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The future of mathematics


Trying to build a strong group
Michael Atiyah Mathematician
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Group theory really had… they had Burnside way back, then they had Philip Hall and, of course, we imported John Thompson, partly because of the strength here. Although group theory has a natural… so much more attraction because it's a subject which is easy to... to, sort of, start off with and concentrate on; it has a natural attraction bringing in students. I think it's very difficult to alter. I mean, and people say whether one should develop strengths in analysis and differential equations, and one does try and do that and bring people in, but it's extremely hard to do that successfully I think, and... and somewhat a bit artificial if you... you… you may put a lot of money in and attract a lot of people, all you end up is rather some second-rate stuff.

So I don't think you can swim entirely against the... the tide, it has to grow naturally out of what you've got. Obviously, you know, if you can attract leading people, you know, we got… Thompson came to Cambridge and Quillen went to Oxford and there are people... Of course there's the reverse brain drain; people go abroad. And if you... if you can succeed in bringing people to... to strength and build up, that's fine. But it's very hard to bring somebody in and say, ‘We're weak in this field, let's import one or two top chaps from France or America and give them lots of money and tell them to build up a big school’. I don't think it works. I don't think it works like that at all. It's a much slower process, you've got to develop in the direction of the strengths you've got, build on that. Obviously attract people when you can, bring in long-term professors or visitors, stimulate… but people I think are a bit too naive sometimes of what you can do just by administrative, you know, procedures. It has to grow organically I think.

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: Cambridge, Oxford, America, France, Philip Hall, John Thompson, William Burnside, Daniel Quillen

Duration: 1 minute, 39 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008