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.

Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.

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

A GREAT discovery solves a great problem but there is a grain of discovery in any problem.

Beauty in mathematics is seeing the truth without effort.

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.