The Libera IRC ##math community [1] has been around for over 29 years now! Originally based on the Freenode network, the community migrated to Libera in May 2021 following a controversial shift in Freenode's management.
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.
If someone is looking for a vertical/columnar math problem generator for kid, you can try this, which is I created for my 8-year-old son.
https://kids-math.xhtml.jp
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.
While not a community itself, Terence Tao's blog (https://terrytao.wordpress.com/) is a good source of high quality, clearly explained maths. As you may know, he has a very broad range of interests, and there might be something for you to pick up and get involved in. He has also been involved in several collaborative math communities, which he writes about at length in his blog. I recall Polymath project and recently some project involving Lean Theorem Prover that even showed up on the first page of the HN.
Note that math.stackexchange.com and mathoverflow.net have different audiences. On math.stackexchange.com mortals like me can ask math related questions, while mathoverflow.net is targeted at people doing research level math.
AOPS is a great community but it's for competitive mathematics (AIME, AMC, USAMO, etc.)
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.
ok, I guess from what you say Math Overflow might be my best bet then, I'd like to have the competence of a professional mathematician, even if I work as a software engineer because it pays more :)
The kind of maths they do on Mathoverflow is PhD level and above... they probably get paid more if they leave academia, but then they are hired to do the kind of maths on math.stackexchange.
Not really, as a former theoretical physicist who also got offers from many math PhD programs and have many math PhD friends, by far the most recruiting emails we get are from quant trading firms, and you won’t find that kind of math on Math.SE.
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.
The Libera IRC ##math community [1] has been around for over 29 years now! Originally based on the Freenode network, the community migrated to Libera in May 2021 following a controversial shift in Freenode's management.
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
If someone is looking for a vertical/columnar math problem generator for kid, you can try this, which is I created for my 8-year-old son. https://kids-math.xhtml.jp
I recommend the math discord in addition to mathoverflow and mathstodon. https://discord.gg/math
I got help with grad-level problems there. There's discussion there from high school through research, and is quite active.
We have a little IRC/Matrix-based computer science and mathematics discussion community called Bitwise. The connection links are:
* 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.
https://mathstodon.xyz/
https://github.com/metamath/set.mm , if you do not object to your theorems being machine-provable.
https://boards.4chan.org/sci/
This. I got more help from /g/, /sci/, and /wsr/ than anywhere else on the internet
Lean[1] Zulip chat[2]
[1] https://leanprover-community.github.io/ [2] https://leanprover.zulipchat.com/
While not a community itself, Terence Tao's blog (https://terrytao.wordpress.com/) is a good source of high quality, clearly explained maths. As you may know, he has a very broad range of interests, and there might be something for you to pick up and get involved in. He has also been involved in several collaborative math communities, which he writes about at length in his blog. I recall Polymath project and recently some project involving Lean Theorem Prover that even showed up on the first page of the HN.
Physics Forums[1] has an awesome math section as well. Got a lot of great help during my uni years.
[1]: https://www.physicsforums.com/
+1 for this. There are some communities on Discord as well surprisingly but they are invite only so I'm not posting any links on here.
https://leanprover-community.github.io/meet.html
https://artofproblemsolving.com/community
https://math.stackexchange.com/
https://mathoverflow.net/
Note that math.stackexchange.com and mathoverflow.net have different audiences. On math.stackexchange.com mortals like me can ask math related questions, while mathoverflow.net is targeted at people doing research level math.
Cross Validated Stack Exchange.
aops
AOPS is a great community but it's for competitive mathematics (AIME, AMC, USAMO, etc.)
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.
ok, I guess from what you say Math Overflow might be my best bet then, I'd like to have the competence of a professional mathematician, even if I work as a software engineer because it pays more :)
The kind of maths they do on Mathoverflow is PhD level and above... they probably get paid more if they leave academia, but then they are hired to do the kind of maths on math.stackexchange.
Not really, as a former theoretical physicist who also got offers from many math PhD programs and have many math PhD friends, by far the most recruiting emails we get are from quant trading firms, and you won’t find that kind of math on Math.SE.
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.
That's interesting - what kind of maths do you use in quant trading?
Warning: on Math Overflow they do not tolerate noobs and noob questions. They will redirect you to the Math stack exchange (which is a different one).
ok, thanks for the warning :)
https://www.reddit.com/r/math/
It's one of the more wholesome communities on reddit.