A mathematics teacher is a midwife to ideas.

Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had gone off to become a poet. Hilbert is reported to have remarked: 'I never thought he had enough imagination to be a mathematician.'

Mathematics consists in proving the most obvious thing in the least obvious way.

An idea which can be used only once is a trick. If one can use it more than once it becomes a method.

The open secret of real success is to throw your whole personality into your problem.

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

To write and speak correctly is certainly necessary; but it is not sufficient. A derivation correctly presented in the book or on the blackboard may be inaccessible and uninstructive, if the purpose of the successive steps is incomprehensible, if the reader or listener cannot understand how it was humanly possible to find such an argument....