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.

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

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

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.

Mathematicians do not study objects, but the relations between objects.