The HLF Portraits: Charles Louis Fefferman

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The HLF Portraits: Charles Louis Fefferman
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2019
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English

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Process (computing) Observational study Multiplication sign Direction (geometry) Archaeological field survey Gradient Physicalism Infinity Calculus Distance Dean number Mathematics Spring (hydrology) Strategy game Energy level Modulform Musical ensemble Family Körper <Algebra>
Point (geometry) Computer programming Mathematics Theory of relativity Natural number Universe (mathematics) Moment (mathematics) Gradient Physicalism Student's t-test Pressure
Axiom of choice Ocean current Point (geometry) Computer programming Group action State of matter Decision theory Connectivity (graph theory) Multiplication sign Direction (geometry) Range (statistics) Student's t-test Distance Junction (traffic) Hypothesis 2 (number) Subset Explosion Expected value Mathematics Many-sorted logic Thermodynamisches System Term (mathematics) Natural number Boundary value problem Modulform Energy level Körper <Algebra> Position operator Social class Physical system Gradient Moment (mathematics) Mathematical analysis Physicalism String theory Perturbation theory Numerical analysis Faculty (division) Logic Universe (mathematics) Right angle Mathematician Arithmetic progression Fundamental theorem of algebra Sinc function
Direction (geometry) Multiplication sign List of unsolved problems in mathematics Frustration Mereology Mathematics Strategy game Atomic number Different (Kate Ryan album) Analogy Elasticity (physics) Körper <Algebra> Process (computing) Mass flow rate Gradient Moment (mathematics) Physicalism Variable (mathematics) Flow separation Oscillation 19 (number) Connected space Arithmetic mean Angle Order (biology) Quantum mechanics Duality (mathematics) Right angle Mathematician Arithmetic progression Resultant Spacetime Ocean current Point (geometry) Functional (mathematics) Divisor Observational study Routing Student's t-test Partial differential equation Frequency Term (mathematics) Natural number Electric field Modulform Energy level Set theory Condition number Complex analysis Validity (statistics) Weight Model theory Mathematical physics Cartesian coordinate system Numerical analysis Calculation Game theory Pressure Distortion (mathematics)
Point (geometry) Ocean current Statistics Multiplication sign Characteristic polynomial 1 (number) Translation (relic) Student's t-test Mathematics Goodness of fit Many-sorted logic Atomic number Different (Kate Ryan album) Körper <Algebra> Series (mathematics) Curve fitting Position operator Social class Predictability Dot product Closed set Surface Projective plane Moment (mathematics) Model theory Gradient Multilateration Flow separation Approximation Category of being Calculation Object (grammar) Mathematician Arithmetic progression Family Fundamental theorem of algebra
Mortality rate
[Music] you so I'd like to begin even before you
with your parents tell me a little bit about who they were what they were interested in doing at the time you show them into the world sure so let's see my father was an economist he had dual career alternating between the insurance industry in which he was treated very well that was somewhat bored and and the government in which he was treated pretty badly but was fascinated by the work the direction of his work so he so his his last job was that he was the Economist on the Joint Committee of Congress that dealt with taxation so if if a tax bill was introduced a lot of lawyers would focus on exactly how to phrase it and this and that and my father try to explain what might happen if the bill got passed now also his job would explain he's living very near Washington DC and so yes you yes tell me a little bit of that well before we go there your mother okay so my mother know my mother was a housewife huh she she was born in Germany and flipped the Nazis in 1939 well a smart family well a confident family my my grandfather was a successful businessman who felt that when things got bad he could bribe his way out and so at the last possible opportunity he he managed to do that well yeah so she said how long your father is working in various forms of economic strategy you come into the world in Silver Spring yes tell me a little bit about your family are you an only child no no I have I have a brother my brother for a long time was the Dean of physical sciences at the University of Chicago so so and and when when not an administrator he is a professor of math so math is the family business he's younger okay so you're you're the first show some mathematical ability yes and the story is almost famous about how you discovered an infinity for math but tell me about your age and the reason short so I think I was about nine I was very interested in science I'm afraid I've told this story enough times that I tell what is the same I'm sure all will be hearing it for the first time let's see so so I became interested in how Rockets work the kitty explanation didn't satisfy me I took out a freshman college physics book from my local public library and understood nothing my father explained to me of course you can't understand this it uses math okay can I study math alright what so he didn't simply say no that's ridiculous and it was very wise so he said to me all right what level are you one I'm in whatever fourth grade okay I'll buy you a fourth grade math textbook and I zipped through it maybe it took me a day or two I asked my father for the next math textbook oh come on you can't have read it