A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

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

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

Chance ... must be something more than the name we give to our ignorance.

How is error possible in mathematics?

Analyse data just so far as to obtain simplicity and no further.

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