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Oppenheimer on Princeton


Michael Atiyah Mathematician
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It was fairly normal practice, when you finish your PhD, to try to go in those days… to go to America, and Princeton was the obvious place for me because of Kodaira and Spencer were at Princeton and the Institute for Advanced Studies had all these visitors. And so Hodge was... Hodge had been himself a year in Princeton way back in the ‘30s and Lefschetz was at Princeton University, so Hodge as well. So he actually went to a conference in Princeton, round about ‘53, ‘54, and talked to Kodaira and Spencer, and showed them work that I was doing at that stage, which they were interested in, so more or less Spencer said, you know, ‘Come over’.

And so I finished. I applied for a Commonwealth fellowship which I got and that paid for me to go. If I hadn't got that I might have got helped by Princeton University, and then Spencer said, ‘Well don't come to the university, go to the institute because the institute has better facilities for visitors’.  And so he... he suggested I apply to the institute. So I went there. But, I mean, at that time there were… opportunities for people to go were much more limited than they are now, and very few places you could go to so easily as the institute. So there was a big concentration of visitors to the institute, and also it was the kind of post-war period.

A lot of people's careers had been upset by the war, so there was a kind of whole concentration of many, several generations, you know, overlapping together. So when I went to the institute in Princeton, there was a galaxy of talent, the people that I met. Bott was there and Serre was there and Hirzebruch was in the university. Singer came… so there was a whole range of people, many of them older than me, all arriving at the same time and spending a couple of years at the institute. So it was very… and then we had the older people, Spencer and Kodaira in the university, and Lefschetz was still there, and Hermann Weyl had just died before I arrived, as had Einstein. But it was obviously the right place to go at that time and you know, enormously beneficial in terms of opening up your outlook.

I mean Cambridge was pretty… was reasonable, you know, with Hodge and people; but we didn't have many of the kind of visitors you get streaming through nowadays. You had… you kept in touch by looking in the journals as they appeared and you corresponded with people internationally. Much weaker than now, they didn't have email. But, for example, I got my fellowship at Trinity, end of my second year of research, and my work on, sort of, vector bundles and also the work on integrals of the second kind which I did with Hodge simultaneously. My third year, I think here was probably a kind of fallow year really because there was… my research had sort of come to a natural end. I wasn't quite sure where to go. There was nothing more I could get from the environment around me, you know. We still had seminars and so on, but… so, I don't think the third year here was terribly profitable in some sense.

I enjoyed being a fellow of the college and all that sort of thing and I… no doubt I learned a few things, but it wasn't… but when I went to Princeton it was totally different. I went to lectures, Bott gave lectures on Morse theory, and Lefschetz and Kodaira was giving lectures on sheaf theory and algebraic geometry, and Spencer… and Serre was giving seminar on this and that. So in a very short period of time I was exposed to a whole range of new things, new… I didn't know much about Lie groups before, and I picked that up a bit from Bott, and I learned a lot from Serre, direct contact with him and with Hirzebruch with characteristic classes. So, you know, the opportunity was enormous and as I said, I didn't have that at Cambridge.  So that year – I spent a year and a half in Princeton – I learnt a whole lot of new ideas, pushed in new directions a bit. I came back with, sort of, lots of things to work on and also made contact with all these people who I subsequently saw much more of over the years to come. So it was a tremendous impact on my whole career really… and the right stage. I mean, although I could have gone a year earlier and also benefited probably.

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: Princeton, William Hodge, Kunihiko Kodaira, Donald Spencer, Jean-Pierre Serre

Duration: 4 minutes, 15 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008