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.
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.