Interview at CIRM : Curtis McMullen transcript

[Music] H um yes it's it's I find it puzzling because um when I was young I I was interested in logarithms and U powers of two uh but I really didn't like math I hated doing addition exercises anything repetitious uh so I didn't like math in school until we started doing geometry which I really enjoyed uh partly because it was continuous progress you could do it at your own pace uh partly because there were no equations um but um I think what really sparked my imagination in in mathematics was not so much math itself as computers and I grew up in a small town in Vermont 2,000 people and um uh I in sixth grade I I found a book in uh my father's closet which uh was a guide to Fortran 4 programming language and so I learned there was such a thing as a computer program and I really wanted to try this and uh they had a computer at the University in Vermont and a teletype in the high school which was 10 mies away and so I went and programmed on the teletype which would print 10 characters per second and I programmed The Game of Life and um a few other things I found that really exciting I liked the um immediate feedback and um in mathematics there's a lot of logic and reasoning but um if if you make a mistake in a proof it's very hard to know but if you make a mistake in a computer program it doesn't work at all so I really enjoyed having this sort of ratification of uh of what I was working on so I became interested in computers I would say more than math um then when I went to college I was open to many different um disciplines I went to a small liberal arts college Williams College in Western Massachusetts and studied uhy pschology and philosophy and American literature and uh Cinema and uh but also physics and math and what I really liked about math was that I could sometimes do the homework during the class and then I had more free time so I think I what I really valued was I mean I enjoyed math but I also really enjoyed having unstructured free time and it gave me this uh so then when I graduated from college College I didn't really know what I wanted to do so I went to Cambridge England for a year on a scholarship and I um took math courses there and I discovered I really didn't like the way they taught uh College in England and I had one application with me which was to Harvard University for graduate school and I sent this off and I I barely got in so then I went and uh and um I was suddenly surrounded by people who were real mathematicians and I hadn't really had much education in mathematics and it was very exciting and very intimidating at the same time um and I thought you I might very well have a career in some some other field I would probably complete my PhD in math but who knows what would happen after that um and then I um I got to know some more about the world of mathematics and I have to say that France and and the IHS and the French Alps and my image of mathematicians in France played a big part in reshaping how I thought about mathematics as a career and how I thought about mathematicians as people and I I sort of heard some very romantic stories about mathematicians sitting silently around a fire in a small cabin in the Alps and uh and about what the IHS and Bureau was like and um so this began to change my interest in mathematics or my vision of what it was to be a mathematician um that it wasn't all about problem solving and winning the puam exam or the Olympiad and by the way I wasn't very good at those problem solving contests so in some sense I was missing part of what um is expected of a research mathematician but the thing that um I was good at my teachers would say was asking the right questions and uh I Now understand that in research this can be as important as having the technical power to answer the questions um uh so uh luckily that helped benefit me eventually in my career but the I would say the next thing that happened was I began um becoming very interested in in a connection between computers and Mathematics which had to do with some beautiful pictures of FR fractals that David Mumford was drawing at um Harvard and I became his computer programmer and I really enjoyed the graphics and the uh the the visual artistic uh patterns that would emerge and I enjoyed the computer programming and I enjoyed starting to learn the mathematics behind it and um uh but then um it turned out that David mford who's really an algebraic geometer didn't consider this as a field in which he could be an adviser adviser for me um and Harvard is pretty small so there were only um a a small number of field in which one could work if you wanted to really work within the discipline of your adviser but I was a little headstrong and I got a hold of some lecture notes that Dennis Sullivan had written and he was at that time a um professor at the IHS and I started a small seminar and and I lectured on these notes and learned a lot about what was going on in complex Dynamics which I found to be a great subject uh I really liked it because one of my favorite subjects in math was one complex variable it and it's in a way very Elementary and very geometric and yet some really magical things happen um and emerg there and so then I I I was entering my fourth year of graduate school and I had no thesis adviser and I had no thesis and the chairman David mford sort of took pity on me and called Dennis Sullivan in New York and said would you talk to this graduate student of ours he seems interested in what you're working on