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.

A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

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

Beauty in mathematics is seeing the truth without effort.

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.

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.