Freeman Dyson - Pure mathematics at Cambridge: the influence of Besicovitch (23/157)
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Dyson
So then I come to Cambridge in 1941 as a 17-year-old. And before, I'd always been interested in physics and applied mathematics of all sorts. And one of the textbooks that I bought as a prize was a textbook in aerodynamics, which I think was because of James Lighthill. And so I 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 cryptoanalysis or various other things. So they'd all disappeared. And all that was left was the pure mathematicians. So I just had a wonderful feast of pure mathematics for the two years that I was in Cambridge. And I had the great luck to have Bezikovic 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 Bezikovic gave me problems which would have been too hard for a graduate student. But nevertheless, they taught me a tremendous lot.
Dyson
Yes, he was also geometry, but it was metrical geometry rather than algebraic. But the kind of problem he gave to me was to understand the properties of measurable sets in fractional dimensions. It's hard enough in one dimension or two, but when you come to fractional dimensions, it gets worse. I had a great time struggling with that, but of course nothing much came out of it except just a taste for his style. Bezikovitch's style has stayed with me all my life, and that'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 and fewer as you build one story on another until finally you get the keystone at the top. So you have this hierarchical structure, which played a big part in all Bezikovitch's work. 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.
Interviewer
And you were conscious of that at the time in interacting with Besikovits, that this is an approach of how he does mathematics?