Intuition is more important to discovery than logic.

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.

Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose.

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

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

It is by logic we prove. It is by intuition we discover.

All of mathematics is a tale about groups.