The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.

'Obvious' is the most dangerous word in mathematics.

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

Guided only by their feeling for symmetry, simplicity, and generality . . . creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.