The heart of mathematics is its problems.

The library is the mathematician's laboratory.

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

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.

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

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.