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

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

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time.

Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself

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.

If there is a problem you can't solve, then there is an easier problem you can't solve: find it.