The very basis of creative work is irreverence! The very basis of creative work is bold experimentation. There has never been a creator of lasting importance who has not also been an innovator.

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

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.

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

The only royal road to elementary geometry is ingenuity.

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

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