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.

As Bertrand Russell once wrote, two plus two is four even in the interior of the sun.

The sudden hunch, the creative leap of mind that "sees" in a flash how to solve a problem in a simple way, is something quite different from general intelligence.

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.

A god whose creation is so imperfect that he must be continually adjusting it to make it work properly seems to me a god of relatively low order, hardly worthy of any worship.

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.

Consider a cow. A cow doesn't have the problem-solving skill of a chimpanzee, which has discovered how to get termites out of the ground by putting a stick into a hole. Evolution has developed the brain's ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems.