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Geometry or algebra? The Cambridge approach

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First year at Cambridge
Michael Atiyah Mathematician
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When I first came up I didn't have much exposure to the faculty, the staff. I was on my own. I went to the library, I read books, I was given the literature and so on. And… but once the term started, well of course your first exposure is your supervisors and the characters vary quite a bit. My first clear memory is being supervised by Besicovitch who was a real character – a big Russian, large shock of white hair and strong Russian accent and very particular kind of questioning techniques – and so he was a very impressive figure. He made an impact on me.

The person whose mathematics I found most interesting at that stage was Todd. I remember reading his book, which I found very fascinating – all this algebraic geometry in the old style – although as a character he was the opposite extreme, very self-effacing, quiet, difficult to converse with, but I went to his lectures. So I found the geometry was still the subject I enjoyed most. I benefited quite a bit from the lectures. I went to… I suppose, again having come out of the Army I was just full of enthusiasm… I went to enormous numbers of lectures, you know all the lectures you could go to, all the optional lectures. I remember in my second year I think I was going to four lectures a day, six days a week, whatever it was, dashing around on a bicycle from here to there. Probably quite ridiculous, you can't really benefit from all those lectures, but it was… you know, I really felt I should get everything I could out of what was going.

And the other thing of course, you benefit a lot […] is your fellow students. Especially in Trinity, there were large numbers of other mathematicians, a lot of them very able. You got to know them, and you spent a lot of time… I mean one of my early friends there was John Polkinghorne and we used to spend a lot of time discussing and arguing with Frank Adams and Ian MacDonald. It was a good year. We had a lot of able mathematicians in that year and we spent a lot of time discussing things amongst ourselves. I think you got more benefit that way than you did actually from the people who were there to be supposed to be teaching you.

[Q] So Adams, Polkinghorne and MacDonald were all in Trinity?

Yes, Adams, Polkinghorne, MacDonald, and also the subsequent Dean Mackay, the Lord Chancellor. They were all in our year, and John Aitchison became Professor of Statistics. Yes, it was a very good lot, all in Trinity, and I think we had the top few people in the Tripos all that year, so it was a particularly good year and I think you benefited a lot from the stimulus that they provided – and the competition. I mean you were aware that when you came in, you'd been at school, you think you're the bees-knees; then you come to Trinity and it's a little while before you realise… find out what the competition's like and it was pretty competitive for the first year or so until you knew where you stood. Ronald Shaw was another of the interesting lot.

[Q] Were they all taught by Todd, or were you specifically allocated Todd?

Well, you'd be taught by different people, different years, different terms for different subjects. So, I'd get taught by Besicovitch to do analysis; I'd be taught by Todd to do geometry; I'd be taught by Kemmer to do the physics side – so I think they were all, went through the same collection of supervisors, more or less. Subsequently I got Todd a bit more often when it was clear my interests were geometrical. But at the beginning it was everybody was cycled round all the supervisors really.

Eminent British mathematician Sir Michael Atiyah broke new ground in geometry and topology with his proof of the Atiyah-Singer Index Theorem in the 1960s. This proof led to new branches of mathematics being developed, including those needed to understand emerging theories like supergravity and string theory.

Listeners: Nigel Hitchin

Professor Nigel Hitchin, FRS, is the Rouse Ball Professor of Mathematics and Fellow of Gonville and Caius College, Cambridge, since 1994, and was appointed to the Savilian Professorship of Geometry in October 1997. He was made a Fellow of the Royal Society in 1991 and from 1994 until 1996 was President of the London Mathematical Society.

His research interests are in differential and algebraic geometry and its relationship with the equations of mathematical physics. He is particularly known for his work on instantons, magnetic monopoles, and integrable systems. In addition to numerous articles in academic journals, he has published "Monopoles, Minimal Surfaces and Algebraic Curves" (Presses de l'Universite de Montreal, 1987) and "The Geometry and Dynamics of Magnetic Monopoles" (Princeton University Press, 1988, with Michael Atiyah).

Tags: Cambridge, Trinity College, Abram Besicovitch, John Todd

Duration: 3 minutes, 39 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008