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Relationship with Besicovitch


Pure mathematics at Cambridge: the influence of Besicovitch
Freeman Dyson Scientist
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So then I come to Cambridge in 1941 as a 17 year old and before then, I mean, I'd always been interested in physics and applied mathematics of all sorts, and one of the text books that I bought as a prize was a text book in aerodynamics which I think was because of James Lighthill and so I'd thought of myself as becoming an aerodynamicist, as a serious possibility - that seemed to be a field where mathematics could really be helpful, and flying of course was exciting. But anyway, I arrived in Cambridge and all the applied mathematicians were gone. There was nobody there except pure - and all the applied mathematicians and physicists were fighting the war and they'd gone to do radar or crypto-analysis or various other things. So they'd all disappeared and all that was left were the pure mathematicians, so I just had a wonderful feast of pure mathematics for the two years that I was in Cambridge. I had the great luck to have Besicovitch as my tutor, who was a great mathematician as well as being also a Russian so I could talk Russian with him, and we became very close friends, and so with him I actually did serious mathematics and I got, again, deep into problems which I never solved but which gave me enormous satisfaction. I remember Besicovitch gave me problems which would have been too hard for a graduate student, but nevertheless they taught me a tremendous lot.

[Q] And he was primarily interested in measure theory and such problems?

Yes, he was, and also geometry. I mean, I suppose it was metrical geometry rather than algebraic but the kind of the problem he gave to me was to understand the properties of measurable sets in fractional dimensions. Well, it's hard enough in one dimension or two, but when you come to fractional dimensions it gets worse. Anyway, so I had a great time struggling with that, but of course nothing much came out of it, except just a taste for his style, and Besicovitch's style has stayed with me all my life and it's the way I do science in all fields. It's a very distinctive style, which is kind of an architectural style in which you take very simple components and then build hierarchical structures which become stage by stage bigger as you build one storey on another until finally you get the key stone at the top. So you have this hierarchical structure which played a big part in all Besicovitch's work. And so out of these simple components you get this very powerful structure, and then the theorem you want to prove falls out as a consequence of the overall structure. So it's a kind of architectural style of reasoning which is very powerful and I used that in quantum electrodynamics.

[Q] And you were conscious of that at the time in interacting with Besicovitch, that this is an approach of how he does mathematics?

I'm not sure whether I was conscious of it, but certainly I absorbed it, and it's very visible in everything that I do.

[Q] And so Besicovitch is an important resource for you?

Yes, I mean certainly the tools that I use are basically Besicovitch tools.

Freeman Dyson (1923-2020), who was born in England, moved to Cornell University after graduating from Cambridge University with a BA in Mathematics. He subsequently became a professor and worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics and biology. He published several books and, among other honours, was awarded the Heineman Prize and the Royal Society's Hughes Medal.

Listeners: Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

Tags: Cambridge University, 1941, WWII, James Lighthill, Abram Besicovitch

Duration: 4 minutes, 17 seconds

Date story recorded: June 1998

Date story went live: 24 January 2008