Mathematics is a dangerous profession; an appreciable proportion of us go mad.

The infinitely competent can be uncreative.

I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now.

The first test of potential in mathematics is whether you can get anything out of geometry.

The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.

A heavy warning used to be given that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety.

I listen only to Bach, Beethoven or Mozart. Life is too short to waste on other composers.