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Talks at Princeton

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How mathematics can become an obsession
Michael Atiyah Mathematician
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Well my research at the institute, in terms of my own published papers, ended up, there was… I did this work on complex analytic connections in fibre bundles, which was partly influenced by Serre, and I talked about it in Mexico which was how you can describe Chern classes as obstructions and doing things in terms of sheaf cohomology. So that was one of the things which partly I learnt from Serre and partly I put together other bits of connections.  Well, it arose out of my own original work on fibre bundles, but that was a dimension of one and then I learnt the general theory and what was going round. And then I pursued in much greater detail the classification of bundles on elliptic curves, and that was the other sort of topic.And aAgain Serre was quite interested in that.

And the third one was this rather odd paper I wrote about the Krull-Schmidt theorem for […] sheaves, which arose again out of my discussion with Serre and he encouraged me and I wrote up this little rather abstract paper. The one on classification of bundles of elliptic curves, I do remember rather clearly, because I was working on that I think over the summer, when we did this big tour. And I remember very clearly these long drives – you know, in America you drive for sort of five hours non-stop across these big spaces, nothing much distracts your attention, not much traffic in those days either. I remember sort of spending many of these hours thinking about this problem, you know, my mind solving little bits and pieces of the problem. I have a very clear memory of exactly various bits to the puzzle being solved, because you had many hours to think and you know, it was fairly safe to think about those problems on that kind of roads.

[Q] Did you have to stop to write them down?

No, no, no. You solved the idea and then you… once you'd seen how to do it, you'd check it up next time. I shall have to ask my wife whether she remembers whether I spent my time writing up, but I remember just thinking about them on the journey. Well one does… mathematics I always do. You have a problem which you're engaged with, it tends to sort of dominate your whole life. You know, you think about it when you can't sleep at night, when you're shaving in the morning, over your lunch break – so it's constantly there. Much of the time it doesn't make much progress, it just goes round and round and round. Every now and again you make a bit of an advance and then you sort of chalk it up and you write it down. So when one was driving, the same sort of thing would be happening, you know, you'd keep thinking about this problem, you're half way through, you'd turn it round and then an idea would emerge every now and again and you'd write it down.

So I do remember that period. So those are the three papers that emerged out of my stay at the institute. I was interested in many other things, went to all these seminars, learnt much which had influence over me later on. These were kind of, I would say, transitional, they partly emerged out of what I'd been doing before.

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: America, Jean-Pierre Serre

Duration: 3 minutes, 1 second

Date story recorded: March 1997

Date story went live: 24 January 2008