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“No One Had Ever Accused Me of Proving a Theorem Before” Gunther Cornelissen, Jan van Neerven Interview with Kenneth Ribet NAW 5/18 nr. 2 juni 2017 115 Gunther Cornelissen Jan van Neerven Mathematical Institute Delft Institute of Applied Mathematics Utrecht University Delft University of Technology [email protected] [email protected] Interview Kenneth Ribet, winner Brouwer Medal 2017 “No one had ever accused me of proving a theorem before” On April 12th, 2017, Gunther Cornelissen and Jan van Neerven interviewed Ken Ribet at the classes. I was in a programme that, believe occasion of him winning the Brouwer Medal 2017. it or not, was called the ‘maximum learn- ing programme’. The students in this pro- Professor Ribet, congratulations on win- everyone up to the same level, but instead, gramme went from class to class together ning the Brouwer Medal! We would like to they would identify specially talented stu- (this was called ‘block programming’), we ask you some questions about your scien- dents and put them in exceptionally strong got to know each other very well and we tific career and endavours. had among the best teachers in the high school, so I had a very good preparation High school: the ‘maximum learning pro- in mathematics, science, English and so- gramme’ cial studies. Foreign languages were not block programmed because some people How was your high school education? You took French and some people took Span- went to the same high school as Feynman ish, but all of the core courses were block (and Madoff, for that matter): the no-longer- programmed.” existing Far Rockaway High School. “I grew up in a part of New York City that Then was it already clear before you en- is pretty far away from the centre. Students tered high school that you had a ‘science- in New York City who were very oriented talent’? towards mathematics or science tended “Well, the New York school system identi- to apply to specialised high schools, like fied me as a ‘smart person’, but some of the Bronx High School of Science, Stuyve- the students with me in the programme sant High School, or Brooklyn Tech. I didn’t were talented in English, social studies or want to spend hours every day on the bus history. It was not focussed specifically on or the subway, so there was one local high science.” school, and that was my high school. At that time, the educational system How was the mathematics education? had not yet developed this idea that lots Gil Cavalcanti Photo: “It was great. First of all, I learnt a lot of resources should be spent on bringing Ken Ribet at the NMC 2017, holding the Brouwer Medal from the teachers, but we also had a math 116 NAW 5/18 nr. 2 juni 2017 Interview with Kenneth Ribet Gunther Cornelissen, Jan van Neerven team and I learnt a lot from the other stu- programme for science students at Brown be I will major in chemistry.’ And over the dents. There is one fellow who went on University, which is actually the university I summer, when I learnt about epsilons and to do research mathematics, another be- ended up attending and I was attracted to deltas, I completely changed my mind and came a specialist in mathematical prob- the university because I enjoyed that sum- decided that mathematics was going to be lems and he published many books about mer so much. We had three courses. One my subject. In fact, by the time I got to that. We were always pushing each other in computer programming where I learnt university, I decided to abandon chemistry to learn clever techniques to solve ge- how to write programmes in original For- completely.” ometry and algebra problems. I learnt a tran (typed into punch cards); another in little bit of calculus from these other stu- calculus that was taught by an engineering Your story on epsilons and deltas is quite dents even before I had my first calculus professor, who had absolutely no interest interesting. What is your opinion on the course.” in limit arguments and mathematical sub- big calculus books that nowadays precede tleties, but he taught us how to compute a decent class in analysis? Did you also take part in competitions, and it was great! That’s how you should “I think the American system is fairly rea- such as Math Olympiads? learn calculus at first, through calculations, sonable, that students learn calculus and “Math competitions weren’t so well organ- and I really liked that. Then there was a then they take a separate course in real ized in those days, but we did a few, and third course in material science — which analysis and they learn what really goes I was OK. I was not a big star but I would coincidentally is the specialty of my older on in calculus. The reason the books are sometimes get an honourable mention.” daughter — but in that course, I learnt ab- so thick is simply that the publishers want solutely nothing. to be able to sell to the largest number It is quite surprising that these kind of spe- There was another thing that was some- of universities and each university has cial schools already existed in those days. what special. We had a kind of ‘math tal- some necessary conditions that have to Nowadays it is rather common to offer ent class’, an additional math class, when be satisfied by a calculus book, so it tries special programmes to talented students. I was in my last year of high school, where to satisfy all of them. So you get these “My high school had something like 3000– we did a lot of problems from a book big books, it is a big juggernaut, with sup- 4000 students, and this programme was from around 1891 called ‘Higher Alge- plementary material, online homework, just for a very small number, something bra’ by Hall and Knight.1 It was just full guide for the instructor, guide for the stu- like 50 students per year.” of tricky problems from the competitions dent, solution manual. All of this has to in Cambridge University and I learnt a lot be prepared, so the whole thing is a very What were the typical topics and what was of strange mathematics; algebraic manip- big project.” the level? ulations, discrete mathematics, all sorts “Just the standard high school topics, but of topics.” Undergraduate years at Brown University: during the summer of 1964, before my interacting with Ireland and Rosen last year in high school I was in a summer In hindsight, has this benefited you? “Oh, I am sure. I got very excited about Then you went to Brown University. How math, and by the summer after I left high was that? Short biography of Kenneth A. Ribet school, I really understood about epsilons “Oh, I loved it. Brown — where my younger Kenneth Alan Ribet was born on 28 June and deltas for the first time, I found it re- daughter is a student now — is the same 1948 and grew up in New York, where he ally great. So I was full of enthusiasm and now as it was back then: there is lots of attended a selective programme at Far ready for university. research, but there is a big focus on the Rockaway High School, before entering Godement used to say that in France, undergraduates; on giving them lots of Brown University to study mathematics. the students in the Lycée were just stuffed attention and lots of time and opportuni- He received his PhD from Harvard, di- full of information and by the time they got ties to learn different things. The profes- rected by John Tate, in 1973. After some to university, they knew quite a lot but they sors in the Brown Math Department liked postdoc years at Princeton, he moved were very tired. In the USA, students learn me and were willing to spend lots of time to Berkeley, where he has been a pro- much less, but when they get to college, with me. The first course I took was a year- fessor ever since. they are really ready to learn. I think that long course in linear algebra and multi- He published about 60 papers and had was true for me. I was very excited about variable calculus, but it was an honours around 25 graduate students, and was going to university, I was 17 years old and course, so the linear algebra was abstract an editor of many journals and book I was in great anticipation of what I would linear algebra, which I learnt for the first series, including the acclaimed Springer learn there from these professors, whom I time and which I thought was absolutely Graduate Texts series. considered to be humungous figures.” beautiful. He is a member of the U.S. National I also liked multivariable calculus. We Academy of Science, and has received But you enrolled in chemistry. had a book called Modern Multidimension- the Fermat Prize in 1989, and, this year, “That is not exactly correct. What hap- al Calculus by Monroe 2 and I never exactly the Brouwer Medal of the Royal Dutch pened is that I had a very strong high knew what was going on, but I liked the Mathematical Society. Since 2017, he school chemistry teacher. When I was grad- fact that there was actually a formal defini- serves as President of the American uating from high school I thought: ‘You tion of what a differential was, as a linear Mathematical Society.
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