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

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.

Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better.

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.

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.

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