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

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.

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.

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

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

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