What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

The mind uses its faculty for creativity only when experience forces it to do so.

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

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

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

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.