One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

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.

All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.

It is through science that we prove, but through intuition that we discover.

We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.

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

Every good mathematician should also be a good chess player and vice versa.