already yes I did he asked me a few questions oh yes you did okay I'll buy you the next one and this kept on going until until I got through calculus and then in the course of what a few months well so let me think I'm trying to remember it seems to me that that I was 11 by the time I delivered calculus banasur okay okay so so then what to do after after that my father could could test my knowledge and and could could help me with questions through calculus but not after that so what to do well my father had a friend whose son was interested in math and and way ahead and and was being privately tutored by a professor at the University of Maryland and I lived within striking distance of the University of Maryland so my father investigated and and we found a professor who was willing to work with me Jim Hummel and I took private lessons with him the age of 11 at the age of 11 ish yes yes Jim introduced me to to some of the other professors at the University of Maryland in particular to the chairman of the department Leon Colin Oh a wonderful fellow who took me under his wing and and arranged for example for me to take to sit in on first math courses and then math and physics courses at the University of Maryland and then
after a couple of years of that for me to skip high school and enter the University of Maryland as a freshman I'm not going to let you go there yet okay although we're the at the borderland I'm going to use that often use word a little heavy the famous word prodigy okay and ask you what was the culture of around you of
being such a precocious young person where your peers gasping where your parents showing you off where your teacher showing you off what was that like okay so let's see my I well let's see no one was showing me off my parents and my teachers were very concerned lest I be pushed or made to feel extraordinary pressure even even self-generated I think they slowed down my education a little wow my peers were very nice of course my peers were first University undergraduates and then University grad students and it couldn't be a completely natural relation relationship with them but they were very nice to me and I didn't feel I didn't feel like an alien creature as the human is I'm a little worried about the rest of your education well or you were joined in your worries by by my father who occasionally would give me a history book or an economics book or a novel and asked me to read it and I would dutifully read whatever he asked and then put it aside and continue studying math and physics I did read and maybe this was just an aside there was a moment at least you flirted with the idea of being a painter and that's that's true I took I took art lessons as a kid and and at some point I was trained very well and and I liked the best two or three things that I produced and so for a while if you ask if one asked little Charlie what are you going to do the answer was well I'm either going to be a painter or a scientist and and then has it happens thank God I might talented in in visual arts to say the least is not equal to like talented math so okay so we're on the right course now yes we didn't deviate into painting I'm gonna let you enter the university now at wait 14:14 and how was a program established
for you this is just a normal abnormal age but a normal undergraduate well it it was I would say heavily concentrated in math and physics but it was in the normal range I fulfilled the university requirements I took I took two english courses intended for English majors that was an interesting experience I I gather that most students consider math and physics to be the most difficult subjects to study but I can still remember opening my report card in those days it was it was mailed in you know snail mail and I remember opening the fold and seeing the lower half of the sea and being delighted that I succeeded in thank God getting a C in Shakespeare for English majors oh well that gave me some needed humility I got a lot more needed humility when when I got to graduate school so having having been having been a child prodigy in undergraduate school I was used to being the best of the brightest and and people were sensitive and nice and and and so I think I was not obnoxious but but in graduate school I remember hearing many many many times especially in the first year sentences beginning with you mean you don't know and and so that that taught me consider in a way really any of your education in the sense of no one would you don't know well that perhaps that was the beginning that certainly continues I mean I suppose it's a cliche the more right the older one gets in the more one learns the the more the less one you have the less the less one knows but certainly for graduate school I'm sure it was pretty automatic but the decision is to where to go to graduate so how was that shape um how was it shaped I visited the four graduate schools to which I applied I was given advice by my by my teachers at Maryland as to where to apply I had interesting interviews when I arrived at Princeton actually I got confused and missed the little local train to go from the from Princeton Junction to to the town of Princeton and and that played havoc with the schedule but but when you are this one 18 I was 17 and I wondered now let's see why was it that I picked Princeton I can't remember anymore I'm sure that that they spoke to me I I had fantastic guidance from the University of Maryland all along the way from from my first contact as a little kid through through undergraduate school is there there's no one mentor in Maryland I know you'll you'll have one later right like that well there were several what I usually say about this is that although