> 01:38:12,880
is because in our everyday life like i

2865
01:38:15,750 --> 01:38:14,639
mentioned to you we do use the word game

2866
01:38:17,510 --> 01:38:15,760
and chair and i

2867
01:38:19,109 --> 01:38:17,520
but those are actually ill-defined like

2868
01:38:20,870 --> 01:38:19,119
what is a chair maybe it's something to

2869
01:38:22,629 --> 01:38:20,880
sit on but then you get stumps

2870
01:38:23,910 --> 01:38:22,639
and then but what is i the more you look

2871
01:38:25,910 --> 01:38:23,920
at i what

2872
01:38:28,470 --> 01:38:25,920
what defines i and you you know there's

2873
01:38:30,709 --> 01:38:28,480
various well i i'd say everything is

2874
01:38:32,629 --> 01:38:30,719
ill-defined but but some things are more

2875
01:38:35,590 --> 01:38:32,639
ill-defined than others so

2876
01:38:37,189 --> 01:38:35,600
so chair i will normally know whether

2877
01:38:40,070 --> 01:38:37,199
something is a chair or not

2878
01:38:40,870 --> 01:38:40,080
um whereas something like god i just no

2879
01:38:43,990 --> 01:38:40,880
idea

2880
01:38:46,629 --> 01:38:44,000
um it's it's it's much i mean chair and

2881
01:38:49,109 --> 01:38:46,639
god may both be ill-defined but but

2882
01:38:50,629 --> 01:38:49,119
but but god is a lot more ill-defined

2883
01:38:52,709 --> 01:38:50,639
than chair

2884
01:38:54,870 --> 01:38:52,719
before we were talking about ramanujan

2885
01:38:56,470 --> 01:38:54,880
and you mentioned that when he

2886
01:38:58,310 --> 01:38:56,480
said that he got his ideas from his

2887
01:38:59,750 --> 01:38:58,320
prayers his visions meditations and so

2888
01:39:00,709 --> 01:38:59,760
on that probably he didn't he had a

2889
01:39:03,350 --> 01:39:00,719
secret mechanism

2890
01:39:03,910 --> 01:39:03,360
that he wasn't revealing and i'm curious

2891
01:39:06,229 --> 01:39:03,920
do you

2892
01:39:07,590 --> 01:39:06,239
have a secret technique to mathematics

2893
01:39:11,750 --> 01:39:07,600
that you don't reveal

2894
01:39:13,430 --> 01:39:11,760
uh no um and and i i don't know about

2895
01:39:17,350 --> 01:39:13,440
romantic either i'm just sort of

2896
01:39:21,750 --> 01:39:19,270
giving an answer to a slightly silly

2897
01:39:23,430 --> 01:39:21,760
question i mean it's it's

2898
01:39:25,189 --> 01:39:23,440
as i said it's just very difficult to

2899
01:39:28,070 --> 01:39:25,199
analyze your own mind and figure out

2900
01:39:29,510 --> 01:39:28,080
where ideas are coming from

2901
01:39:31,669 --> 01:39:29,520
what do you think would be the

2902
01:39:34,470 --> 01:39:31,679
implications that fermanagh did indeed

2903
01:39:37,669 --> 01:39:34,480
get his formulas inexplicably from his

2904
01:39:40,950 --> 01:39:37,679
visions and so on from a goddess or god

2905
01:39:44,550 --> 01:39:40,960
well i think that would just be his

2906
01:39:46,070 --> 01:39:44,560
explanation of explain what's going on

2907
01:39:48,709 --> 01:39:46,080
in his subconscious brain

2908
01:39:50,470 --> 01:39:48,719
i mean you here we call it subconscious

2909
01:39:53,990 --> 01:39:50,480
other cultures might call it

2910
01:39:55,910 --> 01:39:54,000
um a vision from a goddess i mean

2911
01:39:58,950 --> 01:39:55,920
but they're both ways of saying we have

2912
01:40:00,790 --> 01:39:58,960
no idea what's going on

2913
01:40:03,430 --> 01:40:00,800
you mentioned before that modular forms

2914
01:40:04,790 --> 01:40:03,440
are a field that you find to be the most

2915
01:40:07,270 --> 01:40:04,800
fascinating or provocative or

2916
01:40:08,550 --> 01:40:07,280
stimulating i don't recall which one of

2917
01:40:11,669 --> 01:40:08,560
those adjectives you used but

2918
01:40:14,790 --> 01:40:11,679
why is that the case um

2919
01:40:17,750 --> 01:40:14,800
well so so what modular forms do

2920
01:40:19,430 --> 01:40:17,760
is is they they they seem to turn up in

2921
01:40:19,830 --> 01:40:19,440
all sorts of areas of mathematics that

2922
01:40:21,430 --> 01:40:19,840
that

2923
01:40:22,950 --> 01:40:21,440
appear to have nothing to do with

2924
01:40:26,070 --> 01:40:22,960
modular forms

2925
01:40:27,510 --> 01:40:26,080
um obvious one i i used quite a lot was

2926
01:40:28,790 --> 01:40:27,520
they turn up in the theory of the

2927
01:40:30,470 --> 01:40:28,800
monster simple group and

2928
01:40:34,629 --> 01:40:30,480
simple groups seem to have nothing to do

2929
01:40:40,070 --> 01:40:38,229
marina via kovska um used them to

2930
01:40:42,790 --> 01:40:40,080
solve the sphere packing problem in high

2931
01:40:44,629 --> 01:40:42,800
dimensions and again that has

2932
01:40:46,149 --> 01:40:44,639
no obvious relation to modular forms

2933
01:40:47,510 --> 01:40:46,159
andrew wiles used them to

2934
01:40:49,270 --> 01:40:47,520
prove fermat's last theorem which

2935
01:40:50,310 --> 01:40:49,280
there's no obvious reason why they

2936
01:40:52,229 --> 01:40:50,320
should turn up so

2937
01:40:54,070 --> 01:40:52,239
they're turning up and completely

2938
01:40:56,950 --> 01:40:54,080
unexpectedly in all these

2939
01:40:58,470 --> 01:40:56,960
completely separate mathematical areas

2940
01:41:01,109 --> 01:40:58,480
and whenever they turn up

2941
01:41:02,149 --> 01:41:01,119
all these utterly bizarre coincidences

2942
01:41:06,950 --> 01:41:02,159
start happening

2943
01:41:09,109 --> 01:41:06,960
i mean in order for modular forms to

2944
01:41:11,590 --> 01:41:09,119
solve a problem you need a whole chain

2945
01:41:13,750 --> 01:41:11,600
of bizarre numerical coincidences and

2946
01:41:17,510 --> 01:41:13,760
these numerical bizarre coincidences

