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And topological K-theory was born


My mathematical growth
Michael Atiyah Mathematician
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My own evolution, my mathematical development had never actually moved by consciously saying I'm going to stop doing this and do that. Some people have done that in the past. I think Hilbert you know, said, you know, his life was divided into compartments. He was doing number theory here, then he was doing geometry here and I think he sort of switched off and for five years he would do… I couldn't do anything as, sort of, clean cut as that. I just simply talk with people and things evolve and I suddenly found my interests had moved a bit and there were new problems and you'd have to learn a bit. And usually the learning was done by, sort of, osmosis. You talked to people, you went to the seminars, occasionally you'd have to brush up by looking at some textbook to get the details. Before you knew where you were you'd drifted quite a long way down line. So it was a, sort of… and that happened more or less continuously, you know, ending up with theoretical physics. But it was never a conscious process to actually make the move, you know, just in some sense swimming with the tide or trying to keep your head afloat really.

And actually there’s a nice story. I remember Henry Whitehead telling me at one stage that – about this business of shifting your fields – that he said he'd been a topologist all his life, he had all his friends were topologists, he so much enjoyed having so many friends, he said it would be terrible if one of these days I suddenly decided I discovered something new in functional analysis and I had to be function analyst, I would, you know, lose all my friends. He really got very… and oddly enough, eventually I actually moved into a bit of functional analysis myself in some direction, but because I didn't switch off from one to the other, but just kept these things together, I kept all my friends, so I didn't lose them. But I always remember him saying this, he said it in a kind of way that was, you know… I mean it was a kind of cri de coeur… he said, ‘Wouldn't it be terrible if I had this sort of fundamental choice, you know, I had to shift my field of interest and cut loose from all my old collaborators and friends?’ He would be… cut him to the heart, although he never had to make the choice. But it was… I was very fortunate, although I shifted fields very often, by being gradual and continuous, I never actually felt that I've cut off my, you know, people I knew before, just increased them, the band so to speak.

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: Henry Whitehead

Duration: 2 minutes, 11 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008