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Magnetic monopoles


Continuing relevance of early studies
Michael Atiyah Mathematician
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[Q] Does the classical geometry with which you began, twisted cubics and things like that, still hold an attraction for you?

Oh, yes, yes, very much so. Well, of course, much of it sort of recurs in various special forms – particular examples higher up. Whenever I... I have some particular problem I always try it out on... on my familiar friends, you know, the problems I […] around with. So they're always there in the background and... and they always still have an attraction for me. Every now... now and again I get in some little problem and I find actually something I was interested in 40 years ago, you know, really comes back, and it gives me a great satisfaction. I think it's… I'm still... still… you know, early loves are still, sort of, still with you. I... I still enjoy it and... and I felt I think that sometimes people feel when they start off with something like that which they really enjoy, then they go off on something else. You feel like you've deserted the cause and, you know, there are people who've stayed with classical geometry and you feel you're a kind of deserter. But I don't feel that way because I think the things that I moved into incorporate the other stuff in a... in a good form, and it still appears and I still go back and, sort of, check… show my credentials by using a bit of nice algebraic geometry and… just to show that I really haven't lost touch with its roots. So no, it's still part of my, sort of, background culture very much.

[Q] When did you last have cause to use an argument from classical geometry?

Well, actually about… last summer, or the summer before. I was working on a problem and it turned out that… I was doing some calculation checking it out and it turned out what I needed was something I actually wrote in my very first paper, the paper I wrote when I was even an undergraduate, as far back as that. So that was really… closed the circle as it was.

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: classical geometry, early education, algebraic geometry, undergraduate student

Duration: 1 minute, 41 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008