>>11534057In a certain sense, math doesn't work like other stuff, not even hard sciences like physics or chemistry. You can't just summarize your thing in general, natural language for the layperson and then go into details which other experts will understand but where the layperson may still glean something. Math is (not entirely, but to a large extent) vertical; the reader is absolutely required to already have a clear understanding of whatever specific concepts are prerequisite to the discussion, because the things being discussed in the first place are abstract ideas which, the more abstract they are, are the more difficult to form any physical, social or "natural" intuition for. If you're an algebraist people have to know about groups/rings/fields/algebraic structures generally before they can approach whatever you've written, and similarly for other specialities, because that's the vocabulary.
I do agree that mathematcians could be a bit better about the "proof left exercise for reader/proof: think" stuff, but even this has its limits. Depending on the thing, a proof may be a tedious thing (but important for a student to go through) which actually doesn't warrant treatment in the work because it'd take too much space and make the work prolix. You have to economize and only show the important stuff. A certain amount of gatekeeping/not spoonfeeding is important in math. As it stands, mathematics PhD dissertations are (last I checked) among the shortest in terms of page count, while history's are among the longest. This is valid. History has to drop a lot of prose in a readable style, whereas math is just math, and can be expressed concisely especially since it assumes background.
Consider the alternative. Instead of an n page article that only ten people have actually read and understood, imagine an article of length, say, 2-4n with all the details worked out. It would be tedious and unnecessary to the very few even motivated to read the thing at all.