2947
01:41:19,510 --> 01:41:17,520
often seem to happen um so

2948
01:41:20,870 --> 01:41:19,520
you know that there's there's something

2949
01:41:24,629 --> 01:41:20,880
very weird going on

2950
01:41:27,109 --> 01:41:24,639
um as to why modular forms turn up

2951
01:41:31,350 --> 01:41:27,119
in all these places i just have no idea

2952
01:41:34,390 --> 01:41:32,709
is one of those connections those

2953
01:41:36,390 --> 01:41:34,400
coincidences the one nine six

2954
01:41:37,430 --> 01:41:36,400
eight eight three yeah yeah yeah exactly

2955
01:41:39,270 --> 01:41:37,440
so there's this

2956
01:41:41,669 --> 01:41:39,280
that that's a typical example of this

2957
01:41:43,669 --> 01:41:41,679
bizarre numerical coincidence you

2958
01:41:45,510 --> 01:41:43,679
you take a representation of the monster

2959
01:41:48,070 --> 01:41:45,520
group and it happens to be

2960
01:41:52,629 --> 01:41:48,080
almost the same as a coefficient of the

2961
01:41:56,149 --> 01:41:54,709
okay now i'm going to read to you a

2962
01:41:57,189 --> 01:41:56,159
thought from another mathematician i

2963
01:41:58,950 --> 01:41:57,199
recall you saying that you believe

2964
01:42:00,709 --> 01:41:58,960
mathematics is discovered

2965
01:42:02,070 --> 01:42:00,719
and he says it's invented and i don't

2966
01:42:02,950 --> 01:42:02,080
know which mathematician this is so

2967
01:42:04,709 --> 01:42:02,960
don't worry

2968
01:42:06,470 --> 01:42:04,719
this is an anonymous mathematician he

2969
01:42:08,470 --> 01:42:06,480
says mathematics is created because it's

2970
01:42:09,910 --> 01:42:08,480
a language used by humans so that we can

2971
01:42:10,550 --> 01:42:09,920
understand and make sense of the world

2972
01:42:12,709 --> 01:42:10,560
around us

2973
01:42:13,750 --> 01:42:12,719
for mathematics to be discovered you

2974
01:42:15,510 --> 01:42:13,760
would assume

2975
01:42:17,270 --> 01:42:15,520
that the way humans perceive the world

2976
01:42:18,950 --> 01:42:17,280
is absolute truth and in

2977
01:42:20,470 --> 01:42:18,960
some way establish humans as the

2978
01:42:22,870 --> 01:42:20,480
universal standard

2979
01:42:24,390 --> 01:42:22,880
of everything i might be rambling here

2980
01:42:25,750 --> 01:42:24,400
but i get the feeling that if you choose

2981
01:42:27,510 --> 01:42:25,760
to see mathematics

2982
01:42:30,550 --> 01:42:27,520
as something that was discovered by

2983
01:42:32,790 --> 01:42:30,560
mankind you are taking a human-centric

2984
01:42:34,550 --> 01:42:32,800
and deterministic view on the universe

2985
01:42:35,030 --> 01:42:34,560
we only created it to make sense of

2986
01:42:37,030 --> 01:42:35,040
things

2987
01:42:38,790 --> 01:42:37,040
just like we created the spoken word to

2988
01:42:39,270 --> 01:42:38,800
communicate so what are your thoughts on

2989
01:42:43,189 --> 01:42:39,280
that

2990
01:42:45,109 --> 01:42:43,199
rambling as he suspects

2991
01:42:46,310 --> 01:42:45,119
um the point about mathematics is

2992
01:42:48,470 --> 01:42:46,320
suppose there's a

2993
01:42:51,270 --> 01:42:48,480
another civilization on say alpha

2994
01:42:53,830 --> 01:42:51,280
century

2995
01:42:55,030 --> 01:42:53,840
and they will have the same mathematics

2996
01:42:56,310 --> 01:42:55,040
that we do i mean that

2997
01:42:58,550 --> 01:42:56,320
obviously they won't use the same

2998
01:42:59,189 --> 01:42:58,560
notation or terminology in the same way

2999
01:43:01,270 --> 01:42:59,199
that

3000
01:43:03,189 --> 01:43:01,280
you know english and french people do

3001
01:43:04,709 --> 01:43:03,199
the same mathematics but they do it in a

3002
01:43:06,470 --> 01:43:04,719
different language so they will

3003
01:43:08,070 --> 01:43:06,480
they will have the same mathematical

3004
01:43:10,229 --> 01:43:08,080
theorems

3005
01:43:11,669 --> 01:43:10,239
expressed in their own weird language

3006
01:43:12,950 --> 01:43:11,679
and they will have found the monster

3007
01:43:14,550 --> 01:43:12,960
simple group and they will have found

3008
01:43:16,070 --> 01:43:14,560
modular forms and they will have found

3009
01:43:19,430 --> 01:43:16,080
everything else

3010
01:43:21,030 --> 01:43:19,440
so it's not a human centric way of

3011
01:43:22,709 --> 01:43:21,040
viewing the world it's a universal way

3012
01:43:24,149 --> 01:43:22,719
of viewing the world

3013
01:43:25,750 --> 01:43:24,159
i mean at least that's why i think maybe

3014
01:43:29,510 --> 01:43:25,760
it's me who's rambling but

3015
01:43:31,430 --> 01:43:29,520
um i i would say it's disgus it's it's

3016
01:43:33,350 --> 01:43:31,440
discovered not invented because any

3017
01:43:35,510 --> 01:43:33,360
other advanced civilization will have an

3018
01:43:37,109 --> 01:43:35,520
equivalent mathematics

3019
01:43:40,229 --> 01:43:37,119
do you think that we'd share an idea of

3020
01:43:43,350 --> 01:43:40,239
what the few key theorems are

3021
01:43:47,590 --> 01:43:45,910
the book it it it's it's a very

3022
01:43:49,590 --> 01:43:47,600
speculative question that

3023
01:43:51,510 --> 01:43:49,600
this is in some sense meaningless but in

3024
01:43:53,350 --> 01:43:51,520
spite of that i will say yes i i would

3025
01:43:54,149 --> 01:43:53,360
guess that other advanced civilizations

3026
01:43:56,790 --> 01:43:54,159
will on the whole

3027
01:43:58,470 --> 01:43:56,800
share the same key theories maybe not

3028
01:44:01,270 --> 01:43:58,480
exactly but

3029
01:44:03,109 --> 01:44:01,280
um let me be more explicit as to what i

3030
01:44:06,870 --> 01:44:03,119
mean

3031
01:44:07,590 --> 01:44:06,880
