There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

Mathematics is not a spectator sport!

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

There are many questions which fools can ask that wise men cannot answer.

It is better to solve one problem five different ways, than to solve five problems one way.

You should not put too much trust in any unproved conjecture, even if it has been propounded by a great authority, even if it has been propounded by yourself. You should try to prove it or disprove it.

If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.