so I flew down to New York City and met Dennis and after meeting him a couple of times I said well would you be my thesis adviser and since he was a professor at the IG he had he had had no graduate students basically maybe he had W when he was at Princeton so he asked what that would involve and I said nothing and then he sort of thought for a moment he said well you better come with me to France this fall then and um and so I went to to to the IG for the fall semester and I met Steve smil at lunch at the IG the first week I was there and he gave me a problem which became my thesis problem and I worked on it very hard through a whole rainy fall in bu and then um that became my thesis and it was it was very exciting and uh so I went from having no adviser to to having a good result and um so when I was about to graduate I I had several possible career paths including one maybe working more uh with computers I had been working in the summers at IBM's Research Center um but I realized that it was it was very hard to move back into mathematics if you if you left so I thought I would I would give it a chance and now here I am [Music] yes this is pretty hard I I I um so I like learning new things and I like um answering or working on questions that are to me seem obvious but that maybe haven't been addressed even by the experts in the field so I often in stumbling into Fields where I'm not an expert and trying to do something which uh um maybe people consider well known or something like this but um uh so my research directions are are um originally I worked in complex Dynamics so the dynamical systems over the complex numbers with these beautiful Julia sets and so on and um and uh Dennis Sullivan was probably the leading mathematician in that area as well as du and hubard who I met here in France um at the time and uh and then I but but I also after graduating I went to uh Princeton University where where thirston was at one of the most active stages of his career and I learned a fantastic amount from being around him and the community that uh he had formed so that was three-dimensional hyperbolic geometry that was um became another element of um my mathematical world and there's a beautiful idea of Sullivan's um called Sullivan's dictionary which says here's here's this discipline of Dynamics here's this discipline of geometry and actually you can sort of go back and forth between these two and there's there's and he had just proved a very deep result called the no wandering domains theorem by taking a famous result in the theory of Clan group and more or less just translating it using this dictionary and I found that mode of doing mathematics fantastic uh and uh his his um ability to to capture a field in a broad and Visionary way really um inspired me so anyway those so those became my main um fields and I think that's still the area I feel most comfortable complex Dynamics remon surfaces tyer Theory quasi conformal Maps um but I eventually ended up at Harvard and those fields are not very well represented there um and one of my best friends uh my colleagues at among my colleagues at Harvard's was Dick gross who's a number theorist representation theorist so I started to learn in a kind of um amateurish way um uh how to do some number Theory how to do some algebraic geometry and um and I'm still I'm a little bit like a dilatant I'm like somebody who has taught thems how to play the guitar so they don't actually know how to do it right but uh but I'm a deletant in many different subjects and so what I'm working on now um involves all sorts of different things uh K3 surfaces cem numbers low-dimensional topology um and uh so it's a it's a broad field and it doesn't have a name but to me and to many of the other people working in the field it's very clear that it's a single [Music] subject well this is interesting because I I wasn't on the fields metal committee so um I I have to say I don't really know but I can tell you what I had personally considered um uh the the work that I was very happy with at up to that time so I I think there were two areas um where I had had established some some good results one was on the classical problem of solving polinomial equations like the quadratic formula so this was something smil got me started on the question was whether you can solve polinomial by iterating rational maps that depend in some simple way on the equation you're trying to solve and the answer turned out to be um no for degree four or more and uh and and yes for degree three there was a new algorithm that people had not discovered so I found a new way of solving cubic polinomial and I uh proved that you couldn't solve fourth deegree pooms and it sounded very strange because what people know classically in mathematics is you can't solve fifth deegree polinomial so why can't you solve fourth degree polinomial it was because of the very strict rules smil had imposed on what you're allowed to do so with Peter Doyle we weakened those rules and then we discovered we could solve fifth degree polinomial and so that was that was one of the most exciting uh um research programs that I that I had carried through um when I was young um and the solution involved a beautiful fractal object with the symmetries of the do decahedron and so I've I think I've always been attracted to low dimensional concrete but perhaps canonical mathematical objects and it was amazing to sort of discover a new one and draw a picture of it on the computer of something no one had ever seen before it was