the University of Maryland was a big state school you'd felt like an army of private tutors and so I had I had perhaps half a dozen mentors who took very seriously exactly how my education should be handled was there an undergraduate thesis to be done there was no required undergraduate thesis but I published a couple of papers as an undergraduate talk about that before we get to assured school short at what age did you publish maybe 16 and what was the direction of the world it was mathematical logic and so I think the way my first publication arose there was a course in in mathematical logic we were going through a book and the book gave an example of something or other and the example was very complicated and I couldn't understand the explanation and so I thought that maybe it would construct my own example which turned out to be much simpler than the one in the book and also much more general and so the professor in my in my logic class suggested to me that maybe I work on generalizing it and then published the generalized version and she helped me to to find a journal and prepare the article and it was accepted and that was my first published certainly commend you to Princeton's attention when you apply among among other things but having decided on and having come to Princeton what kinds of decisions must you make in terms of intellectual specialty as you arrive as a graduate student well first of all what what to study but to what to specialize in and Princeton has a program that that Accords extraordinary freedom to the graduate students from the very beginning so for example one of my fellow students decided that one semester he he was interested in none of the math courses but he always wanted to learn Sanskrit and so he did that there was that much freedom right so for the for the first year I studied various things on my own I talked to my fellow grad students I didn't have much contact with any professor the second year in graduate school I took a course from a weisstein and I was blown away by that course and I and so then I considered him as as a finalist among among the people whom I would ask and in the end he was my first choice and in retrospect it should have been obvious and and he agreed what was his so his particular interest is Fourier analysis now let's see all right so I I gather that that many of the people for whom we're doing this know what that is but maybe I just read a little bit okay so well so consider a vibrating string say a piano string it has a fundamental note into first overtone and a second overtone and so on and the the full sound of the vibrating string can be taken apart into those components and and the components can be put together to form the sound of the piano string that's the origin of the subject and it has grown greatly in the whatever 200 and some years since since the vibrating string was the was on the forefront of research but that's the origin again maybe a very too basic question but what is the nature of research in mathematics oh okay okay well first of all there are there are problems that no one knows how to solve there are problems that that have been studied but but untouched or problems on which there is partial progress there are problems that sound compelling when formulated but which no one has thought of yet there are concepts which which are very useful in solving problems or which perhaps which sound with very natural and compelling when formulated but have not been formulated yet and all of these things interact so by solving problems one has led to concepts and by thinking about concepts one has led to problems we're clearly says I understand so again here you are launched in a graduate career violently a future as a mathematician right does one toss around phrases like yet like pure mathematics is supposed to apply there are those irrelevant oh context or the culture has changed when when I was a graduate student there was a very clear distinction between pure math and applied math and I think the the pure mathematicians looked down on the rest of the world which was insane the pure on knew okay you've had it long seemed to me and I'm happy to say it's now I think that the prevailing view that that the distinction between pure and applied is completely artificial there's a distinction between interesting and less interesting and both of those cross cross boundaries but not that not that no ok so you were invited into or chose the world of pure mathematics um now
let's see I never considered specializing in applied math yet okay if we fast forward a few decades mike-mike current work is sort of on the fringe of applied math but maybe we stick moving up tap later in there but not have you considered apply okay presumably your mentor right is involved with pure math yes yes so you launch into that world of analysis yes again because I'm interested in the progression of your curiosity okay within that how do you then set upon choosing the problems to address well um I was very lucky in my choice of mentor because Eli Eli has had I think for his whole career an enormous collection of research problems I had all levels and he sizes up the student and supplies an appropriate problem hmm so to begin with simply my adviser posed posed a question now he obviously had a very high opinion at me because he gave me what was considered at the time a major unsolved problem to think about I made very little progress on it he gave me an easier problem and then still plenty hard and I solved it in a few months and then he gave me another problem he also also solved in a few months a couple of years later I was able to solve the first problem that that he posed to me turns out that what people