that they would have the same idea as

3032
01:44:10,709 --> 01:44:07,600
that

3033
01:44:12,550 --> 01:44:10,719
they would share the same theorems it

3034
01:44:14,390 --> 01:44:12,560
might just be one line as a lemma but we

3035
01:44:15,830 --> 01:44:14,400
consider it to be a holy grail

3036
01:44:18,229 --> 01:44:15,840
and they would also consider it to be

3037
01:44:20,310 --> 01:44:18,239
something of i think there'd be a a lot

3038
01:44:20,870 --> 01:44:20,320
of overlap i mean i mean even between

3039
01:44:24,070 --> 01:44:20,880
different

3040
01:44:26,629 --> 01:44:24,080
mathematical um

3041
01:44:27,750 --> 01:44:26,639
i mean before the world sort of became

3042
01:44:31,350 --> 01:44:27,760
unified there were dif

3043
01:44:31,750 --> 01:44:31,360
different mathematical um cultures like

3044
01:44:33,910 --> 01:44:31,760
the

3045
01:44:35,030 --> 01:44:33,920
greeks and indians and japanese all had

3046
01:44:36,229 --> 01:44:35,040
slightly different approaches to

3047
01:44:37,990 --> 01:44:36,239
mathematics and they

3048
01:44:39,669 --> 01:44:38,000
they weren't exactly the same on what

3049
01:44:41,189 --> 01:44:39,679
they agreed were the

3050
01:44:42,950 --> 01:44:41,199
central theorems or approaches of the

3051
01:44:44,310 --> 01:44:42,960
subject but there was there was a lot of

3052
01:44:46,229 --> 01:44:44,320
overlap

3053
01:44:47,350 --> 01:44:46,239
yeah recall someone's estimation for pi

3054
01:44:50,149 --> 01:44:47,360
was four

3055
01:44:51,109 --> 01:44:50,159
i don't recall which time uh spatial

3056
01:44:53,270 --> 01:44:51,119
location

3057
01:44:54,870 --> 01:44:53,280
yes there'd been some very weird

3058
01:44:58,070 --> 01:44:54,880
estimates for pi

3059
01:45:00,830 --> 01:44:58,080
okay so tori ko says what does he enjoy

3060
01:45:03,750 --> 01:45:00,840
or find meaningful about math

3061
01:45:07,109 --> 01:45:03,760
uh

3062
01:45:10,470 --> 01:45:07,119
well i i like it because because it's

3063
01:45:12,709 --> 01:45:10,480
it's really describing how the universe

3064
01:45:13,109 --> 01:45:12,719
works in some very fundamental way i

3065
01:45:16,070 --> 01:45:13,119
mean

3066
01:45:17,990 --> 01:45:16,080
um as i think i mentioned earlier the

3067
01:45:20,229 --> 01:45:18,000
universe seems to be

3068
01:45:21,830 --> 01:45:20,239
running on mathematics in some very deep

3069
01:45:24,070 --> 01:45:21,840
sense that

3070
01:45:26,310 --> 01:45:24,080
you know physics like the standard model

3071
01:45:29,510 --> 01:45:26,320
or general relativity

3072
01:45:31,430 --> 01:45:29,520
is is really just an application of

3073
01:45:33,189 --> 01:45:31,440
mathematics

3074
01:45:34,950 --> 01:45:33,199
so when you're discovering something new

3075
01:45:36,550 --> 01:45:34,960
in mathematics you can think of it as

3076
01:45:40,310 --> 01:45:36,560
being discovering something new about

3077
01:45:43,990 --> 01:45:42,470
so to me when you say that if i didn't

3078
01:45:44,950 --> 01:45:44,000
have any context as to who you were i

3079
01:45:46,629 --> 01:45:44,960
would have thought you were either a

3080
01:45:50,149 --> 01:45:46,639
theoretical physicist or a physicist

3081
01:45:50,470 --> 01:45:50,159
in some capacity why is it do you think

3082
01:45:53,669 --> 01:45:50,480
that

3083
01:45:55,350 --> 01:45:53,679
math somehow has a more direct access to

3084
01:45:59,750 --> 01:45:55,360
the

3085
01:46:02,870 --> 01:45:59,760
no i mean

3086
01:46:03,750 --> 01:46:02,880
mathematics has access to the way the

3087
01:46:05,510 --> 01:46:03,760
universe works

3088
01:46:07,189 --> 01:46:05,520
through theoretical physics i mean

3089
01:46:08,870 --> 01:46:07,199
theoretical physics is the interface

3090
01:46:11,910 --> 01:46:08,880
between mathematics and the

3091
01:46:12,629 --> 01:46:11,920
actual physical world in some sense i

3092
01:46:14,229 --> 01:46:12,639
mean not

3093
01:46:15,910 --> 01:46:14,239
not all mathematics seems to have a

3094
01:46:17,430 --> 01:46:15,920
direct relation to the physical world i

3095
01:46:19,669 --> 01:46:17,440
mean that no one's found the monster

3096
01:46:21,750 --> 01:46:19,679
simple group in in

3097
01:46:23,669 --> 01:46:21,760
in in in our four-dimensional universe

3098
01:46:27,350 --> 01:46:23,679
yet but um

3099
01:46:30,390 --> 01:46:27,360
there's there's a lot of overlap i mean

3100
01:46:32,149 --> 01:46:30,400
um it's it's quite

3101
01:46:33,830 --> 01:46:32,159
hard to find an area of mathematics

3102
01:46:37,350 --> 01:46:33,840
which has nothing whatsoever to do with

3103
01:46:41,830 --> 01:46:38,709
what type of mathematician would you

3104
01:46:44,229 --> 01:46:41,840
consider yourself a pure mathematician

3105
01:46:45,590 --> 01:46:44,239
if you have to divide mathematicians up

3106
01:46:47,510 --> 01:46:45,600
like that then i guess i

3107
01:46:49,270 --> 01:46:47,520
count as pure rather than rather than

3108
01:46:52,070 --> 01:46:49,280
applied or a physicist

3109
01:46:53,910 --> 01:46:52,080
i mean i as i said i i sort of tried

3110
01:46:55,350 --> 01:46:53,920
doing theoretical physics a bit and that

3111
01:46:58,870 --> 01:46:55,360
didn't work out so well

3112
01:47:00,550 --> 01:46:58,880
so um is that the only reason why you

3113
01:47:01,990 --> 01:47:00,560
abandoned theoretical physics in favor

3114
01:47:03,830 --> 01:47:02,000
of pure mathematics because

3115
01:47:05,350 --> 01:47:03,840
you just had a difficult time or is that

3116
01:47:08,550 --> 01:47:05,360
something that seems to be a perfectly

3117
01:47:11,910 --> 01:47:08,560
