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.

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.

Obvious is the most dangerous word in mathematics.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

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

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.

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.