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Interaction between maths and physics


Individual contributions
Michael Atiyah Mathematician
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Well that dinner in Annie's, I always think at that stage I was... I was really more a back… listening in. Graeme Segel had made a lot of earlier ideas on... on conformal theory, but it was really Witten who took charge that evening and, sort of, put it all together and showed how to go about it. But earlier on my... my role, I think, had been to interest Witten in the Jones invariants and say, ‘Look at these invariants; they look jolly interesting and they should have something to do with gauge theory. Here are a few ideas’. My ideas weren't quite right, but it was all pushed in the direction.

And I'd learnt from Graeme Segel about his axiomatic approach to conformal field theory, and I was trying to formulate similar approaches to Donaldson theory, and that pushed Witten in the direction. So I was... I was acting in the background, providing a bit of, sort of, stimulus and encouragement, and Ed Witten was doing all the work and Graeme on the other hand was, sort of, suggesting other ideas. It was a, sort of, interesting mixture, and the dinner, of course, was the nice culmination of it, but it had been going on for a while at different levels.

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: Annie's Restaurant, Graeme Segel, Ed Witten

Duration: 1 minute, 2 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008