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

It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

Mathematicians do not study objects, but the relations between objects.

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?

It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.

Analyse data just so far as to obtain simplicity and no further.

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