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

All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.

Just as houses are made of stones, so is science made of facts.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

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.

One geometry cannot be more true than another; it can only be more convenient.

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?