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.
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 pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.
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.