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.

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

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

The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.

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.

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

The library is the mathematician's laboratory.