I've gotten back into doing maths more seriously lately, and was wondering if there were any good online maths communities. Part of this is because there are some problems I'm stuck on, and part of it is because I think that much like hanging out on HN can help one become a better programmer, hanging out on a good math forum could help me become a better mathematician.
Does anyone know of any good communities? Math Overflow maybe?
This community played an instrumental role in my early days of beginning to study mathematics seriously. During its prime, weekly mathematics seminars [2] were organised by the members, which I thoroughly enjoyed. I still vividly remember the IRC user "TRWBW", who seemed to have an answer for every question, no matter how complex. TRWBW's ability to explain even the most challenging concepts with clarity and precision was very impressive. Sadly, he hasn't been seen in several years.
Although many of the original regulars have come and gone over the past three decades, the community continues to remain active. It still remains a good forum for discussing mathematics as well as asking and answering questions.
[1] https://web.libera.chat/##math
[2] https://freenode-math.fandom.com/wiki/Seminars#Past_Seminars
I got help with grad-level problems there. There's discussion there from high school through research, and is quite active.
* https://web.libera.chat/#bitwise (i.e., #bitwise on irc.libera.chat)
* https://app.element.io/#/room/#bitwise:matrix.org (i.e., #bitwise:matrix.org)
Both channels above are bridged together. So joining either one of them is enough to follow all conversations.
This isn't specifically targeted at professional mathematicians though. Most members come from a computing background. However, mathematics is a central topic here, with much of the discussion revolving around computer science and mathematical literature. Recent reading and discussions have been about topics like theorem provers (Z3, Lean, etc.), real analysis, Galois theory, distributed consistency, compiler and interpreter development, Standard ML, etc.
[1] https://leanprover-community.github.io/ [2] https://leanprover.zulipchat.com/
For OP: I think the problem with your question is that "math" is too broad, e.g. Math Overflow is for professional mathematicians, things like AOPS are very specific and most online communities are about what you would call "recreational" math (think 3blue1brown or standupmaths), likely far below what you want.
But yeah, roughly speaking you need to at least be a math PhD student who have passed your quals to be at the entry level of MathOverflow.