God created infinity, and man, unable to understand infinity, had to invent finite sets.

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

Stan Ulam was lazy, ... He talked too much ... He was self-centered ... . He had an overpowering personality.

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

Theorems are not to mathematics what successful courses are to a meal.