...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.

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.

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

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.

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

Mathematics - this may surprise or shock some - is never deductive in creation.

The heart of mathematics is its problems.