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

Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

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

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.

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.