The HLF Portraits: Andrei Okounkov
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The HLF Portraits: Andrei Okounkov

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No Open Access License:
German copyright law applies. This film may be used for your own use but it may not be distributed via the internet or passed on to external parties. 
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2019

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English

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00:00
Area
Metre
Square number
Musical ensemble
Table (information)
Family
01:13
Complex (psychology)
Observational study
State of matter
Multiplication sign
Direction (geometry)
1 (number)
Student's ttest
Wave packet
Mathematics
Goodness of fit
Manysorted logic
Thermodynamisches System
Strategy game
Term (mathematics)
Circle
Social class
Process (computing)
Moment (mathematics)
Gradient
Neighbourhood (graph theory)
Computability
String theory
Physicist
Musical ensemble
Mathematician
08:28
Axiom of choice
Building
State of matter
Decision theory
Multiplication sign
Correspondence (mathematics)
Parameter (computer programming)
Fraction (mathematics)
Mathematics
Plane (geometry)
Manysorted logic
Körper <Algebra>
Algebra
Representation theory
Physical system
Social class
Process (computing)
Generating set of a group
Gradient
Moment (mathematics)
Stress (mechanics)
3 (number)
Funktionalanalysis
Perturbation theory
Degree (graph theory)
Arithmetic mean
Right angle
Mathematician
Point (geometry)
Geometry
Vacuum
Standard error
Observational study
Link (knot theory)
Blind spot (vehicle)
Student's ttest
Distance
Event horizon
Hypothesis
Goodness of fit
Term (mathematics)
Natural number
Energy level
Genetic programming
Lie group
Dependent and independent variables
Physical law
Neighbourhood (graph theory)
Division (mathematics)
Mathematical physics
Cartesian coordinate system
Numerical analysis
Logic
Network topology
Universe (mathematics)
Charge carrier
Family
25:06
Randomization
State of matter
Equaliser (mathematics)
Multiplication sign
Direction (geometry)
Decision theory
1 (number)
Mereology
Mathematics
Plane (geometry)
Manysorted logic
Strategy game
Different (Kate Ryan album)
Körper <Algebra>
Partition (number theory)
Position operator
Descriptive statistics
Social class
Process (computing)
Structural load
Conic section
Gradient
Curve
Computability
Connected space
Arithmetic mean
Right angle
Mathematician
Arithmetic progression
Sinc function
Resultant
Thomas Bayes
Geometry
Classical physics
Point (geometry)
Computer programming
Observational study
Variety (linguistics)
Student's ttest
Theory
Mixture model
Goodness of fit
Latent heat
Causality
Term (mathematics)
Operator (mathematics)
Antiderivative
Computability theory
Combinatorics
Dependent and independent variables
Eigenvalues and eigenvectors
Counting
Line (geometry)
Limit (category theory)
Numerical analysis
Logic
Family
41:43
Classical physics
Group action
Building
Observational study
State of matter
Latin square
Multiplication sign
Range (statistics)
Student's ttest
Solid geometry
Mathematics
Goodness of fit
Manysorted logic
Different (Kate Ryan album)
Term (mathematics)
Energy level
Circle
Körper <Algebra>
Monster group
Eccentricity (mathematics)
Scaling (geometry)
Generating set of a group
Chemical equation
Weight
Projective plane
Physical law
Measurement
Proof theory
Arithmetic mean
Universe (mathematics)
Right angle
Mathematician
Family
Resultant
00:00
[Music] you professor take me to the apartment of your childhood there we are first of all where are we are there books on the wall what is the the the culture of your childhood oh we had a I had a really nice apartment it was uh it was so well I'm I have a brother so was a little younger than I so well so my parents and the two of us a little before people we had a nice charming could you know what I know chuckle had two rooms and it's not the two bedroom just two rooms and in the kitchen which was five square meters area but it was so very was very difficult for us to just fit around the dinner table it's in Moscow yeah Moscow some was in the tenth floor of an apartment building and when you were born it ya know the Soviet Union yes of course yeah so is this does
01:14
your father or mother have privileges in terms of having access to this kind of place what what work do they do so uh my my father first had the careers professional athlete and then as he finished that career he impacted while I was small he went to grad school and his his graduate studies were around so this is not called sociology in in the West I think it's comic like apply sociologists and that would be public opinion polls I like and so this was this were the very early days of computers so we had the punch cards everywhere in fact you know a lot of things were written on punch cards and yeah and then say the eightyearold let's just pick it for you ha ha has a computer in his no of course not the first personal computer came to Moscow when I was a student so this this I was student Moscow State we got the first post the first two personal computers and then those were used around the clock we had a computer we had a machine from from Norway I was called North it that was a machine
02:29