expected to be true I mean the expectation was that it was true but not but it was very hard to prove but it turned out not to be true but but it took me maybe longer than it took most students to make the transition to picking my own problems precisely because I had an advisor with such an incredible supply amazing questions yeah yes well how do we the doctor'll again dieded or completely guided so that the the problems that my advisor gave me were each I mean he were doctoral topics the first one would already be a thesis or I find so that the feeling was oh okay great now you have an insurance thesis slip let's let's try a harder problem oh great you've got that and actually there was a third stage I actually made partial progress on on the big one and so those three things together were my doctoral thesis you are now what age and I am twenty you're twenty okay well some would consider this a problem to be twenty and have to now decide the future direction but you've you've proven your abilities yes presumably you have a range of options before you know yes no are they well but so first of all I I was it seemed obvious to me and to everyone I spoke to that I should pursue an academic career in the particular in the particular field of analysis that that I was working in there was one obvious place that was the best in in the United States probably the best in the world so I stayed I stayed at Princeton for one more year as a lecturer the the most junior form of a faculty and then and then went off as an assistant professor to the University of Chicago I go again to belabor the obvious but it's important to say it this registered a kind epic moment in terms of age and position oh okay yes so at least at the time I think no longer definitely no longer but at the time I was the youngest and would see was when oh wait wait wait this is all right so I was an assistant professor at 20 21 at 21 I think but I was promoted to tenure with a competing offer from Princeton when I was 22 and so when I was 22 I was the youngest tenured professor in the United States of some satisfaction I'm sure ah it felt wonderful and guaranteed you your future yes yes always the critical thing yes yes yes your future is guaranteed at a good age and you have many good years to then proceed yes I'm gonna ask just at this stage of general question because it's either a name or comes to the heart of something and I myself decided this okay that is the famous question about youth and mathematical insight and even genius that in mathematics number one it's not unknown mm-hmm to make great progress at a young age and later on I'm gonna ask you whether it's only at a young age okay we'll get there okay right now you're in the in the right right right do you find that true that there was something first of all about the world accepting the possibility of your contribution at such a young age that in mathematics this was not unknown oh well in in mathematics this is certainly not unknown in terms of the world accepting it I never I never I'm trying to think I think it happened once that that I felt a lack of acceptance it was it was that I met someone not not at the universe not at any university I forget the context I met someone who who had been a professor in a medical school in we're in I'm thinking in Vienna but I don't remember and I was introduced to him and it was explained to him who I was and and he simply said this is a professor and well yes it was oh yes yeah yeah so you're in a protein moment you have a position right you have the right to pursue your own interests right at Chicago what do you take on as so at Chicago I was interested in broadening out at some point I decided after after a very successful first year or two at Chicago all right I've I'm very happy about my achievements in this field of math let me find something else to do I was I was lucky to find to find a problem actually if the problem was suggested to me it was floating around and considered one of the hot problems in math which which was not in my field but in which knowledge of my field was an asset and and so it was the right distance and I worked on that and solved it actually that that happened twice now that I think about it it's I think it's important for a mathematician maybe for a researcher in any field I'm not sure to pick a succession of problems that are the right distance from prior knowledge so if you if you stick with the same old stuff you don't grow and if you strike out completely anew god help you and and so you have to strike the right first sounds in a way was provided by you for right now you yourself are trying to find that else so I myself am trying to find it I still had a lot of input from from colleagues or a long time I think I just completely followed my own interests after a while I think one by being in a top mathematical environment when simply absorbs enough enough knowledge and has enough experience to have some sort of individual taste you know basic question about the the culture of math mathematical discourse okay where of course so often the mathematicians lives in his or her mind oh yeah for obvious reasons right theoretically but also there's a system of circumstance mmm-hmm of interchange yes how how does that happening the DM professor alright um let's see I am going to a lot of seminars I am talking to a lot of
