What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

It is not order only, but unexpected order, that has value.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.