that had for me was an eye computer by the time it was at health at the time it has 40 megabytes memory for the whole thing for the whole department so that was considered a lot and so this a rounded by the old kind of computer with your books maybe yes well I'm saying cuz that's how it end and then and on my mom she was trait there's a railroad engineer but what she she had a career not not actually working on the railroad but instead editing industry journals I'm not just against I'm that's that's a so in the classes over Union they're middle class oh yeah so let us talk about how they encouraged you again this is mostly the history of your curiosity and your intellect so were they interested in your education did they push you in any direction um so I don't think it's just my parents I would debate the way I recall it it's from every direction we were we were encouraged to learn and somehow learning was some cemented itself and to say so you'd somehow it's good to learn and this was not like if you you know you learned so that you passed that exams that you have a good job yeah it's not it's just it's just a just rather abstract or you can do somehow Russian this this sort of abstract pursuits like chess or ballet or or they've just kind of pure celebration of human spirits they're they're popular with Russians yes exactly this is it's it's like it's it's cool it's not me it's not everybody was of course a good student but it's a the I think the culture were such that the good students are good at the best foods are bad yeah and so it's not know which was kind of elementary  maybe middle school did you go to I say in the way it works it's it was one school you entered with under the 7/7 when their sevenyearold first grade and then after 10 years you finish it so it's not the same school same same school is called time yeah how I have the feeling you have the experience of whether or not there's a kind of talent scout strategy among the teachers who that are looking for abilities helping guide them in certain directions so what certainly isn't very much in Russian tradition is to have this kind of circles Olympiads and that that we had in many many subjects and I didn't do it in meaning that I did Olympics but it wasn't you know somehow it wasn't it wasn't so central to me I know later yeah but that's it's it's so we had the limp it's in everything like like like I won I when I studied it in Columbus Department so I did like economics Olympics and I even took them to music a little bit once I'm terrible music but it's required writing an essay so that was good again you move you you are I'm hearing in an environment that encourages learning yeah but isn't pushing you in any particular way no no no particular way no in fact ya know now we have it at school but we're free to pursue anything we want so what course we're being boys but we know we spend a lot of time playing chess or going to the gym should basketball or even we had that so in they used to be like some kind of like a military training course and would sometimes hang out there so it's have you been preselected it wasn't the closest school to to earlier to where maybe I had to walk 20 minutes to I mean there were schools closer to my I mean mosque was pretty densely populated so in principle I couldn't gun somewhere closer right it's a but it's but so this was this was sort of the best school in some broadly defined neighborhood I mean a little bit more they were not the ones that you really shown and was not math but what were they music I but what are your strengths perceived strings what what Olympiads did you do well um I did a lot of subjects oh well I guess they since I put most of time into this economics which is for brief moment of time was my profession I guess I did better than that but it's actually I really liked chemistry for example and I I wanted to be a physicist but but that didn't work out maybe in the future the same with economics um first of all I'm not really quite sure whether or not it would have been perceived differently in the Soviet context in the capitalist West I would have assumed so but maybe not but more it more importantly because you later become a mathematician as you look back the young economist or the potential economist did you think of it as a science oh I wanted it to be science yeah this is the way any economist one yeah happen and the reason you saw and there is an IIR yeah I was happy to switch to Meritus I maybe I thought this is not gonna be a science in my lifetime and it's not it's not it's just for the actual complexity of the subject it's not for for for lack of effort or mental abilities of people who try to make it asides rush it's just really hard so you I won't say you drop economics but you shift yeah at what age so this is after
08:31
I went to the army so I decided when I came back from the army so while in the Army I had I had some time to think and I felt like maybe I should do something else there the army comes after over for University this is in the middle so this is this is the so traditionally in in Russia students don't have to serve in the army but this little this law has been changing and they're in the circular specifically changing you know warrant when I was a student because I mean I'm not quite sure than what the numbers are but I think there was a you know it's like you know like my parents are the people who were small during the war and so there's there's a there's a there's a demographic dip in me yeah and so this is and general I guess the generals decided they want the students to serve  and they didn't have enough soldiers so then the normal is 18 with 18 you got to serve in the army and so we were first called to serve and then sent back from from the University now we always have to be aware particularly with your generation and the incredible changes happen here at this time so when you go into the army is this that's the last year of Afghanistan and so then everybody's very happy that they withdrawing the troops except the does those officers that want to go and then fight them all in every country there's right of course during the United States they're people who aren't happy with the collapse the slow collapse of the Soviet Union happens when you're in your early twenties or maybe even just before um it's uh yeah those were kind of complicated processes it's