Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance.

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.

Time makes fools of us all. Our only comfort is that greater shall come after us.

The only royal road to elementary geometry is ingenuity.

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

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

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.