You are allowed to lie a little, but you must never mislead.

The best way to learn is to do; the worst way to teach is to talk.

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.

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.

Applied mathematics will always need pure mathematics just as anteaters will always need ants.

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

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.