this it's like it's like many processes in life they've the the process of collapse they sometimes look like a dirty Jew Venetian first and ssp when were worried when I was at my economics here it's also got amazing gears because that's were the years when Russia was beginning to you know open up to new ideas and people would come from more older world and it's a place for economic thought it was a place for incredible activity and so that was those the good years since this is but then then they turned the little star as we were like when we were my wife and I were married in in 91 yeah just before the economic reforms in so to speak freemarket reforms so that's a which it just bring a serious austerity like driver yeah and someone mark when our first daughter was born in 92 was a little it was it was great was still the best time of my life but there was a little required it required more of me than it required of my parents to raise to raise my brotherinlaw right I I still need to understand of course you lived it but how the implication of the political system affects the education system I mean this is when you are making quite critical decisions in terms of your own intellectual life is this happening in a vacuum is this happening in as a response to events we there many things how going together at the same time and they happen in different in different planes so to speak in different levels and so this is there is a there's my wife and I starting our family this is this this is one super happy development then there is me finding quoted what is that what is it I want to do in mathematics and they were still enough people around to do some guide me through this I was very happy a lot of people left very very quickly and then right but they were still a lot still and you were determined at that point to stay so notice as I was finishing so switch to math I also came back from the Army in like 89 something about it and so this is and by that time at Moscow State University already a good fraction of professors have left and so this is as there was a major major center of mathematics and in which you'd have a specialist on every single subject but now many of them were gone and then but still being after but we're still enough people and could help me navigate the world of math so this work this was very interesting time and then of course that there's a then there is a there's a question and what to do like once I finished my studies how do I'm gonna construct my professional yeah and there it's just a question of chance really we were with some people I met invented me to come to Chicago that's what kind of math you're doing how are you making those decisions what field are you aspiring to pure mathematics well I don't know I mean somehow good math is this is a real point will everybody mil make to you that'd be good that good math is math it's a positive it's not like people said typically typically tools for creating it for solving any given problem are not found next to the problem it's like if you have a door locked with the key the key usually doesn't lie right in front of his doorstep it has to be some different so if you're it's it's in that just only the general development the thing brings tools and on the applications together you can't really start out you it's good thing to have some goal but it's also good thing to realize that you know you're gonna do some good in trying to achieve those goals but you're probably not gonna not gonna solve the particular goal you set out to the world is organized still around theses that's right so this is my my advisor so I had I had an official advisor who was Curiel it was this great Russian mathematician and you had obviously under huge influence of him and his he was a student of Gelfand insurance of this kind of back in some sense come from this whole girl from school and also had an unofficial adviser who was there in Moscow to in Carroll of having essentially moved to the west and so this is a chance key I was there in Moscow to actually actually babysit me through the door not just babysit just kind of help grow up and but that comes from the same general telephone schools this is was some mix of so III now classify myself as mathematical physicist but I started out my official the name of the official is called whatever they the division within the mathematics that I was graduating from it's called functional analysis was really was representation theory more representation Theory better so this is this is this is what the field was the decision to look for the next stage you have you were at this point I know it's not a PhD but it's called it's well I essentially had said when I bought as I finished my undergrad I essentially had my PhD ready it's just it's just this were there was a little difficult to assemble the actual Defense Committee so it took like two years to assemble the defense community because softening yeah people were in the wrong the yeah I'm just interested in the stages of life and the building of a career I know huh it's a career in your head and not just oh I must be at this level but the decision to look at the West for the next stage is this happening at the
16:47
