The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.

When a student comes and asks, "Should I become a mathematician?" the answer should be no. If you have to ask, you shouldn't even ask.

Feller was an ebullient man, who would rather be wrong than undecided.

Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.

Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.

The heart of mathematics is its problems.