Mathematics is not a spectator sport!

I am too good for philosophy and not good enough for physics. Mathematics is in between.

Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.

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

An idea which can be used only once is a trick. If one can use it more than once it becomes a method.

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

To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.