Hardy: reference for Pólya at ETH
I have a very high opinion of Pólya both as a mathematician and as a person, an opinion which greatly strengthened during his stay here. I feel too that it is very probable that the best has not yet been seen of him; that he has, perhaps, got a little discouraged during recent years; and that the encouragement derived from an improvement in his position would be very likely to stimulate him to even better work. He always seemed to feel that his leisure was scanty, and that he dared not risk squandering any large part of it on a difficult problem that might lead nowhere; and of course, when a fine mathematician begins to feel like that, there is always a serious danger that he may not do justice to his powers.
What is peculiarly characteristic of Pólya is that he has beautiful ideas - sometimes, of course (as in the classic case of the 'Carlson-Pólya' or the 'Pólya-Carlson' Theorem - where all the ideas were his), his ideas have run away from his executive powers! But all his work in that field is singularly beautiful. I have of course collaborated with him twice on a considerable scale, and was always astonished by the intensity of his aesthetic sense. Where Littlewood and I were content to get at the results somehow, and have it at that, he simply could not rest until he had got the whole corpus of theorems into perfect aesthetic shape (it is because of that, of course, that Littlewood and I were so determined to get him as a collaborator in our proposed 'inequality' tract.) Apart from that, he once rescued Littlewood and me from a month of sheer despair. In or triangular paper it was he who provided the happy idea that finally led to success. The situation then (this is naturally a piece of 'unofficial' information) was that Littlewood and I had formulated, and thought we had proved, a collection of theorems of which we foresaw all sorts of applications. At the last moment - when part of our work stood already in print - we found that our main argument was entirely and in principle fallacious. we were altogether unable to put it right, and it was Pólya's intuition - a quite new 'maximal' idea - which saved the situation and on which the whole investigation was ultimately based.
But this is a small and special affair. In general I would say that I have read many of Pólya's memoirs, and never yet found one which did not show real insight and originality, or some really interesting theorem expressed in a beautiful way.
When Pólya came here, he was an immense success in every way. I happened to have several quite good pupils at the time, and you can imagine what a difference it made to have a first rate analyst in the place; especially one with that 'algebraical' touch that is becoming more and more important in analysis. He was extraordinarily good in helping me with them, though he was under no kind of obligation to do so, both in taking part in my lectures and classes and in providing my pupils with ideas. You can see something of the results still, if you turn over the pages of the new London Math. Soc. Journal, and observe the number of interesting little papers in the 'inequality' field. I am sure that if Zürich can provide him at last with a position commensurable with his abilities, it will be doing a very great service both to its own reputation and to science.
JOC/EFR March 2006
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