Well said.

I'd say the ability to take complicated definitions and to not have to through a rigorous definition every time the ideas are referenced are, in a sense a form of abstraction, and a necessary requirement to be able to do advanced Math in the first place.

My entire being is anthithetical to this type of gatekeeping.

> You expect the players of the game to learn the rules before they play.

TFA is literally from a 'player' who has 'learned the rules' complaining that the papers remain indecipherable.

> You expect the players of the game to learn the rules before they play.

Actually, I expect to have to teach rules to new players before they play. We are different.

Many mathematicians do in fact teach the rules of the game in numerous introductory texts. However, you don't expect to have to explain the rules every time you play the game with people who you've established know the game. Any session would take ages if so, and in many cases the game only become more fun the more fluent the players are.

I'm not fully convinced the article makes the claim that jargon, per se, is what needs to change nor that the use of jargon causes gatekeeping. I read more about being about the inherent challenges of presenting more complicated ideas, with or without jargon and the pursuit of better methods, which themselves might actually depend on more jargon in some cases (to abstract away and offload the cognitive costs of constantly spelling out definitions). Giving a good name to something is often a really powerful way to lower the cognitive costs of arguments employing the names concept. Theoretics in large part is the hunt for good names for things and the relationships between them.

You'd be hard pressed to find a single human endeavor that does not employ jargon in some fashion. Half the point of my example was to show that you cannot escape jargon and "gatekeeping" even in something as silly and fun as a card game.

The article does not complain about notation. It describes how the different fields of mathematics are so deep and so abstract that it’s hard to understand them as a professional mathematician in a different field. That’s a hard problem worthy of discussion, but as the article says, it’s not as much a problem of notation or of explanations, rather than it’s just intrinsically difficult and complex because these are abstract and deep fields.

It’s not gatekeeping. It’s just hard.

The only thing that sentence says is that it’s impossible to understand math without understanding the language of math and how it is constructed. Not sure how that is controversial or gatekeeping. If you are annoyed at that comment saying “learn” instead of “be taught”, I think that’s a pedantic argument because the argument wasn’t about that at all.

"Can I enter your gate?"

"In order to enter this gate you must know what this symbol means."

"I am unfamiliar with that symbol."

"Well, I expect you to learn what it means before I allow you to enter this gate. Now go away."

Again, learning notation is part of the process of learning math. No one is gatekeeping anything, at no point you need to do an exam or magically be aware of notation that you never saw. Every book and every class will define new notation at the beginning, in most cases they will do so even when there’s no new notation. I am not sure what your argument is.

Every good mathematical textbook introduces the notation it’s using.

That’s a very good gate to keep. Some things are just meant to be gatekept so that the cranks and dilettantes that wastes everyone’s time can stay far outside.