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

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

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 reason. What you do is trial and error, experimentation, guesswork.

Mathematics - this may surprise or shock some - is never deductive in creation.

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.

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.

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.