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.

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 present trends continue, our country may soon find itself far behind many other nations in both science and technology nations where, if you inform strangers that you are a mathematician, they respond with admiration and not by telling you how much they hated math in school, and how they sure could use you to balance their checkbooks.

Biographical history, as taught in our public schools, is still largely a history of boneheads; ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant general the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.

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.

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