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.

We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

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

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.

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