If you ask me to tell you anything about the nature of what lies beyond the phaneron… my answer is “How should I know?”… I am not dismayed by ultimate mysteries… I can no more grasp what is behind such questions as my cat can understand what is behind the clatter I make while I type this paragraph.

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.

If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.

All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.

The computers are not replacing mathematicians; they are breeding them.

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.

Modern science should indeed arouse in all of us a humility before the immensity of the unexplored and a tolerance for crazy hypotheses.