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

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

Geometry is the science of correct reasoning on incorrect figures.

I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms.

Beauty in mathematics is seeing the truth without effort.

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