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

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

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

A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.

In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.