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.

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.

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

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

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

The most spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.