colleagues listening to what they do absorbing some of it having fun part of a part of being an assistant professor is to feel a lot of pressure but I was promoted early enough in my career that that it preceded this the the steady pressure my my one year as an assistant professor I thought well gee I better think of something because otherwise I won't get tenure in here but yeah but but I did and so I think I have I have never felt the kind of pressure that that academics typically feel in order to go through the process the opposite of pressure it's all related which is an inspiration right those around you or perhaps even from students I'm interested in that process too it has it all right so so inspiration from students comes sometimes I remember supervising a wonderful grad student with whom I would meet every week or two and and the usual the usual interaction with grad students would be okay here's what I've done and here's where I'm stuck and I would think about it for a little while and say well why don't you try blah blah blah and the student would go off and think about it and the process would be repeated the next week but with the student I remember he would say I'm stuck on blah blah blah and I would say why don't you try whatever and he would and he said to me well yes that's the obvious thing but here's why it doesn't work and so I would typically say hmm yup well why don't you think about it some more and the following week he came back and had overcome that and was stuck on the next thing so so and I've been I've been lucky to have some wonderful grad students several so I'm now prepared for you to leave Chicago okay and where you come and I come back to Princeton on what terms presumably lieutenant Oh wit with tenure so let's see so I went when I accepted tenure at Chicago already I had a competing tenure offer from Princeton which they kept open for a few years I I gather that inspired by by the case of of Charlie's recruitment tenure offers these days come with deadlines you must accept me by this date or the offer disappears hi felt I felt internal pressure I was spared the certainly the the worst of of you know the anxiety of an assistant professor wondering about tenure but but I did feel okay the you know the world thinks I'm wonderful gee I should really do something right am I going you know am I going to do something of the right level and and it took I think a long time for me to feel comfortable with myself yes which is a good human trait by the way I think it's it comes in many things time to do yeah yeah again in this banquet of possibilities yes which direction are you choosing to pursue in your mathematical research um so let me see at that at that time I was let's see for awhile I I worked on partial differential equations I was then interest I became interested in mathematical physics a particular set of mathematical problems inspired by physics I wound up spending many many years on the question of why it is that many electrons and many protons under the right conditions will combine to form many hydrogen atoms or many hydrogen molecules it's it's a textbook discussion in in every quantum mechanics book that one proton and one electron will will combine under the right conditions to make one hydrogen atom but already if there are two protons and two electrons it's not such a walkover and in let's say in a you know balloon filled with hydrogen gas there are I don't know ten to the perhaps ten to the twenty eighth protons and ten to the twenty eighth electrons I'm making up the big nerve and and mathematically the the problem is to find a function of that many variables or three times that many variables in fact and so even if one has given the answer to the problem it's beyond the human mind to to absorb completely what the answer is but yet there are salient features of the answer to this very high dimensional problem that have the significance that that many electrons and many protons combine to form to form many hydrogen atoms or many hydrogen molecules so I worked on that problem for a very long time I was attracted to it because at the same time it was mathematically a deep and interesting problem and it obviously had something to do with the real world so the real world is not of no interest oh not at all not at all so so I find it very attractive to to work on problems that have some connection to the real implications on the other hand I don't at all feel compelled to produce work with practical applications I understand is there again speak very simply a Eureka moment in this process of inquiry that leads to something that you become associated no work so there were there were several the first so I think the the first was that there was a particular number it is roughly it is it is the temperature at which at which hydrogen ionizes and and that that one number is is measurable in the laboratory but and in principle is the solution to a math problem but the exact the the calculation of that number from from first principles rather than from experiment is is very daunting so I discovered I could say the first Eureka moment was was that if one could pin down that number to within a factor of two mmm-hmm then I could prove that under suitable conditions hydrogen atoms of hydrogen atoms form and if I can pin down that number more precisely hydrogen molecules form I then spent a long time trying to calculate that number with sufficient accuracy I wound up getting I think some interesting results and making interesting progress but I think that number to this day is not calculated from first principles with sufficient accuracy to guarantee why atoms and molecules form nope so I think then in the end the the contribution from oh my god 15 years or so husband that I spent on this problem was was to understand on some level why it is that that many that if you put many particles in a box and shake well you get atoms and molecules and so why we see atoms and molecules in nature the preceding textbook explanations were baloney because they I mean what for a very simple reason that people interested in the problem know perfectly well which is that electrons are what's called fermions again maybe your your audience will understand this very well there are fermions and bosons and if electrons were bosons atoms wouldn't form and the world wouldn't form them in the way it looks now everything would implode right and that's not what happens and if you look at the usual explanation for why for my atoms and molecules form these equities alleged explanations apply equally well if the electron is a boson so it couldn't possibly be right I'm gonna embrace a word that you came up with baloney about the wrong route you can just say how in