like finding a new planet or maybe a planetoid Beyond Pluto um so that was one thing but I think maybe the more significant thing was there was something called cross Theta conjecture which is a problem very classical problem in complex analysis but uh it could be viewed as a Lynch pin to prove a a very deep result of Bill thirston in fact the one for which he uh got the fields metal I would say this geometrization conjecture which was recently Revisited by Pearlman and you know resulted in the proof of the panre conjecture in the end anyway thirston had a very geometric approach to this problem and very few people were able to absorb all of the mathematics necess necessary to understand it um and by studying this this analysis problem I was able to give a new analytic proof of the hardest step in that theory so um uh I I think that those two things were probably um what this award was for but I I have to say um that uh so Litman Bears uh who was one of my mentors also a complex analyst used to say mathematics is something we do for the begrudging admiration of a few close friends and I never expected to get more out of it than that and I think mathematics is plenty rewarding without any bigger recognitions and I felt very lucky to um have have even been considered for the fields medal I think there are many other people who would have been great candidates those [Music] years okay so Eureka moments okay so the so um I let me try to interpret your question so um it's definitely true that when you're immersed in a certain kind of mathematical problem that you are really struggling with some sort of central difficulty and um you get to know the problem inside out and and this difficulty uh becomes a sort of something you face personally and can carry around with you look at from a different aspect every day and then if you're very lucky at some moment you just understand how to get through it and um so I remember very well uh um was probably my first moment of this type so um actually this I can draw at the Blackboard but maybe I should not now because so so when I met um hironaka who was a professor at Harvard when I was a graduate student he told me a problem um in uh about the Computing the dimension of a certain fractal shape based on drawing the letter M and then drawing it again inside of itself over and over and uh interestingly enough he dis had discussed this problem in a popular book for the Japanese public and he had studied the problem himself he wrote about it in this popular book but he didn't know the answer and uh so I thought wow this can be a problem for me to work on and when you're a young graduate student it's not clear what is uh worth pursuing that will make a difference to other people so I started working on this problem and I really knew it inside out at some moment and it was becoming almost impossible to write down exactly my understanding of it there were very complicated formulas there were a lot of different mechanisms going on but I remember walking home from The Graduate School about 8:00 at night it was dark out I was crossing a street in Cambridge and I remember very clearly when I got to the other side of the street I knew the answer to this problem and so that was uh that was a and I and in in my experience um real insights often happen when I'm walking around they almost never happen by sitting down at a desk and doing a calculation uh um in fact I think I need some kind of stimulation whether it's by working in a cafe or by moving around or something uh um talking to other people to be able to really move forward on uh an argument if I already know what I want to say I can write down and work on it but being inventive or creative is not something that comes easily to me sitting down um so that's that's one example of that was maybe my first example of a real Eureka moment [Music] I think uh serm is great and I think in general uh I have a very positive feeling about mathematics in France I as I said my thesis adviser although he's from Texas was a professor at the IHS and um you know there's also many other fantastic mathematicians in France uh when um there was a conference in honor of Pearlman solution of the pon CR conjecture it was at the institute on Pon and um the the there was a dinner with the mayor of Paris and this would never happen in the United States uh the mayor said there are more streets named after mathematicians in Paris than in any other city in the world uh so I think there is a um there is a real appreciation of mathematics um which Sam represents as a um a part of culture and by a part of culture I mean something akin to um to music to art as well as to science it's not that it's not scientific but it's that it's a um it's the intellectual side of the process I think is valued and respected um here in a way that you don't feel all the time when you're a university professor and you're teaching undergraduates perhaps who don't want to learn calculus so I feel there's a lot of um uh joy in coming to a place where mathematics is considered as a special discipline mathematicians are considered special and and of course it's just uh it's very um super relaxing to have to not think about anything so the your meals are there the Kon is there for recreation the lectures are happening and uh and people that you might want to talk to all the time are suddenly all around you for a week uh so it's it's um yeah I think Sam is great and I I really I visited here many many times and uh I'm enjoying this visit as [Music] well