The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.

We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"

Our faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.

Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.

The progress of mathematics can be viewed as progress from the infinite to the finite.

The lack of real contact between mathematics and biology is either a tragedy, a scandal or a challenge, it is hard to decide which.

If we have no idea why a statement is true, we can still prove it by induction.