'Obvious' is the most dangerous word in mathematics.

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

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.

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

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.