the process of intellectual discovery do problems get stuck do who is emerge that in the end have no validity oh okay well so how does one get stuck let me let me give my favorite analogy so doing research in math is like playing chess against the devil in which however you get to take back moves but the devil does not so in the in the first many games you are simply immediately crushed but eventually by sheer luck you you make a clever move and it takes instead of the devil crushing you in ten moves it takes fifteen moves oh well maybe this is a good idea why is this a good idea why did the why did the devil have a little bit of trouble crushing me well let's try a slightly different move and see whether it also makes trouble nope nope that other move makes no trouble and I'm crushed in ten moves well alright so when one begins one begins to build up a set of ideas in math as opposed to chess it's it's very important to look at well I shouldn't say anything about chess I play on a very low level okay but in but in matter it's very important to look at examples if you want to understand some big general thing you'll have to try to find a little simple example in which the general idea nevertheless resides and it can be a great art to come up with a good example or even with what an example means because if you pose the same general problem in different ways then the meaning of an example changes okay back to chess so alright eventually you get enough understanding to know what an instructive example might look like and you come up with one or a few and you solve easier versions of the problem armed with that you go back to the full problem and there is then a middle stage between between a long period of being completely stuck and and an end game in which you see basically what to do but but it doesn't quite work and then that that's actually the most fun because then there's a a kitchen of ideas and you put ingredients together and see what works and and on any given day you can make a new discovery or realize that you overlooked something in your last month's work is baloney seems to me one attribute that the chess player shares with the devil yes stubbornness ah so alright the in in this model well alright so I remember from what is it from the Master and Margarita the devil saying we'll consider consider only a very short time period say a thousand years so alright maybe from the point of view of the devil not much patience is required from the point of view of the mathematician one of the main qualifications with a job is tolerance of frustration so so you have to be you have you have to continue even while well being hopelessly stuck in in my case that arises from love of and obsession with the problem at the moment the role of the wards is in the culture of mathematics okay is significant and you begin to get a number although still shockingly young but let's talk about what you got the field metal floor alright let me see I think for basically for the work that I had done at the University of Chicago and at Princeton before it but probably not not for any of the work that I did at Princeton afterwards but what was that was it so they were well so all right I'm going to say but it's it's a speculation because the you never see here no but alright nobody told me so so there was one well I think there were there were two things that were probably most spectacular when one was called the duality of h1 and BMO and and so again let me let me guess the the level of the audience so h1 is something that comes from complex variables and so for people who don't know what complex variables means it's one of the great achievements of 19th century math if you look at two dimensional incompressible fluids or or electrostatic fields and flow of current or the making of maps that don't distort angles or various other things or all of all of these are turn out to be mathematically the same thing and by by changing your point of view from let's say the making of maps to the study of electrostatics and back again but by bouncing from one point of view to another one what builds up a deep and very useful and beautiful body of knowledge that that wouldn't at all have been discoverable by by just one point of view that's complex variables on the other hand BM so that's that's that's h1 I'm sorry which did I say any weights h1 that arises from complex variables BMO originally arose from a study of elasticity but maybe it's most easily explained with probability imagine that that you you've you enter in a casino with a roulette wheel and you're allowed to place any bets you like the bets may be conservative or they may be absurdly large and grow more and more absurdly large with time and and the question is what does a conservative strategy really mean and if you think about it carefully you arrive at the notion of BMO bounded mean oscillation the oscillation is the oscillation of your fortune over time even though again that's not how it was discovered that's I think a natural way to explain it and I discovered that these two ideas are different sides of the same thing the technical the technical thing to say is that as Bonoff spaces they are dual to each other so so this is a connection between two things each of which seem very interesting in its own right especially complex variables but yet which apparently excited happens from no the no connection one of one of my one of my personal satisfactions came from from discussing one of the people who from discussing with with one of the people who did the pioneer work on BMO and and I explained to him that that h1 and BMO are duel and he misunderstood he thought I was conjecturing it rather than saying that I had proven it and he said to me that's ridiculous they have nothing to
