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.

The first lecture of each new year renews for most people a light stage fright.

A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.

In passing, I firmly believe that research should be offset by a certain amount of teaching, if only as a change from the agony of research. The trouble, however, I freely admit, is that in practice you get either no teaching, or else far too much.

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

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

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.