good reason for abandoning something

3118
01:47:13,910 --> 01:47:11,920
um yeah harris chandra apparently did

3119
01:47:15,750 --> 01:47:13,920
the same he started off as a theoretical

3120
01:47:16,390 --> 01:47:15,760
physicist and switched to mathematics

3121
01:47:22,149 --> 01:47:16,400
because

3122
01:47:25,270 --> 01:47:22,159
he he found it too difficult

3123
01:47:26,709 --> 01:47:25,280
terry co torical the same person says

3124
01:47:28,470 --> 01:47:26,719
what does he think about biology

3125
01:47:32,070 --> 01:47:28,480
psychology philosophy

3126
01:47:32,870 --> 01:47:32,080
do you think that you would gain as much

3127
01:47:37,350 --> 01:47:32,880
of a sense of

3128
01:47:40,070 --> 01:47:37,360
understanding by exploring those fields

3129
01:47:41,669 --> 01:47:40,080
um well again i have the caveat that i

3130
01:47:42,310 --> 01:47:41,679
don't actually know a lot about these

3131
01:47:45,590 --> 01:47:42,320
fields

3132
01:47:47,510 --> 01:47:45,600
um biology i tried reading some biology

3133
01:47:51,109 --> 01:47:47,520
textbooks and they're incredibly

3134
01:47:53,669 --> 01:47:51,119
scary and you read a biology book on the

3135
01:47:55,830 --> 01:47:53,679
way that a cell works for example and

3136
01:47:57,510 --> 01:47:55,840
it's perfectly obvious that a cell can't

3137
01:47:58,310 --> 01:47:57,520
possibly work in the way it describes

3138
01:48:01,830 --> 01:47:58,320
it's just so

3139
01:48:03,669 --> 01:48:01,840
complicated that that um

3140
01:48:05,430 --> 01:48:03,679
the way cells work is so complicated and

3141
01:48:05,830 --> 01:48:05,440
bizarre it's very hard to believe to

3142
01:48:07,750 --> 01:48:05,840
exist

3143
01:48:08,950 --> 01:48:07,760
i'm sort of worried that if i if i read

3144
01:48:10,870 --> 01:48:08,960
a biology book

3145
01:48:12,229 --> 01:48:10,880
you know the universe will suddenly

3146
01:48:13,830 --> 01:48:12,239
catch up with this and i'll drop

3147
01:48:16,709 --> 01:48:13,840
dead so i think biology is a bit

3148
01:48:20,790 --> 01:48:16,719
dangerous to study because it seems so

3149
01:48:23,590 --> 01:48:20,800
so incredible also just so much of it

3150
01:48:25,830 --> 01:48:23,600
i mean i i just hadn't quite dawned on

3151
01:48:29,590 --> 01:48:25,840
me and just how horrifically complicated

3152
01:48:31,350 --> 01:48:29,600
cells are timber finn says

3153
01:48:32,550 --> 01:48:31,360
is nature fundamentally mathematical or

3154
01:48:33,350 --> 01:48:32,560
something else now i know you touched on

3155
01:48:36,629 --> 01:48:33,360
this but

3156
01:48:38,709 --> 01:48:36,639
again for timber finn well

3157
01:48:40,390 --> 01:48:38,719
depends what you mean by fundamentally

3158
01:48:42,310 --> 01:48:40,400
um i would say if you go

3159
01:48:43,990 --> 01:48:42,320
deep enough into anything you eventually

3160
01:48:45,990 --> 01:48:44,000
get to mathematics i mean you

3161
01:48:48,229 --> 01:48:46,000
you might start with you know trying to

3162
01:48:49,189 --> 01:48:48,239
understand nature via biology and if you

3163
01:48:50,910 --> 01:48:49,199
look really

3164
01:48:52,229 --> 01:48:50,920
deep into biology you find it's really

3165
01:48:53,590 --> 01:48:52,239
biochemistry

3166
01:48:55,510 --> 01:48:53,600
and if you're trying to work out how all

3167
01:48:57,109 --> 01:48:55,520
these biochemical molecules work you

3168
01:48:58,629 --> 01:48:57,119
discover it's really quantum mechanics

3169
01:49:00,149 --> 01:48:58,639
which is physics and if you look at how

3170
01:49:01,830 --> 01:49:00,159
physics works you suddenly find you're

3171
01:49:04,870 --> 01:49:01,840
down to mathematics

3172
01:49:08,870 --> 01:49:04,880
so mathematics is sort of at the core of

3173
01:49:13,350 --> 01:49:11,189
bernardo fitzpatrick asks i would like

3174
01:49:15,830 --> 01:49:13,360
to know does the professor

3175
01:49:17,350 --> 01:49:15,840
know of italian mathematician dr olivia

3176
01:49:19,510 --> 01:49:17,360
carmelo

3177
01:49:21,270 --> 01:49:19,520
and if so what does he think of her use

3178
01:49:23,270 --> 01:49:21,280
of alexander garthande

3179
01:49:24,709 --> 01:49:23,280
tawpos's as a unifying theory in

3180
01:49:27,270 --> 01:49:24,719
mathematics

3181
01:49:28,870 --> 01:49:27,280
and her interpretation of tapas's or

3182
01:49:31,750 --> 01:49:28,880
topoi as bridges

3183
01:49:33,109 --> 01:49:31,760
in order to facilitate this unification

3184
01:49:35,750 --> 01:49:33,119
well i i

3185
01:49:38,950 --> 01:49:35,760
don't don't remember the name off-hand

3186
01:49:41,910 --> 01:49:38,960
but toplesses have indeed been used as a

3187
01:49:42,950 --> 01:49:41,920
um unifying thing in mathematics so

3188
01:49:44,790 --> 01:49:42,960
topos is this

3189
01:49:45,990 --> 01:49:44,800
construction that alexander grothenbeck

3190
01:49:47,669 --> 01:49:46,000
came up with

3191
01:49:49,430 --> 01:49:47,679
and it was shortly afterwards realized

3192
01:49:52,629 --> 01:49:49,440
by law vera i think that

3193
01:49:53,350 --> 01:49:52,639
toppos was really a sort of almost a

3194
01:49:56,229 --> 01:49:53,360
sort of

3195
01:49:58,149 --> 01:49:56,239
intuitionistic model of set theory or or

3196
01:50:01,030 --> 01:49:58,159
a weak version of set theory

3197
01:50:02,709 --> 01:50:01,040
so you can in fact do most mathematics

3198
01:50:06,229 --> 01:50:02,719
inside

3199
01:50:08,470 --> 01:50:06,239
a suitable topos and in fact this is

3200
01:50:10,390 --> 01:50:08,480
this is almost one theme of growth index

3201
01:50:11,030 --> 01:50:10,400
