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Mathematicians of the past
Michael Atiyah Mathematician
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But I think this idea of, you know, what a great mathematician of the past would... would make of what we currently do, is a very good kind of a intellectual exercise to conduct oneself. You know, there's this vast amount of mathematics we do and you want to say, ‘Well, what... what is the real value?’ And it's hard within the system to... to assess the importance of various things; their relative magnitudes and scale, and... and so historical perspective is a... is a good measure. And if you take a great man from the past and bring… imagine him being brought forward, you can imagine that it would only take him a short while to master any technical details of… you know, which were related to something significant. And so you feel that with a short crash course you ought to be able to explain the really important things to the great man of the past. And that would… and then if you look and see what it is you've got to do, and work out how much you've got to do and... and you strip it away... strip it all away, what would be left? Sometimes you might find there wasn't very much there, you know. If it's all kind of self-contained and there's nothing connecting with a strand of mathematics that goes back into the past, which... which you could bring forward, then you begin to wonder, ‘Well, is it really of value?’ So I think it's a... it’s a good exercise, it's quite amusing to do, and so I've played with that idea quite often in the past. I think I... I like it.

[Q] Who are your heroes of the past?

Well, of course, it depends on how far back you go. I mean, having come to Trinity College and being in the Royal Society, I have to say Isaac Newton, you know, and bow down and all that sort of thing. And you know, when I came here I read a lot about Newton, I thought I had to. And then he... he, from being a kind of just a abstract figure, he became somebody more real to me and he's, just in mathematical terms, or mathematical and physical terms, an enormous figure. Much bigger I think than any... any other single person, be it Einstein or anybody else.

But coming down to, sort of, more recent times, Hermann Weyl was the person I most clearly identified with in mathematical terms. I mean, almost everything I ever did, you know, was... was… you could trace back to things that Hermann Weyl did, I mean very closely related the things… he would be interested in most of them. He did... he did other things that I didn't get into. He was… he covered a very wide range of things from theoretical physics and mathematical logic, number theory and certain group theory, and... and I've sort of moved in many of those, similar things. And a kind of rather a direct, sort of, follow on to many of his ideas of work, so I... I felt his spirit, you know, behind me all the time practically. And I got to a new area, I'd flick through, and gosh, Hermann Weyl's name would appear as somebody who contributed a key idea. So he I think is certainly one of my heroes.

I never… I didn't actually… I met… saw him once. He talked to the International Congress in Amsterdam in 1954 where he gave out the Fields Medals to Serre and Kodaira, and I was a, sort of graduate… second year graduate student attending my first international conference; I... I saw the great man but he died the following year. When I went… he was in Zurich but he had been in Princeton, and so I never actually got to... to meet him, but I knew a lot of people who had met him, Bott and people who that... that worked with him. He was an interesting man. He was... he was apparently nicknamed by the friends who knew him, he was called Heiliger Hermann, sort of, Holy Hermann; he was, because he was a little bit pompous and sort of self-important, but I think it was a kind of friendly nickname that they gave him. So he was certainly… and of course, well Gauss was a, I suppose, an enormous figure too. But he was more of a number theorist in many ways, and the centre of gravity of interest were a bit different; although he did so many other things, and he's a bit further away. It's hard to… I find it hard to… also as person I think Gauss was a bit hard and harsh. His treatment of Lobachevsky and people like that was a bit ruthless, so I didn't warm to him as a person. I think Newton also was a bit tough. But Hermann Weyl I think was a... was a more rounded man, he also had very broad cultural interests and I think would have been a very nice man to know.

Eminent British mathematician Sir Michael Atiyah (1929-2019) 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: Trinity College, Royal Society, Princeton, Amsterdam, Zurich, Isaac Newton, Albert Einstein, Hermann Weyl, Jean-Pierre Serre, Kunihiko Kodaira, Carl Friedrich Gauss

Duration: 3 minutes, 53 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008