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

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

The only royal road to elementary geometry is ingenuity.

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

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.

Fashion as King is sometimes a very stupid ruler.

Obvious is the most dangerous word in mathematics.