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

John von Neumann was the only student I was ever afraid of.

The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line.

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

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

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

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.