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.

Fashion as King is sometimes a very stupid ruler.

Obvious is the most dangerous word in mathematics.

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.

Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.

If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.

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