do with each other and that he was a very nice fellow and had no intention of putting me down but but that was his honest view but that's one of the issues in the whole question of intellectual progress the amount of times that people hear that's ridiculous and see right right is proven otherwise um so one of the characteristics of a good mathematician I think is is to be willing to ignore that's ridiculous ridiculous things are usually false but when they are true they are pretty good I'm going to now let you be the age you are now okay you're no longer prodigy can i play now right that certainly accomplished but not a prodigy what is that this and I mean this seriously although not terribly seriously in the question of how one thinks at a later point in life from that golden young man Matt mathematician how one thinks oh is it any different I mean how do you think differently now I don't know analyze differently well I I think differently about which problems to choose I'm willing to spend much much longer on one problem that that's that's not a recent development again I think maybe starting in the 80s I embarked on a 15 year project but but I'm willing to spend much longer on one on one project I wonder I'm certainly not as quick as I was but I'm somewhat less ignorant hey it's very hard for me to compare my present self with my past self because well it's it's always hard to understand any human being and in particular one's self well then let's stay with yourself okay to say okay what is fascinating you particularly at the moment at the moment alright I'm interested in several different things the one that I have been pursuing the longest and in fact about 15 years is his notion of fitting a smooth object to data so let's say as a poetic example imagine that this room on a dark night is filled with fireflies if the fireflies are are sort of uniformly distributed in the room there is no nice smooth surface that passes through or close to all of them but it's conceivable because of heat currents or I don't know what that there is a night that there is a nice smooth surface that passes if you're more close to all of the fireflies that is actually a fundamental idea in statistics because perhaps one quantity is related to one or several others you don't know in advance what the relationship is but you have some data the data or the fireflies how do you get from the data to the to the relationship will you guess that the relationship is smooth it may or may not be but if it is then then all right find find a smooth relationship that agrees with the data and if if there is no such because the data just are in a in an unfortunate position then your guess is wrong discover that so that problem translates into into perhaps a dozen technical questions in math and they have fascinated me and alone and with co-authors I've have succeeded in solving some of them and others I have absolutely no idea how to crack and still others I made some progress on and hope to work them out so that's one problem the thing with that and remembering the importance of your mentor yes to you yes do you then distribute some of those questions to your graduate students oh yes oh yes so some of some of the work that I have done on on this class of problems is joint work with first with my grad students then with now with my former grad students so I learned from them is there another family of problems you're taking on right yes yes then with with a friend at Columbia with whom I'm going to Skype later this afternoon I'm working on a series of papers about graphene so graphene is is one layer of carbon atoms let's say from from the sir from the writing surface of a pencil it has very remarkable properties they are observed experimentally they are perhaps of practical importance they were many of them not all many of them were predicted by a back-of-the-envelope approximations and my friend and I are working to understand a much more realistic model of of graphene taking into account that for example it's not actually a collection of little dots it's more a collection of atoms and the electrons that flow among them and and to try to understand why this behavior occurs and and in fact to predict other behavior which which was not so far experimentally observed so so I'm actually excited that we've that there is there were a couple of teams of experimentalists working to verify some of our theoretical predictions that hadn't been made using back-of-the-envelope calculations so to conclude we could go on a long time but just to finish out what I see is the habit of challenging assumptions yes a kind of benign cussedness in in the face of people telling you what's true or not feeling with that swell foot and continuing ongoing curiosity in your field woods I would guess is as fresh as when you were oh yeah when you were young oh yeah thank you very much thank you you're a good interviewer yeah
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