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?

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

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

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

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.

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.