graduate level or the postgraduate level it's so when I am as I was a sort of so there was this moment when I finished my undergrad and I was and there was no there was no point to be a graduate student at Moscow State because first of all there was no financial support only duties and and so I was a grad student by sort of correspondence which is which is which is was fine enough since I already had my essentially I had my thesis forged on and simultaneously I was involved in some couple of other can math centers in Moscow so this this was this time which was of between 93 and 95 were the times of great great uncertainty in Russia in general core and so and so this is actually so the way we lived is that my wife had the business the small innocence which which was provided for not only for our family but also for my baby also giving it to my parents with my wife's parents and so this is she didn't she wasn't hundred percent sure she wants to dance she wants to give this up and move to the well I was thinking yeah arguments leaving yeah exactly she tried but then but then it work out off with voter and super because she I like I said I was invited to come as a postdoc to Chicago to work with Victor Ginsburg another student of Korea love like a chance kid so again another person from this tree of gelfand and she was able to get into the business scholar in Chicago somehow miraculously we were able to pay for it I mean she actually said this is my um in in high school so in the universe I didn't take in you mean I took some French classes but it is high school I took German classes and all actually the journal link beside it pretty well though so but so this is my but but still professional life and professional mathematician doesn't require so such an eloquence in in foreign language I made it this far was the wisdom with the with the terrible error English that I speak is that what you mean no I'm just saying the language no no it's just it's it's it's a first of all it's it's it's I do appreciate when math is well written well presented with with correct choice of beautiful English words but but for most of math the deceitful get type of a vocabulary is is is sufficient to get to get the to get the the message animals I'm asking and so you don't need so many know so many English words to communicate to communicate math but tell me the process of communication hot that it happens mostly through symbols I mean you our community I actually really prefer to write it in words but but but but it's true that you you can read the paper in a language you don't understand and you can figure out what roughly it says just from the simple it uses okay so you're in Chicago she's in Chicago your town in Chicago I still say for her that the language question must have been more difficult than for you absolutely but she also investors invested much more than I and to study in English yeah but she and she's been studying it for much longer she studied in school in high mean it through through the school it's not a big problem yeah I wished it was here she would sushi in Chicago the nature the department the kinds of choices you make you are now how old that's a good question so so we arrived to Chicago that was 96 I think it'd make me 26 maybe the shock was I had the vaccination because when Carrillo file carrier while I was a grad student I mean that I I came to visit gorillas for a couple of month and pan and those were the old days at pan when it was it was really kind of a rough neighborhood Iran yeah yeah and so in fact the Bhangra team was killed and that so that was so I was prepared to come to Chicago to the south side of Chicago Hospital prepared right and in fact we never experienced anything what about a longing for Moscow and its cultural life and rhythm and so for this it's it's a big change it is a big change it's it's maybe the the way we were then fixated on on eNOS getting through her MBA degree and our our second daughter was born in Chicago and and now I had to mean postdoc it's kind of a stressful time hmm so maybe there was just really no time to to worry about don't worry about it there were some other attraction like with so Michael Jordan play which yes not bad given us by both my wife and I well I'm not I'm not I'm not the best basketball player in my family but so my life my father brought pretty good I want to know about how you proceed to think about the problems that you you want to take on I think I was really lucky in Chicago in that so did they what happens in what what that what ideally would what happens in this kind of political stage is that you exit the nest of your adviser and here's some how you what thinks which you previously you previously thought they're all you know this is what the math world is this is what the important problems are yes all of a sudden you look at from from a big distance and you realize that math is very very big and your advisors nest is relatively small and this and then you somehow have to find yourself in a bigger landscape and and in Chicago was a really good place for that because I've I made friends with people who not only friends in personal sense but also in some kind of you know appreciating certain new kinds of math that I didn't really appreciate before so I made very important matter important people there so like of course I've been at work upon a partner with whom I wrote a lot of papers little later in life and then the Tulsa but also like I didn't interact off my food Ginsburg either with in Moscow softly but Ginsburg good valence and rental there and Fulton was a huge influence on me to this I this whole my whole interest in algebraic geometry that I was that was lightened it's a English word latent before before before Chicago when I became went to the in to kill stage there so build your own nest what is it made out of you said you give you give up the nest of your matter your teachers and you begin to build your own so what is it made of um not sure so actually so in both in kind of personal life and and in mathematical eyes we're a bit of know months actually so it's like we're you know one kind of consider both Moscow New York City my home now but we flipped in so many places I never threw my career in a merit I also I could sort of just follow follow a gets my curiosity and the logic of the subject so I I don't I never thought this would be you
25:07
