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

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

It is true that I should have been surprised in the past to learn that Professor Hardy had joined the Oxford Group. But one could not say the adverse chance was 1:10. Mathematics is a dangerous profession; an appreciable proportion of us go mad, and then this particular event would be quite likely.

The infinitely competent can be uncreative.

It is possible for a mathematician to be "too strong" for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)

I've been giving this lecture to first-year classes for over twenty-five years. You'd think they would begin to understand it by now.

The referee said it was not acceptable, but the Press considered they could not refuse to publish a book by a professor of the university.