Math isn't just about proofs. It's a way to communicate. There are several different ways to communicate how a neural net functions. One is with pictures. One is with some code. One is with words. One is with some quite dense math notation.
I would not call the notation ‘dense’ rather it’s ‘abused’ notation. Once you have seen the abused notation enough times, it makes just makes sense. Aka “mathematical maturity” in the ML space.
My views on this have changed as a first year PhD in ML I got annoyed by the shorthand. Now as someone with a PhD, I get it — It’s just too cumbersome to write out what exactly you mean and you write like you’re writing for peers +\- a level.