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.

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

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.

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

Science makes no pretension to eternal truth or absolute truth.

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.

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