Deviner avant de démontrer! Ai-je besoin de rappeler que c'est ainsi que se sont faites toutes les découvertes importantes.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

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.

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

Intuition is more important to discovery than logic.

Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.