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?

Sociology is the science with the greatest number of methods and the least results.

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.

Thought is only a flash between two long nights, but this flash is everything.

Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?

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.