know they've built myself a lot of chicken wire and then surround some piece of land and say well this is going to be the nest was your phrase right right right right right right right so this is this is it it's it's good to me conversation to reuse the mental majors the metaphors yeah so so this is fun I kind of moved from subject to subject like I said following my interest and following the logic of the subject this one day you're gonna get a field matter what is that gonna be for and how do you get there I think it says for like making connections or something you're working on something and that something will be recognized what is it your work now but really it's it's like like this this there's some that I don't know I mean maybe so this is the the way I'd like to describe this person to my grad students is that that's me not just math science in general okay it kind of happens by curiosity and luck so it's it's it's not like people if you want to discover penicillin it's not like people set out to discover penicillin it's just just just just build a telescope look at the sky and see what what you discover something answer and so this is I inside here pew if you if you search you can find something so like if it's there's there's you know I found a couple of places where something can you turns out to be applicable to solve some problems people care about so this is because I was lucky and but this was of the kind that you you bring tools from from from Australia to and sell them from you know actually in mathematics there are directions that are acknowledged insights front that are seem to be changing the conversation mmhmm and I suspect you had some insights that began to change the broader conversation at least in in the problems you are taking on what are those problems so this is the oh I don't know I mean it's it could be a little technical so this uh you can deal many people who are listening to this will understand so just broadly so one my lecture they can listen to my lecture so I think it's a so I don't know it's it's they're always kind of infernal question in various branches of mathematics well it's  for example a lot of them has to do but broadly people say it in numerous of geometry but where is the geometry is more of a is more of a label the other in the description what it is it's it's it's just some some some some questions of counting you know how many zero eigen state some operators have and can be said that this is this is a question of counting like how many such and such curve line such as I shall to break variety and so this I have spent a lot of a lot of a lot of a lot of time thinking about that there's sort of questions and this is and miraculous you're not I mean this can be debatable it's not all my insights in sight of many people this are these are related to some other questions also in mathematical physics like like we've if you count just some sort of basic curve counting problems rather famous ones are open everybody and I were able to solve in terms just a basic probability like it thinks it had to do with with partitions this you know there can hold real oldfashioned object and and that it's so forth and I am I right that one of the framework said and intrigued you was rather the question of the random it's part of that I mean it's just it's a few uh if I everything is random so it's this is this is this is I mean if you were to study you know I think myself scientist I can espanha study outside world with tools of mathematics or bring the problems into mathematic from the other side world and I was like well other things random say after somehow that's part of that it you can't you can't really avoid it so this is you have to I guess you have to embrace it and it's it and it's it's beautiful it's beautiful that for some when when some randomness is related to something else which maybe maybe no not random you didn't think it's random at all so if you you think of this like this kind of curve counting problems new to geometry problems so these are the kind of problems like if I have a like a classical problems over for conics in the play or five conics in the plane or how many other conics are tangent to that's a classical problem so you think well what does has to do with randomness it's not a random question it's a very specific question and answer but in fact this counting problems do have direct relations some kind of randomness and you can you can do it in this it's in this way I went to Berkeley and again what's the appeal of what what brings Moberly you know you know at Berkeley I know Burke Burke it's not even California Berkeley is Berkeley Berkeley it's it's kind of a singular place yes it's a also it's also I'm you know I'm not gonna make a secret I have my political views I'm all very mean it's not it's it has very little to do with with being born in Soviet Union it just you know somehow I like the ideas of justice and equality and so forth and so you make the decision no I mean it's just it's a good place it's a very refreshing place to be Berkeley you go there people are free people are very honest and somehow stand stand for good for good for good causes I really I really like people of Berkeley yeah oh yeah absolutely I has a very strong again is there and it has this math Institute  for which I spent a spent a lot of first date first at math Institute really helped me at some point and upin Chicago gave me this is post doctoral limitation they didn't quite have the money the first year to help me support me for the full first year and so I was very helpful for me to go for half of that here to go to this institute burgers I was really super helpful and and then and and and I've but they've doing and this is this a very small thing and but they're doing a lot of good a lot of for for just developing the