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Interaction between science and society


Continued importance of magnetic monopoles
Michael Atiyah Mathematician
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It's true that they've now, they’re… when we studied them, there were… had a kind of interest from the point of view of giving low energy approximation to colliding monopoles, which is of... of interest in some aspects. And we get a nice mathematical story, and then that's sort of finished off and now they've reappeared in more sophisticated form in connection with these new ideas about duality, in theory. And... and, well I think that the… these monopole spaces form mathematically a nice class of manifolds, a nice class of metrics which obviously has lots of nice features. It fits into all sorts of stories, and I think they probably, you know, will have a kind of permanent home as something on the shelves that... that you can pull down and use in different contexts.

But whether you think of them as mathematical objects or as physical objects, I think this kind of slightly artificial distinction, you know, doesn't make much sense after a while. So one shouldn't be surprised if they recur. They have a, kind of, a rather natural fundamental role in the physics and they have, once you've understood them well, a rather natural mathematical interpretation as a class of manifolds of a certain type, which has interest of its own kind. So I think they're... they’re now well established animals, or books, whatever you like to call them – mixing my metaphors – which are of permanent value, 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: colliding monopoles, duality, manifolds, physics, mathematics

Duration: 1 minute, 25 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008