Hardy and Veblen on Erdős

Below are some extracts from correspondence between G H Hardy and Veblen relating to Paul Erdős to be found in the Veblen archive at the US Library of Congress in Washington, DC. Notes are by Douglas Rogers.

GHH to OV, 11th November, 1935
[annotation - copy kept in IAS file; letter on Trinity College,
Cambridge notepaper]

Dear Veblen,

Having occasion to write to you about something else, I find a letter which I got in Sept and have neglected. I have better excuses than usual: (a) I have moved my rooms, and everything has been in disorder; (b) I was knocked down by a motor-cyclist and laid up for 2 or 3 weeks just at the beginning of term. No serious injury.

The other thing is: Mordell says that P Erdős, a young Hungarian, is very anxious to go to Princeton for the session 1936-7. He is undeniably a very remarkable man, extraordinarily quick and fertile; v. Neumann has met him, and should know something about him. Is there any chance of his getting any scholarship or grant? I imagine that his own country can do nothing for him. He is not a "refugee".

His line is theory of numbers in the main; and I am out of touch with it. But I have read some of his papers, and they have an undeniable touch of quality.

Yours ever,

G H Hardy.

Who won the World Series? Widder doesn't know.

GHH to OV, 22nd July, [1939?]
[On New College, Oxford notepaper]

Heilbronn reports to me that Erdős's position is getting very acute, and asks me to write on his behalf. I do this gladly, because I do feel that Erdős is an exceptional man.

I gather that E. has not "made himself popular" in Princeton: I do not mean that he is in any sense actively disliked, but that he has been a bit aloof and not become, so to say, part of the place. Against this you must remember that he must be, scientifically, very isolated - I can hardly think of anyone in Princeton likely to be very interested in his work. An older person like Landau or myself can to some extent get over this, but it must be rather difficult for a quite young man like E. At Manchester it was quite different, since there the centre of interest lay right in his direction. But Manchester did, I think, provide for him for at least 2 years.

Heilbronn suggested - I do not know just on what grounds, and cannot cross-examine him now - that there was some more or less definite chance of his getting a studentship, away from Princeton in 1940-41, if only P could keep him another year. Is that so?

I do not see any chance of getting anything for him out of the "Society for the protection of science and learning". They are still making grants pretty vigorously, but E. is definitely excluded by their axioms - they strictly confine themselves to refugees ejected from a position. E. can go to England before there was a chance of getting one - practically just at the end of his student stage (no doubt judging that he had no chance at home). So if you can do anything for him, I should be much relieved.

{If the year, 1939, assigned to this letter is correct, then Hardy is writing just ahead of the 1939-40 academic year, which would account for Heilbronn's and his sense of urgency. But the second paragraph is a bit curious, in that one might suppose that Veblen would be more directly aware of whatever problems Erdős was facing at Princeton. One also wonders about Erdős's later relations with Selberg and Princeton.}

JOC/EFR August 2007

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