There are alternative wikis for math and they’re way harsher. Wikipedia is the middle ground between math wikis written by current students and professionals vs pedagogues. But I’d argue that if you want pedagogy or step by step proofs, then why not simply buy a well vetted textbook, of which math has many?

That's certainly true, buy I think it also makes it quite unsuited as a reference (except for people who are already familiar with the concepts and just need a quick reminder).

Wikipedia math articles are not useful to get a shallow understanding of a topic. On the contrary, it pulls you into a rabbit hole of dependent concepts just for you just to be able to understand the words in the article's summary.

From an actual reference, I'd expect that it gives a brief, self-contained description of the basic idea of a concept, without going too deep into specifics, possibly with a "see also". That's not what Wikipedia does.

But I think that this is a core difference between an encyclopaedia and a textbook. If you need the topics presented in an order that takes you from a certain level of understanding to the next, you need a textbook.

Well that's the problem. An encyclopedia should neither provide nor need such an ordering. But Wikipedia often does need it, while also not providing it, the worst of both worlds.

Wikipedia math has competition and they are generally much harsher than Wikipedia, which indicates the direction which communities of volunteers wish to go when they disagree with Wikipedia's execution.

https://ncatlab.org/

https://kerodon.net/

https://stacks.math.columbia.edu/

The people who are looking up references to advanced math concepts are likely students who are already on a mainstream pedagogical pathway and are looking to fill in holes to a concept map they're already building.

The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case.

> Wikipedia math has competition and they are generally much harsher than Wikipedia, which indicates the direction which communities of volunteers wish to go when they disagree with Wikipedia's execution.

Okay, but I don't think those communities are relevant to this conversation.

> The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case.

Number 1 is a weird assumption! Unless by "consult" you mean spend weeks studying a textbook, the problem is that consulting is too difficult! And if I understand "harsher" correctly you just said the other sites are harder to use, didn't you?

So then it's just "not an advanced math student", which may or may not be a majority of people on these pages but it's a very significant amount and it's the more important target for a general encyclopedia.

Wikipedia is by definition a reference. If you want to learn something use different material. Trying to make wikipedia articles tutorials is out of scope (not that it isn't nice to get practical examples for concepts, which ime there often are!)

Have you tried Simple wikipedia? Also, wikipedia is a reference, not a textbook.