The library is the mathematician's laboratory.

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.

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

... 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."

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 perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."

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

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.