math and making creating opportunities for mathematicians in this country and abroad to further a research and so I've been trying to kind of pay back that data a lot of work for them you with a position or you know sure I went to Berkeley a tenuretrack but it's not attend attacking our subsequence to tenured so  and how long are you there I was there three years so why do you leave this paradise oh it's so this is where all of you everything's interwoven right so I have a wife and family and my wife works in across the bay in San Francisco works in one of those financial corporations she used to be in the variable' days was Coulter I guess cutter or Kemper and then scattered Kemper and then bought by Zurich and then boy bander shebang and then subsequently moved and s day is the dot the first time the dotcom bubble burst that the what remains of it was moved to New York City so so that's a we
33:27
go east do you have any of these points responsibilities I've talked to mathematicians who have no teaching responsibilities where they are is entirely devoted to their research others who have a mixture of it you begin to have any teaching result all the time yeah I'm avatar ya know I've my whole life I'm teaching yeah so you're in fact in Berkeley was maybe the heaviest teaching load I ever had but that didn't matter I've I thought my favorite course was numerical analysis I was really far from was really far from what I do in my life but it's it's such a concrete course people and so it's a problem you have to solve it in the computer so it's right you know this is super concrete and thereby teacher hands up the course like this which you see is just you undergraduate education no I haven't taught the greatest course in birth it was oh it said there's a long waiting list for that and three years with magicians and computer theorists and a horse there are border lines and non border lines but are you also taking an interest in computer theory at all or not really dumb no no it says I taught a course one course I thought was a new course now it's still continuing it's still continuing to be taught at Berkeley but it didn't exist I was the first person to teach it was basic course in combinatorics and in that course I had a lot of kids from computer science and up and that's really I really enjoy those having those kids in my class I was really nervous it has me again it's basic course this it does require I like I mean I like the subject a lot it's it's it's of course what I was teaching an undergraduate course is not exactly a cutting edge research but it's a it certainly I certainly appreciate that but they'd say I don't know I don't do my own research I do program well I mean do I do code a lot but it's a it's it but this is a strong direction no no it's not it's not it's not the code itself is actually kind of it's a it's substantially very primitive just because I mean the problem is felt so complicated and it's a it's you want to make the code primitive so that if it's something doesn't work out you you know work with the blade number of the computer players I've talked to have said that more and more people are seeing how fundamental mathematics is to where the computer theory will go so and vice versa I mean yeah but not the minute and what I did is just just you're not gonna make any progress without computer because it's it's it's just the exam I mean I mean of course where's their their different approaches to math some people can do it just by somehow contemplating deep ideas which is I can't talk about this right now I'm not I don't see how this works more ordinary scientists like myself I sort of go through examples but the example is just to complicate not to do by hand sorry just you have to do the literally learn what's going on you have to you have to use a computer it's just otherwise it's right good or pretty much everywhere departments of mathematics and computer theory are still quite separate I mean they oh yeah of course yeah they don't have a mind these two but that that makes sense right I mean this is the the math is a subject in computer science is a subject into different subjects is the fact that the mathematicians use computers and computer science as influenced by Malthus is relevant its yeah ok it's like saying in a chemistry and biology are very very interwoven subject but they're not the same right and so so this is so in the East what where is your position I was at Princeton for for a long time before moving to Columbia was that the Institute I'd want to know this the department department department yeah now it's another opportunity to talk a little bit about mathematic education if you that would interest you because I've read since later on you develop a strong connection with the teaching of mathematics both in Moscow and in the United States so more and more you're in a position to look at the different strategies of Education maybe even the different quality of mathematic education and so forth are you beginning to think about this at this point what what what your students are like here and soon what your students will be like in Moscow no I don't think I have such a deep thought about that it's it's here and our students are very international there you have I guess students from from over the world and so this is just some of course the American ones there's some they have their strengths and they have their weaknesses and they and but but but I think this the the maybe one thing i want to say is is maybe some potential student sometimes watching it it's it's how people come to science how people come to math it is obviously important but it not as crucial it's it's you you read the lives of great mathematicians like meaning left shots he was a chemical engineer until be in because when fortune Dyson had