If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.

A mathematics teacher is a midwife to ideas.

A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.

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

Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.

The best of ideas is hurt by uncritical acceptance and thrives on critical examination.

If you cannot solve the proposed problem try to solve first some related problem.