Remix.run Logo
Tainnor 3 days ago

This sentiment comes up all the time here. Mathematics uses formalism because it's easier.

It's easier to read "a(b+c+d) = ab+ac+ad" than

> If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments.

It's well known that good notation is exactly the one that elevates good intuition. For example, the Legendre symbol has the property that (a/p)*(b/p)=(a*b/p), an important visual cue that you wouldn't get from writing down (in way too many words) what the Legendre symbol actually means.

Also, most actually good mathematical textbooks aren't just dumps of formulae and proofs and they do contain motivation, examples, pictures, etc. You're attacking a strawman. But you can't just relegate the formalism and proofs to the appendices, that's crazy.