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

Analyse data just so far as to obtain simplicity and no further.

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

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

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

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.

If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.