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

If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.

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

I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly.

The very basis of creative work is irreverence! The very basis of creative work is bold experimentation. There has never been a creator of lasting importance who has not also been an innovator.

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.

Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance.