In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

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

Look around when you have got your first mushroom or made your first discovery: they grow in clusters.

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.

It may be more important in the mathematics class how you teach than what you teach.

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

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