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.

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

To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.

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

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