Ugh. Math is a collection of concrete symbols for simplifying different problems. It's evolved over thousands of years to help us understand difficult things. We don't make it that way just to piss people off.
His argument is that analyzing a differential equation without exploring it in phase space was like analyzing a piece of sheet music without actually hearing it.
And if music education were taught in that way-- by looking at music purely as the manipulation of concrete symbols-- I imagine some of us would be writing "kill music (as it is currently taught)" blog posts as well.
I'll be honest; I absolute love graph theory. If I had a million lives and financial independence, I would spend several of them solving graph theory problems. I don't really give a shit what the nodes and edges are. Computer network? Rigid structure? Conditional independence of personality traits? I don't care!
Word problems are still abstract manipulation of symbols, you just have to hunt around in the phrasing for the right operands or operations, which arguably makes it harder.
Talking about Math as a single subject is like talking about Sports. Chess, Boxing, Baseball, Snowboarding, Curling, and Luge may have some things in common. However, suggesting that DiffEq and Fractions are equally meaningless to most people seems just as out of place as assuming a chess grandmaster is also a champion snowboarder.
Most of the symbols are pretty recent; if you read mathematics from even 300 years ago, there's a much bigger proportion written in prose. Along the lines of, "Consider two quantities, such that the latter is at least twice the former ...".
The shift to more symbols and more and better notation has also drastically increased mathematical productivity and rigor. In fact, most of the notation emerged together with the axiomatization of the foundations of mathematics in the early 20th century.
If we were to follow this guy's ideas it would cause even more of a class divide between those who can understand the "magical symbols" and those who can't. Doing what he suggests would mean that the non-cognoscenti wouldn't even have access to the understanding of simple algebraic equations.
I remember trying for hours to understand Adaboost before it all clicked (it's an ingenious algorithm, by the way). The paper could certainly do with some more explanation, rather than just "this is the weight updating function, this is the evaluation step, done".
I think AI and machine learning are worse than math in that respect for some reason. Part of it might be the greater focus on 6-page conference papers, which tends to require everything to get squished.
