In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself,….

When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to a paralysis, ….

Rigour is to the mathematician what morality is to men..

Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not….

Every mathematician worthy of the name has experienced . . . the state of lucid exaltation in which one thought succeeds another as if miraculously .….

What is crucial is there be laws..

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

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