algebraic geometry that anything you can

3202
01:50:14,870 --> 01:50:11,040
do

3203
01:50:17,109 --> 01:50:14,880
an arbitrary topos and that that gives

3204
01:50:21,750 --> 01:50:17,119
you a sort of

3205
01:50:27,030 --> 01:50:24,629
does he have an opinion on grothen dick

3206
01:50:28,149 --> 01:50:27,040
um i'm just overwhelmed by him i mean i

3207
01:50:29,589 --> 01:50:28,159
i just

3208
01:50:31,350 --> 01:50:29,599
i mean that there are a lot of great

3209
01:50:33,750 --> 01:50:31,360
mathematicians i sort of think

3210
01:50:35,589 --> 01:50:33,760
well you know i i could have proved that

3211
01:50:37,270 --> 01:50:35,599
guy's theorem if i'd just been a bit

3212
01:50:37,990 --> 01:50:37,280
smarter or worked a bit harder and then

3213
01:50:39,589 --> 01:50:38,000
there are

3214
01:50:41,669 --> 01:50:39,599
other mathematicians i look at their

3215
01:50:43,830 --> 01:50:41,679
work and i realize there's just

3216
01:50:46,149 --> 01:50:43,840
no way i could possibly have done that

3217
01:50:47,830 --> 01:50:46,159
no matter how hard i worked and

3218
01:50:49,510 --> 01:50:47,840
you know growth and dick's one of them

3219
01:50:51,669 --> 01:50:49,520
and you know there are a few others like

3220
01:50:53,669 --> 01:50:51,679
john thompson's work on finite groups i

3221
01:50:56,470 --> 01:50:53,679
could just never have done and

3222
01:50:58,470 --> 01:50:56,480
andrew wiles's work on firma's last him

3223
01:51:01,189 --> 01:50:58,480
i just couldn't possibly have done so

3224
01:51:02,149 --> 01:51:01,199
so he's one of the ones who just i have

3225
01:51:03,990 --> 01:51:02,159
to admit they're just

3226
01:51:07,910 --> 01:51:04,000
way out of reach of anything i could

3227
01:51:11,510 --> 01:51:07,920
ever have done have you met wiles

3228
01:51:15,030 --> 01:51:11,520
very briefly once or twice

3229
01:51:17,510 --> 01:51:15,040
okay many people this comes from per

3230
01:51:19,430 --> 01:51:17,520
peridot many people decide that they're

3231
01:51:20,550 --> 01:51:19,440
more analytical than algebraic or vice

3232
01:51:22,550 --> 01:51:20,560
versa

3233
01:51:23,990 --> 01:51:22,560
can he expound on a bit on why he

3234
01:51:25,669 --> 01:51:24,000
personally finds inequalities

3235
01:51:27,109 --> 01:51:25,679
unappealing as opposed to equalities

3236
01:51:28,790 --> 01:51:27,119
this goes back to our

3237
01:51:30,149 --> 01:51:28,800
previous conversation they're not

3238
01:51:32,390 --> 01:51:30,159
unappealing i like

3239
01:51:34,390 --> 01:51:32,400
inequalities it's just that you know i

3240
01:51:36,870 --> 01:51:34,400
just don't

3241
01:51:37,750 --> 01:51:36,880
what's the word um they're too messy i

3242
01:51:39,990 --> 01:51:37,760
just haven't got them

3243
01:51:41,910 --> 01:51:40,000
completely internalized i i i don't have

3244
01:51:44,870 --> 01:51:41,920
a good feeling for them

3245
01:51:46,070 --> 01:51:44,880
um the reason for this i i don't know i

3246
01:51:48,070 --> 01:51:46,080
think i just

3247
01:51:50,070 --> 01:51:48,080
it's probably just a matter of practice

3248
01:51:52,790 --> 01:51:50,080
i spent a lot more time working

3249
01:51:53,830 --> 01:51:52,800
thinking about algebra and equalities

3250
01:51:55,510 --> 01:51:53,840
and so on and

3251
01:51:57,830 --> 01:51:55,520
presumably if i'd spend all that time

3252
01:51:59,910 --> 01:51:57,840
thinking about inequalities i would

3253
01:52:01,589 --> 01:51:59,920
be the other way around i mean i i think

3254
01:52:03,750 --> 01:52:01,599
the difference between

3255
01:52:05,589 --> 01:52:03,760
mathematicians who are more algebra and

3256
01:52:08,790 --> 01:52:05,599
mathematicians who are more analysis

3257
01:52:12,149 --> 01:52:08,800
is is is very much what they spent most

3258
01:52:16,950 --> 01:52:14,229
and the last one is from the same person

3259
01:52:17,589 --> 01:52:16,960
peridot he says for the abc conjecture

3260
01:52:19,350 --> 01:52:17,599
question

3261
01:52:21,990 --> 01:52:19,360
can you please allow him to be as super

3262
01:52:23,189 --> 01:52:22,000
detailed as he's as he possibly can be

3263
01:52:25,669 --> 01:52:23,199
and if he says he doesn't know much

3264
01:52:27,189 --> 01:52:25,679
about it ask him what why he thinks it

3265
01:52:28,870 --> 01:52:27,199
hasn't triggered his curiosity i'm

3266
01:52:30,149 --> 01:52:28,880
assuming there was a previous abc

3267
01:52:30,870 --> 01:52:30,159
conjecture question but i can only

3268
01:52:33,990 --> 01:52:30,880
conjecture

3269
01:52:36,470 --> 01:52:34,000
about so let's say

3270
01:52:38,229 --> 01:52:36,480
his last sentence says i am consistently

3271
01:52:39,990 --> 01:52:38,239
curious about the process of how

3272
01:52:40,790 --> 01:52:40,000
mathematicians decide what is and isn't

3273
01:52:42,550 --> 01:52:40,800
worth their time

3274
01:52:44,149 --> 01:52:42,560
from a mathematical perspective so i

3275
01:52:45,669 --> 01:52:44,159
assume he's wondering why haven't you

3276
01:52:46,870 --> 01:52:45,679
tackled the abc conjecture and why do

3277
01:52:48,790 --> 01:52:46,880
you choose this topic

3278
01:52:51,109 --> 01:52:48,800
rather than this one well i don't have

3279
01:52:52,470 --> 01:52:51,119
your interest i haven't tackled the abc

3280
01:52:55,270 --> 01:52:52,480
conjecture because it's just too

3281
01:52:57,109 --> 01:52:55,280
difficult i mean you you have to

3282
01:52:58,310 --> 01:52:57,119
select problems that there's some hope

3283
01:53:00,790 --> 01:52:58,320
of making progress

3284
01:53:03,189 --> 01:53:00,800
in um if you're asking about my opinions

3285
01:53:05,990 --> 01:53:03,199
of machu zuki's work well

3286
01:53:06,790 --> 01:53:06,000
i just have no idea i i think i said

3287
01:53:08,550 --> 01:53:06,800
earlier i

3288
01:53:10,790 --> 01:53:08,560
tried to understand it for a few hours

3289
01:53:11,430 --> 01:53:10,800
and it was became obvious to me that it

3290
01:53:14,790 --> 01:53:11,440
would take me

3291
01:53:16,629 --> 01:53:14,800
many years of study to get a vague idea

3292
01:53:19,830 --> 01:53:16,639
of what was going on

3293
01:53:21,669 --> 01:53:19,840
um so yeah yeah so so mochizuki's

3294
01:53:24,709 --> 01:53:21,679
another one of these guys

3295
01:53:26,790 --> 01:53:24,719
who look at his work and there's just

3296
01:53:28,470 --> 01:53:26,800
no way i would have been able to to do

3297
01:53:30,950 --> 01:53:28,480
that i mean i

3298
01:53:32,229 --> 01:53:30,960
i i mean it's a bit controversial about

3299
01:53:33,910 --> 01:53:32,239
whether it's right or wrong at the

3300
01:53:35,510 --> 01:53:33,920
moment of course but

3301
01:53:38,709 --> 01:53:35,520
you know whether it's right or wrong

3302
01:53:40,790 --> 01:53:38,719
it's still an an incredible

3303
01:53:44,310 --> 01:53:40,800
uh mochizuki's work is still an

3304
01:53:47,910 --> 01:53:45,910
and how do you decide what's worth your

3305
01:53:49,669 --> 01:53:47,920
time and what's not from a mathematical

3306
01:53:52,070 --> 01:53:49,679
perspective

3307
01:53:54,310 --> 01:53:52,080
um if it works it's worth my time and if

3308
01:53:56,390 --> 01:53:54,320
it doesn't work it's not worth my time

3309
01:53:58,229 --> 01:53:56,400
you you you can't tell in advance you

3310
01:54:01,109 --> 01:53:58,239
just have to

3311
01:54:01,990 --> 01:54:01,119
if there's a problem or area you start

3312
01:54:05,109 --> 01:54:02,000
working on it

3313
01:54:07,430 --> 01:54:05,119
and sometimes it just doesn't seem to be

3314
01:54:10,950 --> 01:54:07,440
working out and sometimes it does

3315
01:54:12,470 --> 01:54:10,960
and deciding what is worth your time is

3316
01:54:15,270 --> 01:54:12,480
actually one of the hardest problems in

3317
01:54:17,270 --> 01:54:15,280
mathematics because

3318
01:54:18,870 --> 01:54:17,280
you you know you you may have spent

3319
01:54:20,470 --> 01:54:18,880
several months working on a problem

3320
01:54:21,910 --> 01:54:20,480
maybe you're just about to make a

3321
01:54:23,510 --> 01:54:21,920
breakthrough and if you only spent

3322
01:54:23,830 --> 01:54:23,520
another week on it then you would crack

3323
01:54:27,270 --> 01:54:23,840
it

3324
01:54:28,550 --> 01:54:27,280
but you can't tell maybe you know

3325
01:54:30,390 --> 01:54:28,560
maybe it's a week away from being

3326
01:54:32,149 --> 01:54:30,400
cracked maybe you could spend another 10

3327
01:54:34,629 --> 01:54:32,159
years on it without getting anywhere

3328
01:54:37,350 --> 01:54:34,639
and if you could tell which that this

3329
01:54:39,430 --> 01:54:37,360
would make research so much easier

3330
01:54:42,310 --> 01:54:39,440
so it's really one of the biggest

3331
01:54:45,669 --> 01:54:42,320
problems in research is is figuring out

3332
01:54:49,030 --> 01:54:45,679
um which

3333
01:54:50,870 --> 01:54:49,040
which approaches are likely to work

3334
01:54:52,470 --> 01:54:50,880
how many weeks or months do you usually

3335
01:54:53,430 --> 01:54:52,480
give on a problem before you decide it's

3336
01:54:56,310 --> 01:54:53,440
solvable or not

3337
01:54:56,870 --> 01:54:56,320
by you well i never really give up on

3338
01:54:59,669 --> 01:54:56,880
problems

3339
01:55:01,430 --> 01:54:59,679
what what what you do is you you work on

3340
01:55:02,629 --> 01:55:01,440
problems for a bit and then you

3341
01:55:03,830 --> 01:55:02,639
get a bit depressed because you're

3342
01:55:05,669 --> 01:55:03,840
getting nowhere and then you put it

3343
01:55:08,790 --> 01:55:05,679
aside but

3344
01:55:10,149 --> 01:55:08,800
always come back to it later after a few

3345
01:55:12,310 --> 01:55:10,159
months or years when

3346
01:55:14,390 --> 01:55:12,320
when you i mean what generally happens

3347
01:55:16,709 --> 01:55:14,400
is i i i forget

3348
01:55:18,229 --> 01:55:16,719
why my approach didn't work and and a

3349
01:55:19,990 --> 01:55:18,239
few years later i think oh why doesn't

3350
01:55:20,550 --> 01:55:20,000
this approach work and i try it again

3351
01:55:22,070 --> 01:55:20,560
and then

3352
01:55:24,470 --> 01:55:22,080
then i discover why it doesn't work

3353
01:55:26,070 --> 01:55:24,480
again but but every now and then you

3354
01:55:28,470 --> 01:55:26,080
you you make a little bit of extra

3355
01:55:30,229 --> 01:55:28,480
progress and

3356
01:55:31,830 --> 01:55:30,239
sometimes after coming back to the

3357
01:55:34,390 --> 01:55:31,840
problem dozen

3358
01:55:35,830 --> 01:55:34,400
times you finally managed to solve it

3359
01:55:37,510 --> 01:55:35,840
and there are plenty of other problems

3360
01:55:40,470 --> 01:55:37,520
i've come back to many times

3361
01:55:41,669 --> 01:55:40,480
and that i'm still stuck on them how

3362
01:55:43,350 --> 01:55:41,679
come you forgot

3363
01:55:45,189 --> 01:55:43,360
that you tried a certain technique and

3364
01:55:46,550 --> 01:55:45,199
it didn't work because i would imagine

3365
01:55:48,550 --> 01:55:46,560
you take notes

3366
01:55:49,830 --> 01:55:48,560
and you would have to take notes taking

3367
01:55:53,030 --> 01:55:49,840
notes i mean

3368
01:55:55,990 --> 01:55:53,040
it requires being organized i'm i i i'm

3369