to switch career it so he switched to math really really advanced age and in many people like you should see now once you once you once you're discovering yourself a passion for science passion for math it's it does help a little bit I imagine to to have a few years of head start on others so it doesn't hurt to be a prodigy but it's it's it's not essential but it's also I mean majority of American students they they feel maybe slightly awkward as they start the graduate school because they there's there's people from from Europe from China hold on you know what and they've a lot of things that come Americans just beginning to learn but take a job they they they they grow into really good mathematicians it's a it's a so this counters counters but it it involves the question this may be a cliched it without any meaning which is that mathematical insight comes particularly strongly to the young I mean certainly this inside inside inside no I mean the quickly acumen of course there said there's hard biological evidence to back it up I mean as a young of course your your mind works faster you're you're you're faster at absorbing information you can learn many things that you'd will be very hard to learn later in life but but it takes a as you grow older you compensate by experience by by some kind depth and Lee and it's it's it's not it's not clear which one wins so it's somehow in math it sometimes takes a long time to come around to like sit inside this inside is not it's not something it's not something you typically when the best people don't have it in an instant even though it sounds kind of close but but it usually takes a long time to develop the really to find a really the right way to look at the problem to really do something which is which is deeply not obvious often takes a long time and then another thing I always like to say my students is that is that if you look at the great scientist I mean of course there are exceptions but but typically great sciences have don't have so many great ideas in their life and it's so if you yeah you shouldn't worry that that it takes you a long time to do to come up with one or it's been a long time since
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you had your last good idea it's just it just it's just just on average people don't have so many great ideas but it's still amazing people have some good ideas it's still amazing how do how are basically primates come up with this [Laughter] really drives me then so many of the great mathematical awards are given almost deliberately to the young I mean the field car for example Oh age and so forth so that suggests at least historically maybe even an eccentric interest in youth and mathematics well I think the young people needs more support if you think it's somehow this is this is this is it in math it's always we always try to encourage people to know how to do math and we somehow have to think in this people grow more established more become more important they you know they get two different kinds of recognition and it's a that's that's fine and it's a but I think it's good for a field that to to play this kind of high recognition on on young people again with it it's it's it's I mean of course that this is some kind of weight you also put on people's shoulders but it's but it there but it's good to have a to give a spotlight or the idea somebody's ideas or somebody's work when they need it yeah well maybe we should begin this in history but it'll be a long time before historians or group work you've been there we go but we are we're talking about mathematicians now another thing that strikes me as an on that bit different is how shall I put it the currency of your colleagues that people who died 300 years ago are still in conversation with mathematicians well it's not like in the heretical and you have core course looks like the field with blotto but we don't read other we appreciate the weather but we don't really do people people actually I'm competent to read even Jacobi not because they're out of Latin and the very people read Latin man but the problems that are posed some what'd ya say it's it's a lot of problems are approached and now consider it irrelevant to but it's it's it's German if you ever if you ever if you just kind of study they're working so great might like weather or gas or or it's amazing it's amazing how what they've been sides they had and then it's but of course it's sure that the math has changed beyond recognition since the time of even of cows would you say even in your time oh yeah of course I mean this is the kind of thing that we do now that they all looked beyond impossible when I was without the idea really oh yeah we're talking about somebody who's now and is what late 40s or something yeah it has changed so much it's a change very rapidly yes this is another thing in which young people of course have advantage over over people like eyes that is that the this is math developed you can't mean you you can't do it by yourself you have to kind of right with the peloton and this requires just think current abreast of you know some anything happens just reading a lot of stuff going lots of lectures just working through through papers and you know it's easier when you're young to absorb new information so this is maybe one interest you to talk about it but I'm I'm very interested in your continued commitment to if you will a career or as a teacher perhaps it's that in both Moscow and well New York right how did you go about continuing in a way to live in both worlds well I'm still working on how this exactly gonna so what will be now that our kids are out of us our our younger daughters in college now and our older is finishing grad school so we're my wife and I were preparing for four well where our teen has exactly