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.

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.

The open secret of real success is to throw your whole personality into your problem.

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

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.

A mathematics teacher is a midwife to ideas.

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