The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.
Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.
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.
Out of fifty mathematical papers presented in brief at such a meeting, it is a rare mathematician indeed who really understands what more than half a dozen are about.
I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly.
The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.