The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.

The heart of mathematics is its problems.

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.

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

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

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