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.

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

One day, when I was doing well in class and had finished my lessons, I was sitting there trying to analyze the game of tic-tac-toe... The teacher came along and snatched my papers on which I had been doodling... She did not realize that analyzing tic-tac-toe can lead into dozens of non-trivial mathematical questions.

The universe is almost like a huge magic trick and scientists are trying to figure out how it does what it does.

If 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.

The last level of metaphor in the Alice books is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician.

In no other branch of mathematics is it so easy for experts to blunder as in probability theory.