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.
> 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.
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.
It’s not gatekeeping. It’s just hard.
The sentence I called out, independent of the article's content: "You expect the players of the game to learn the rules before they play."
Is you explicitly stating your goal is gatekeeping.
"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."
Players of magic the gathering will say a creature "has flying" by which they mean "it can only be blocked by other creatures with reach or flying".
Newcomers obviously need to learn this jargon, but once they do, communication is greatly facilitated by not having to spell out the definition.
Just like games, the definitions in mathematics are ethereal and purely formal as well, and it would be a pain to spell them out on every occasion. It stems more from efficient communication needs then from gatekeeping.
You expect the players of the game to learn the rules before they play.