... 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 our Master's exams."

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.

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.

The heart of mathematics is its problems.

The author discusses valueless measures in pointless spaces.

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.

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 average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.