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

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

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

Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?

How is error possible in mathematics?

One does not ask whether a scientific theory is true, but only whether it is convenient.

Mathematicians are born, not made.