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.
Martin GardnerIf you ask me to tell you anything about the nature of what lies beyond the phaneronโฆ my answer is โHow should I know?โโฆ I am not dismayed by ultimate mysteriesโฆ 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.
Martin GardnerAll mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.
Martin GardnerIf 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.
Martin GardnerWhen 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.
Martin GardnerIn 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.
Martin GardnerConsider 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.
Martin Gardner