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

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

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

THE COMPUTER IS JUST AN INSTRUMENT for doing faster what we already know how to do slower. All pretensions to computer intelligence and paradise-tomorrow promises should be toned down before the public turns away in disgust. And if that should happen, our civilization might not survive.

Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist.

A mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.

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