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

'Obvious' is the most dangerous word in mathematics.

The longer you look at an object, the more abstract it becomes, and, ironically, the more real.

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

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

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