Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.

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.

It is with logic that one proves; it is with intuition that one invents.

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.

It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.

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

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