A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

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

Need we add that mathematicians themselves are not infallible?

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?