01:55:58,149 --> 01:55:56,000
very bad at keeping notes of what i do

3370
01:56:00,070 --> 01:55:58,159
i mean i mean scrapbooks of your work no

3371
01:56:02,310 --> 01:56:00,080
well i tried keeping a scrapbook of some

3372
01:56:03,830 --> 01:56:02,320
of my work and i and i looked at it a

3373
01:56:05,589 --> 01:56:03,840
couple of years later it was completely

3374
01:56:07,109 --> 01:56:05,599
illegible and i couldn't figure out what

3375
01:56:10,390 --> 01:56:07,119
on earth i was talking about because i'd

3376
01:56:13,510 --> 01:56:10,400
been too lazy to write up proper notes

3377
01:56:15,510 --> 01:56:13,520
and yeah and it may not be a bad idea to

3378
01:56:17,030 --> 01:56:15,520
sort of forget what the problem was and

3379
01:56:18,790 --> 01:56:17,040
come back to it because sometimes when

3380
01:56:19,910 --> 01:56:18,800
you come back to it you suddenly realize

3381
01:56:23,189 --> 01:56:19,920
that the

3382
01:56:25,030 --> 01:56:23,199
thing you were stuck on it wasn't really

3383
01:56:26,790 --> 01:56:25,040
valid and there's a way around it

3384
01:56:29,350 --> 01:56:26,800
of course most of the time it was valid

3385
01:56:30,629 --> 01:56:29,360
but whatever

3386
01:56:33,189 --> 01:56:30,639
you know i had a note and it's just a

3387
01:56:33,830 --> 01:56:33,199
bullet point it said no ghost theorem

3388
01:56:35,589 --> 01:56:33,840
and it

3389
01:56:36,950 --> 01:56:35,599
reminded me i wanted to ask you if you

3390
01:56:38,709 --> 01:56:36,960
can explain to the audience what the no

3391
01:56:40,390 --> 01:56:38,719
ghost theorem is in string theory and

3392
01:56:43,270 --> 01:56:40,400
then its connection to the

3393
01:56:44,790 --> 01:56:43,280
moonshine conjecture um and you're

3394
01:56:46,149 --> 01:56:44,800
allowed to go into technical detail if

3395
01:56:47,669 --> 01:56:46,159
you feel like the audience well they're

3396
01:56:47,990 --> 01:56:47,679
gonna lose you or even me then that's

3397
01:56:49,510 --> 01:56:48,000
fine

3398
01:56:51,189 --> 01:56:49,520
this i could probably explain if you

3399
01:56:53,589 --> 01:56:51,199
gave me a semester course

3400
01:56:55,109 --> 01:56:53,599
um but here goes first of all the name

3401
01:56:58,149 --> 01:56:55,119
no ghost thing was a sort of

3402
01:56:59,510 --> 01:56:58,159
pun or word play so um in in theoretical

3403
01:57:02,629 --> 01:56:59,520
physics there are things called no

3404
01:57:03,589 --> 01:57:02,639
go theorems which mean something doesn't

3405
01:57:05,830 --> 01:57:03,599
work i mean you

3406
01:57:07,669 --> 01:57:05,840
you can't there are various no go hidden

3407
01:57:10,070 --> 01:57:07,679
variable themes the no ghost theorists

3408
01:57:13,189 --> 01:57:10,080
will sort of play on words

3409
01:57:15,189 --> 01:57:13,199
and what a ghost is

3410
01:57:18,229 --> 01:57:15,199
in string theory is a name for a

3411
01:57:20,390 --> 01:57:18,239
negative norm vector in a hilbert space

3412
01:57:21,830 --> 01:57:20,400
and this is extremely disturbing because

3413
01:57:23,589 --> 01:57:21,840
hilbert spaces aren't allowed to have

3414
01:57:24,070 --> 01:57:23,599
negative norm vectors so if you've got a

3415
01:57:25,990 --> 01:57:24,080
negative

3416
01:57:27,189 --> 01:57:26,000
norm vector that that rather messes

3417
01:57:28,950 --> 01:57:27,199
everything up

3418
01:57:30,229 --> 01:57:28,960
and so in order to get quantum mechanics

3419
01:57:32,390 --> 01:57:30,239
working you've got to make sure there

3420
01:57:34,870 --> 01:57:32,400
are no negative norm vectors in other

3421
01:57:38,310 --> 01:57:34,880
words there are no ghosts because

3422
01:57:40,790 --> 01:57:38,320
negative norm vectors are called ghosts

3423
01:57:42,709 --> 01:57:40,800
so when you take a string and try and

3424
01:57:45,589 --> 01:57:42,719
quantize it

3425
01:57:47,510 --> 01:57:45,599
you find you've got this big space and

3426
01:57:50,629 --> 01:57:47,520
sometimes it has negative normal vectors

3427
01:57:52,470 --> 01:57:50,639
in which is really tiresome

3428
01:57:54,229 --> 01:57:52,480
and the no ghost theorem proof by i

3429
01:57:56,390 --> 01:57:54,239
think it was brower and

3430
01:57:58,390 --> 01:57:56,400
goddard and thorne says that if the

3431
01:57:59,830 --> 01:57:58,400
string happens to be living in 26

3432
01:58:01,830 --> 01:57:59,840
dimensions

3433
01:58:03,589 --> 01:58:01,840
then everything is nice and you you

3434
01:58:06,390 --> 01:58:03,599
don't get any ghosts

3435
01:58:07,589 --> 01:58:06,400
and if it's in 27 dimensions you do get

3436
01:58:10,709 --> 01:58:07,599
ghosts and it's

3437
01:58:11,270 --> 01:58:10,719
really bizarre this this number 26 turns

3438
01:58:13,189 --> 01:58:11,280
up i mean

3439
01:58:15,350 --> 01:58:13,199
you you can imagine something special

3440
01:58:16,390 --> 01:58:15,360
happening in two dimensions or maybe

3441
01:58:19,589 --> 01:58:16,400
three dimensions but

3442
01:58:22,950 --> 01:58:19,599
26 dimensions is just ridiculous

3443
01:58:25,910 --> 01:58:22,960
so um that that that's why string theory

3444
01:58:27,830 --> 01:58:25,920
works in 26 dimensions is because this

3445
01:58:29,990 --> 01:58:27,840
there's no ghost theorem and then you

3446
01:58:32,310 --> 01:58:30,000
you get super string theory whether

3447
01:58:33,750 --> 01:58:32,320
where the critical dimension is 10

3448
01:58:35,910 --> 01:58:33,760
rather than 26

3449
01:58:37,350 --> 01:58:35,920
and that's still a bit tiresome because

3450
01:58:38,229 --> 01:58:37,360
we want to bring it down to four

3451
01:58:41,510 --> 01:58:38,239
