Every mathematician worthy of the name has experienced ... the state of lucid exaltation in which one thought succeeds another as if miraculously... this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work...

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

Quoted in H Eves *Mathematical Circles Adieu* (Boston 1977).

Rigour is to the mathematician what morality is to men.

First rate mathematicians choose first rate people, but second rate mathematicians choose third rate people.

Quoted in D MacHale, *Comic Sections * (Dublin 1993)