exactly where we're still figured out how exactly how exactly our but the new balance will be between Moscow in New York and probably spending more time in Moscow but I've always I always felt that I mean somewhere and Moscow is money made both places my home and so it's my parents are there other children yes my brother's there again I asked a question that may not really be very relevant and that is is there still can you argue an intellectual climate difference between the mathematical world in Moscow away so this is the the I can speak for Moscow the whole because I don't what my brother tells me about his kids schools maybe doesn't sound quite what we had but certainly what I see it at universities that's that's very salient of what we had the young people I I see now is the math students please they could have been me how many years ago so really yeah this is the same state they there's AB there are fewer math majors now it's you know well of course the country's got smaller and also there's all sorts of other careers
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people can pursue so math was also a little bit of like math was also subjected withdraw people who I mean withdraw people who as I mean most politically neutral subject you can probably imagine so now of course and they're people have the climate of learning right do you find that still quite well yeah the universe this yeah that's this absolutely yeah people this is the same very close very close yeah it's it's it's this kind of you know there's something it's not exactly the genes but it's it's some kind of maybe social genes they don't go away in one generation it's a this is I my think is gonna be fine I mean this is this will survive on a smaller scale maybe so this is the there's still math circles functioning climp it's taking place and it's so but some seats of that I've been sown in the United States to like a mountain in the air there are very vibrant math circles community those lots of people participating in math Olympians and so forth so this is New York City to actually sell it sir some of that may even have been seeded by Russians or not necessarily Russians just just some European like Eastern Europe especially but also Western Europe so through the end of our conversation at some very basic things for example the idea of a proof mmhmm can't be as strong in economics the economics that you study is you of your youth as in mathematics can you characterize to me the the notion of a proof to mathematics what huh all right I think proof is overrated okay it's it this is the this is the short version the long version is that is that there are different stages to our understanding and so there's some what what our community places a lot of a lot of emphasis on being somebody to prove a particular statement whereas there is a lot of work before and after so like before is there's a person who realizes something is true somehow maybe the observed a certain phenomenon for first the person realizes it's interesting to look at something then maybe a different person realize oh there's something interesting happens look at me I have this conjectural vision what is going to be and then uh and then there's some maybe intermediate result somebody finally first council de with the first complete proof which is usually is it's some kind of mean but just by the laws of nature usually it's some kind of monster sewn together from pieces of of different ideas in a way in the kind of you know some in in in in the first it's like for the first drafts of something it's it's it's it's it's some it works but it's it's it's like that it's it's it's a building which in which you use the piece of of that and it because it's a piece of cloth is a piece of of concrete and it's just just something and then and then later come people and analyze this and and find what is the essential what is the essential idea that makes this work and then they they they analyze is proof or maybe they come up with different ideas and then finally we come with the proof that is now that it's now really explains what's company this is this is the maybe the highest level of understanding before it starts with kind of sniffing going there must be something to define that not only people understand why what happens and why it happens but also clearly understand why like the real reason why this happens is now being understood and so this is there's a whole I guess that there's a whole range of this sort of development and and it's just different measures of how well we understand how well we understand and it's just like I said to start the beginning I've I come from the background where understanding is good unconditional so the more you understand the better and they have to have a formal proof is a measure and have a formal proof which is moreover is beautiful is the next measure so you can and actually in math way where we spent a lot of time rethinking this is this is a subject which is maybe it's not like classics but it's it's among the scientists of the solids may be unique in in how much time is spent rethinking our foundations and may really in really making sure they've their optimal and they're they really they really been to build we're typically built not on some bid next the next projects typically built not on this kind of shady construction that was the first to prove but it all now works now builds on something solid and beautiful and then we kind of this is the way we build the next the next level I love to use among mathematicians of the term beautiful and elegant uhhuh it's because my own aesthetic acrobatic among the scientists it's the mathematicians who use this word in my experience Oh beautiful I see okay thank you very much
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you you