Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in the gift of clear exposition.

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.

Galois read the geometry from cover to cover as easily as other boys read a pirate yarn.

The only royal road to elementary geometry is ingenuity.

Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.

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

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.