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First proof for the index theorem


Analysis with Singer
Michael Atiyah Mathematician
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I tried to improve my analysis at various stages. I mean I did at one stage go away and plough my way through Dunford and Schwartz, you know, learn all about operator theory and so on, but I picked up a lot of it by just talking to Singer and he would explain things and I would understand them. So most of it was by osmosis like that, but I did make attempts to read one or two books. I read, needless to say that I read Gelfond and Naimark book on normed rings because – C*-algebras – and that was… Singer was very good at it, so I did actually make attempts to sort of read a few serious books.

They were about the first books I'd actually tried to read since I was a student, you know. After you've ceased being a student you don't usually read textbooks; you learn what you need to on the hoof. But since my analysis hadn't been particularly good, I thought I did need to go back to square one and I did actually make a serious attempt to learn a bit. Then subsequently I read Hörmander and other things, and pseudo-differential operators. Yes, so I did try to supplement what I'd picked up from Singer by filling in on the analysis. But all generally with the aim of things related to the analysis I needed on elliptical equations, although subsequently I got interested in hyperbolic equations, so I, you know, branched out here and there in different directions. But it was a mixture of talking... talking to him and then backing it up with some additional reading, yes.

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: Isadore Singer

Duration: 1 minute, 19 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008