dimensions

3452
01:58:43,189 --> 01:58:41,520
and there are various ways you can try

3453
01:58:44,470 --> 01:58:43,199
and get it down to four dimensions but

3454
01:58:47,030 --> 01:58:44,480
none of them seems to be totally

3455
01:58:49,830 --> 01:58:47,040
satisfactory yet

3456
01:58:51,669 --> 01:58:49,840
um and 26 dimensions is really nice

3457
01:58:52,790 --> 01:58:51,679
because it ties up with the monster and

3458
01:58:56,550 --> 01:58:52,800
the leech lattice

3459
01:58:58,550 --> 01:58:56,560
dimensions

3460
01:59:00,310 --> 01:58:58,560
and it turns out that if you've got the

3461
01:59:01,430 --> 01:59:00,320
leech lattice there's a very natural

3462
01:59:03,750 --> 01:59:01,440
construction

3463
01:59:05,109 --> 01:59:03,760
you you sort of embedded in laurentian

3464
01:59:08,149 --> 01:59:05,119
space and that involves adding

3465
01:59:11,350 --> 01:59:08,159
two to the dimension so the

3466
01:59:13,589 --> 01:59:11,360
the 26 dimensions of the no ghost theme

3467
01:59:15,510 --> 01:59:13,599
and string theory is

3468
01:59:17,669 --> 01:59:15,520
is very close related to the 24

3469
01:59:18,709 --> 01:59:17,679
dimensions that the leech lattice lives

3470
01:59:20,229 --> 01:59:18,719
in

3471
01:59:21,830 --> 01:59:20,239
and the leech lattice is connected to

3472
01:59:24,070 --> 01:59:21,840
the monster yeah so

3473
01:59:25,830 --> 01:59:24,080
so actually that's another these bizarre

3474
01:59:27,510 --> 01:59:25,840
coincidences that i mentioned that

3475
01:59:30,629 --> 01:59:27,520
always appears whenever modular

3476
01:59:34,470 --> 01:59:30,639
functions and forms turn up because the

3477
01:59:36,550 --> 01:59:34,480
the the modular forms are working

3478
01:59:38,790 --> 01:59:36,560
doing very special things in 24

3479
01:59:42,470 --> 01:59:38,800
dimensions

3480
01:59:43,910 --> 01:59:42,480
no ghosts but

3481
01:59:45,350 --> 01:59:43,920
there are other flavors of string theory

3482
01:59:46,070 --> 01:59:45,360
so do they have ghosts in other

3483
01:59:50,709 --> 01:59:46,080
dimensions

3484
01:59:52,070 --> 01:59:50,719
happens if you take the simplest

3485
01:59:54,390 --> 01:59:52,080
possible version of

3486
01:59:56,229 --> 01:59:54,400
string theory and as you say there are

3487
01:59:57,669 --> 01:59:56,239
lots of other flavors in string theorem

3488
01:59:59,669 --> 01:59:57,679
these tend to have different critical

3489
02:00:00,950 --> 01:59:59,679
dimensions so that the next simplest is

3490
02:00:03,189 --> 02:00:00,960
super strings and

3491
02:00:04,709 --> 02:00:03,199
ten dimensions and you you can sort of

3492
02:00:08,790 --> 02:00:04,719
fudge around a bit and find

3493
02:00:11,270 --> 02:00:08,800
things going on in 18 or 14 or

3494
02:00:13,109 --> 02:00:11,280
six dimensions but the the these are all

3495
02:00:16,709 --> 02:00:13,119
getting a bit more complicated

3496
02:00:18,550 --> 02:00:16,719
26 is the is the simplest case and

3497
02:00:20,550 --> 02:00:18,560
lower dimensions get more and more

3498
02:00:22,310 --> 02:00:20,560
complicated

3499
02:00:23,510 --> 02:00:22,320
are there higher dimensions than 26 or

3500
02:00:24,229 --> 02:00:23,520
is it just prove that that's the kind of

3501
02:00:27,750 --> 02:00:24,239
anyone

3502
02:00:29,430 --> 02:00:27,760
has managed for the ghosts i mean 26

3503
02:00:30,790 --> 02:00:29,440
seems to be an upper bound for all this

3504
02:00:34,390 --> 02:00:30,800
nice stuff going on

3505
02:00:35,910 --> 02:00:34,400
as far as anyone can tell okay man so

3506
02:00:38,070 --> 02:00:35,920
what's your plans

3507
02:00:40,790 --> 02:00:38,080
for next where can people find out more

3508
02:00:41,669 --> 02:00:40,800
about you where can people find a map

3509
02:00:44,070 --> 02:00:41,679
more about me

3510
02:00:47,430 --> 02:00:44,080
um if i ever find out i'll i'll close it

3511
02:00:51,430 --> 02:00:49,510
i don't know wikipedia maybe i don't

3512
02:00:52,629 --> 02:00:51,440
know your youtube page i'll link it in

3513
02:00:57,030 --> 02:00:52,639
the description

3514
02:00:59,109 --> 02:00:57,040
yeah yeah what's next for you

3515
02:01:00,790 --> 02:00:59,119
what's next to me i'm trying to get this

3516
02:01:02,629 --> 02:01:00,800
problem that i've been working on a long

3517
02:01:03,270 --> 02:01:02,639
time to see if it either works or

3518
02:01:07,430 --> 02:01:03,280
doesn't

3519
02:01:10,629 --> 02:01:07,440
and this well i hope it will be

3520
02:01:12,229 --> 02:01:10,639
sold soon but i've been in this position

3521
02:01:14,149 --> 02:01:12,239
of thinking i've solved at least a dozen

3522
02:01:15,830 --> 02:01:14,159
times in the past and every single time

3523
02:01:19,109 --> 02:01:15,840
it's failed so

3524
02:01:20,629 --> 02:01:19,119
i don't know professor thank you so much

3525
02:01:22,229 --> 02:01:20,639
this has been a pleasure

3526
02:01:25,189 --> 02:01:22,239
oh yeah well thanks for the interview

3527
02:01:26,709 --> 02:01:25,199
it's been a instructive experience

3528
02:01:29,030 --> 02:01:26,719
and i hope you're going to edit out all

3529
02:01:30,390 --> 02:01:29,040
the most embarrassing things i've said

3530
02:01:32,070 --> 02:01:30,400
um it's actually only going to be a

3531
02:01:32,470 --> 02:01:32,080
compilation of the embarrassing things

3532
02:01:34,870 --> 02:01:32,480
you've said

3533
02:01:36,070 --> 02:01:34,880
yes i should have yeah it's it's like

3534
02:01:39,109 --> 02:01:36,080
when you have a newspaper

3535
02:01:40,550 --> 02:01:39,119
interview you you say one dumb thing in