The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profo….

The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method..

The library is the mathematician's laboratory..

Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the ….

It saddens me that educated people don't even know that my subject exists..

The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites..

A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant..

Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reas….

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

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

A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, ….

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mat….

The only way to learn mathematics is to do mathematics..

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 conver….

The heart of mathematics is its problems..

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 ….

A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better..

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

I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a p….

What's the best part of being a mathematician? I'm not a religious man, but it's almost like being in touch with God when you're thinking about mathe….

... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass o….