In an overwhelmingly important sense, pure math has the least 'jargon' of any field. The reason is, math exposition has an absolute requirement: Each use of a

In an overwhelmingly important sense, pure math has the least 'jargon' of any field. The reason is, math exposition has an absolute requirement: Each use of a word not the same as just its dictionary meaning becomes a 'term' and just MUST be defined, and 'well-defined', before it is used. So, what the article is calling 'jargon' is just such terms, but in well written pure math they all have rock solid definitions, and math is the unique field where this precision is true. For the rest of the complaints about 'jargon', these are essentially just necessary given that math, due to its precision and age, is now by far the deepest field of study. So, there are a LOT of terms defined. If the article wanted to claim that for each math result or paper there is a 10,000 foot intuitive view that can be explained in 90 seconds to just anyone on a street, then okay, but the article did not do this. This claim is not quite true, but it is close enough so that some such explanations, maybe with some pictures, and some connections with more elementary topics, can be useful, even in research papers. But the article didn't make this claim, either.