My cultural reading of this notation problem is this: mathematical notation was formalised when scientists were writing papers and letters to each scientists in

My cultural reading of this notation problem is this: mathematical notation was formalised when scientists were writing papers and letters to each scientists in the era of scarce paper and no internet. So focus was on succinctness at the expense of explainability. It is akin to why commands on Unix machine were short, you were talking to an actual serial terminal to machine somewhere away. So saving a letter or two helped. Persisting with cryptic mathematical notation today, we are stuck with an idea well passed its sell by date. Mathematical notation, mostly, is not precise. Sussman (who wrote the famous SICP book) wrote another book structure and interpretation of classical mechanics. Tough book to go through. But they start with the same premise: mathematical notation is confusing (and hand wavy at times). A better symbolic notation should reveal enough details to be able to code up the mathematics in a program. I found this approach to be bang on target, but could never get enough time to actually go through the book. And I realised why the 'let us build it up from scratch' books work. They force you to think about the function signatures and shape of objects passed to each function. This approach reveals gaps in our understanding much better. For example, F=ma is looks like an algebraic statement, hiding the fact that `a` on the right is about time evolution of the system through the derivative. Steven Strogatz made a funny quote in his infinite powers book. (I'm paraphrasing), if Newton was doing this in today's era he might create a flipbook animation to make this point and not symbols.