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.
Martin GardnerMathematics 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 GardnerA surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?
Martin GardnerThe high number from the Middle East is only coincidence, he said. It is no particular choice on our part, ... We accept visa trainees from those countries. We'd accept them from other countries, too, but we don't get their applications.
Martin Gardner