One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery--and more totally useless--than the perfect numbers.

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

The violence and double-talk in the Alice books probably does no harm to children, but the novels should not be allowed to circulate indiscriminately among adults who are undergoing analysis.

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.

When reputable scientists correct flaws in an experiment that produced fantastic results, then fail to get those results when they repeat the test with flaws corrected, they withdraw their original claims. They do not defend them by arguing irrelevantly that the failed replication was successful in some other way, or by making intemperate attacks on whomever dares to criticize their competence.

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

Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.