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Interview with Abel Laureate John Tate

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Interview with Abel Laureate John Tate Interview with Abel Laureate John Tate Martin Raussen and Christian Skau John Tate is the recipient of the 2009 Abel Prize of the Norwegian Academy of Science and Letters. This interview took place on May 25, 2010, prior to the Abel Prize celebration in Oslo, and originally appeared in the September 2010 issue of the Newsletter of the European Mathematical Society. Education questions. My father had several puzzle books. I Raussen and Skau: Professor Tate, you have been liked reading them and trying to solve the puzzles. selected as this year’s Abel Prize Laureate for your I enjoyed thinking about them, even though I did decisive and lasting impact on number theory. not often find a solution. Before we start to ask you questions, we would like Raussen and Skau: Are there other persons that to congratulate you warmly on this achievement. have had an influence on your choice of fields of You were born in 1925 in Minneapolis in the United interest during your youth? States. Your father was a professor of physics at Tate: No. I think my interest is more innate. the University of Minnesota. We guess he had some My father certainly helped, but I think I would influence on your attraction to the natural sciences have done something like physics or mathematics and mathematics. Is that correct? anyway. Tate: It certainly is. He never pushed me in any Raussen and Skau: You started to study physics way, but on a few occasions he simply explained at Harvard University. This was probably during something to me. I remember once he told me the Second World War? how one could estimate the height of a bridge Tate: I was in my last year of secondary school over a river with a stopwatch, by dropping a rock, in December 1941 when Pearl Harbor was bombed. explaining that the height in feet is approximately Because of the war Harvard began holding classes sixteen times the square of the number of seconds in the summer, and I started there the following it takes until the rock hits the water. Another time June. A year later I volunteered for a Naval Officer he explained Cartesian coordinates and how one Training Program in order to avoid being drafted could graph an equation and, in particular, how into the army. A group of us was later sent to M.I.T. the solution to two simultaneous linear equations to learn meteorology, but by the time we finished is the point where two lines meet. Very rarely, but that training and Midshipman School it was VE 1 beautifully, he just explained something to me. day. Our campaign in the Pacific had been so suc- He did not have to explain negative numbers—I cessful that more meteorologists were not needed, learned about them from the temperature in the and I was sent to do minesweeping research. I was Minnesota winters. in the Navy for three years and never aboard a ship! But I have always, in any case, been interested It was frustrating. in puzzles and trying to find the answers to Raussen and Skau: Study conditions in those times must have been quite different from condi- tions today. Did you have classes regularly? Tate: Yes, for the first year, except that it was Martin Raussen is associate professor of mathematics at Aalborg University, Denmark. His email address is accelerated. But then in the Navy I had specific [email protected]. classes to attend, along with a few others of my Christian Skau is professor of mathematics at the Norwe- choice I could manage to squeeze in. It was a good gian University of Science and Technology, Trondheim, program, but it was not the normal one. Norway. His email address is [email protected]. It was not the normal college social life either, This is a slightly edited version of an interview taken with parties and such. We had to be in bed or in a on the morning preceding the prize ceremony: May 25, 2010, at Oslo. 1Victory in Europe day: May 8, 1945. 444 NOTICES OF THE AMS VOLUME 58, NUMBER 3 study hall by ten and were roused at 6:30 A.M. by a recording of reveille, to start the day with cal- listhenics and running. Raussen and Skau: Then you graduated in 1946 and went to Princeton? Tate: Yes, that’s true. Harvard had a very gen- erous policy of giving credit for military activities that might qualify—for instance, some of my navy training. This and the wartime acceleration enabled me to finish the work for my undergraduate degree in 1945. On my discharge in 1946, I went straight from the Navy to graduate school in Princeton. Raussen and Skau: When you went to Princeton University, it was still with the intention to become a physicist? Tate: That’s correct. Although my degree from Photo by Eirik F. Baardsen/ Abelprisen/Norwegian Academy of Sciences. Harvard was in mathematics, I entered Princeton Abel interview, from left to right: Martin graduate school in physics. It was rather silly, and Raussen, Christian Skau, and John Tate. I have told the story many times: I had read the book Men of Mathematics by Eric Temple Bell. That Germany in 1937 and came to the United States. book was about the lives of the greatest mathema- Can you tell us more about his background? Why ticians in history, people like Abel. I knew I wasn’t did he leave his chair, and how did he adjust when in their league and I thought that unless I was, I he came to the States? wouldn’t really be able to do much in mathematics. Tate: His wife was half Jewish, and he eventu- I didn’t realize that a less talented person could ally lost his position in Germany. The family left still contribute effectively. Since my father was a in ‘37, but at that time there weren’t so many open physicist, that field seemed more human and ac- jobs in the United States. He took a position at the cessible to me, and I thought that was a safer way University of Notre Dame in spite of unpleasant to go, where I might contribute more. But after one memories of discipline at a Catholic school he had term it became obvious that my interest was really attended in his youth. After a year or two he ac- in mathematics. A deeper interest, which should cepted an offer from Indiana University and stayed have been clear anyway, but I just was too afraid there until 1946. He and his wife enjoyed Bloom- and thought I never would be able to do much ington, Indiana, very much. He told me it wasn’t research if I went into mathematics. even clear that he would have accepted Princeton’s Raussen and Skau: Were you particularly inter- offer in 1946 except that President H. B. Wells of ested in number theory from the very beginning? Indiana University, an educational visionary, was Tate: Yes. Since I was a teenager I had an inter- on a world tour, and somehow Indiana didn’t re- est in number theory. Fortunately, I came across spond very well to Princeton’s offer. Artin went to a good number theory book by L. E. Dickson, so I Princeton the same year I did. knew a little number theory. Also I had been read- Raussen and Skau: Artin had apparently a very ing Bell’s histories of people like Gauss. I liked special personality. First of all, he was an eminent number theory. It’s natural, in a way, because many number theorist, but also a very intriguing person; wonderful problems and theorems in number the- a special character. Could you please tell us a bit ory can be explained to any interested high-school more about him? student. Number theory is easier to get into in that Tate: I think he would have made a great actor. sense. But of course it depends on one’s intuition His lectures were polished: He would finish at the and taste also. right moment and march off the scene. A very Raussen and Skau: Many important questions lively individual with many interests: music, as- are easy to explain, but answers are often very tronomy, chemistry, history…. He loved to teach. tough to find. I had a feeling that he loved to teach anybody Tate: Yes. In number theory that is certainly anything. Being his student was a wonderful ex- true, but finding good questions is also an impor- perience; I couldn’t have had a better start to my tant part of the game. mathematical career. It was a remarkable accident. My favorite theorem, which I had first learned from Teachers and Fellows Bell’s book, was Gauss’s law of quadratic reciproc- Raussen and Skau: When you started your career ity, and there, entirely by chance, I found myself at at Princeton you very quickly met Emil Artin, who the same university as the man who had discovered became your supervisor. Emil Artin was born in the ultimate law of reciprocity. It was just amazing. Austria and became a professor in mathematics Raussen and Skau: What a coincidence! at the University of Hamburg. He had to leave Tate: Yes, it really was. MARCH 2011 NOTICES OF THE AMS 445 Raussen and Skau: You wrote your thesis with his many friends, give a good picture of him. He Artin, and we will certainly come back to it. After started Princeton graduate school in philosophy, that you organized a seminar together with Artin a year after I started in physics, but he, too, soon on class field theory.
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