John Tate - The Abel Prize interview 2010

Video Description

0:00 Glimpses of the Abel Prize ceremony [In Norwegian] 0:23 Speech by Nils Christian Stenseth, President of the Norwegian Academy of Science and Letters [In Norwegian] 1:15 Tate Receives the Abel Prize from His Majesty King Harald V of Norway 1:41 Interview start [English]. Your father was a professor of physics at the University of Minnesota. We guess he had some influence on your attraction to the natural sciences and mathematics. 4:06 You started to study physics at Harvard University. This was probably during the Second World War? Study conditions in those times must have been quite different from conditions today. Did you have classes regularly? 6:25 Graduation and on to Princeton 7:10 When you went to Princeton University, it was still with the intention to become a physicist? 9:18 When you started your career at Princeton you very quickly met Emil Artin, who became your supervisor. Can you tell us more about his background? Why did he leave his chair, and how did he adjust when he came to the States? 11:27 About Emil Artin 13:12 You wrote your thesis with Artin. After that you organized a seminar together with Artin on class field theory. Could you comment on this seminar: What was the framework and how did it develop? 15:29 On Tate’s thesis 18:25 The title of your thesis was Fourier Analysis in Number Fields and Hecke’s Zeta-Functions. Atle Selberg said in an interview five years ago that he preferred—and was most inspired by—Erich Hecke’s approach to algebraic number theory, modular forms and L-functions. Do you share that sentiment? 21:05 Good definitions and fruitful concepts, as well as good problems, are perhaps as important as theorems in mathematics. You excel in all these categories. Did all or most of these concepts grow out of your thesis? 25:18 Among the Abel Prize laureates so far, you are probably the one whose contributions would have been closest to Abel’s own interests. Could we challenge you to make a historical sweep, to put Abel’s work in some perspective and to compare it to your research? 27:42 The Hasse principle in the study of Diophantine equations says, roughly speaking: If an equation has a solution in p-adic numbers, then it can be solved in the rational numbers. It does not hold in general. There is an example for this failure given by the Norwegian mathematician Ernst Selmer… 30:39 In the arithmetic theory of elliptic curves, there have been major breakthroughs like the Mordell-Weil theorem, Faltings’ proof of the Mordell conjecture, using the known reduction to a case of the Tate conjecture. Then we have Wiles’s breakthrough proving the Shimura-Taniyama-Weil conjecture. Do you hope the next big breakthrough will come with the Birch and Swinnerton-Dyer conjecture? Or the Tate conjecture, maybe? 32:14 Number theory stretches from the mysteries of the prime numbers to the way we save, transmit, and secure information on modern computers. Can you comment on the amazing fact that number theory, in particular the arithmetic of elliptic curves, has been put to use in practical applications? 33:32 Do you have an ongoing personal relation with Jean-Pierre Serre? 34:49 Alexander Grothendieck. Did you meet him while you were in Paris or maybe at Harvard? 35:51 Did you follow Grothendieck’s program reconstructing the foundations of algebraic geometry closely? 36:33 Mathematics - A young mans game? 38:09 Did you read the masters of number theory already early in your career? 39:07 You have had some outstanding students who have made important contributions to mathematics. How did you attract these students in the first place, and how did you interact with them, both as students and later? 40:44 Do you stay in touch with former students? 41:16 Is there any particular work from your hand that you are most proud of, that you think is your most important contribution? 43:35 Would you consider yourself mainly a theory builder or a problem solver? 44:43 Look back on how you came up with new concepts or made a breakthrough in an area you had been working on for some time. Did that usually happen when you were concentrated and working intensely on the problem, or did it happen in a more relaxed situation? 48:14 What developments can we expect in mathematics and particularly in your own field, number theory? 51:26 Are you just as interested in mathematics now as you were when you were young? 52:17 Mathematics, art or science? 54:35 Have you tried to popularize mathematics yourself? 55:47 How can mathematicians communicate better to the general audience? 56:46 Interests outside of mathematics Read the full interview in Notices of the American Mathematical Society: https://www.ams.org/notices/201103/rtx110300444p.pdf Abel interview 2010: John Torrence Tate. Interviewed by mathematicians Martin Raussen og Christian Skau. Produced by UniMedia