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

If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as we now have, and I don't see anything wrong with that.

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 only way to learn mathematics is to do mathematics.

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

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

The library is the mathematician's laboratory.