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

The heart of mathematics is its problems.

Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?

The computer is important, but not to mathematics.

I read once that the true mark of a pro - at anything - is that he understands, loves, and is good at even the drudgery of his profession.

The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.

To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.