Places where one can post open problems (This must have been asked before and exist somewhere in Community Wiki, but I can't find it...)
Where can you post open (math) problems? And what are the advantages and disadvantages?

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*Example: This place (and Math StackExchange), duh.

*Example: The journal AMM had a corner "Unsolved Problems", but no longer. (Editor Stan Wagon told me that he doesn't know any math journal accepting unsolved problems.)

*Example: But then, probably any journal will accept a small "Open Questions" section after a research article.

*Example: USENET once had an useful group. The group still exists. (Yes, I'm that old...)

*Example: Other social media, e.g. Reddit has a math sub.

 A: I am one of the moderators of the Open Problems in Algebraic Combinatorics blog.
First of all, we welcome submissions from anyone who has a good open problem in algebraic combinatorics that they want to advertise (see the top post for info about how to submit).
Secondly, hopefully this blog shows you how it is easy to set up an open problem repository like this for your own subfield.
A: If you have half-a-dozen open problems in some definite area, why not write an article where you explain them, why there are important, what are the difficulties ? I did that once (Five open problems in compressible mathematical fluid dynamics, Methods and Applications in Analysis, 20 (2013) pp 197-210). Of course, you must agree with the editor. This is often appropriate in proceedings of conferences.
A: If it's a problem in Number Theory, the annual West Coast Number Theory meetings have a problem session, and the problems get collected & edited & posted to https://westcoastnumbertheory.org/problem-sets/
If you can't come to the meeting, you can send the problem to me (I'm the editor of the problem sets), and I'll present it for you.
A: Arnold Mathematical Journal has a problems section.
A: The Open Problems Project (TOPP) is
focussed on discrete and computational geometry.
We (Erik Demaine, Joe Mitchell, and I) started it in 2001 but its $78$ problems are now only sporadically updated or augmented. I believe my last update was 2020.
It now has a GitHub Repository.
The annual Canadian Conf. on Computational Geometry
has an open problems session, often feeding into TOPP.
A: The website https://www.scilag.net/ is also meant as a database.
A: If you can motivate the problem and make some partial progress on it, you can try and publish it as a paper in a specialized journal, or at the very least upload it to the arXiv.
If you only have empirical evidence, there are journals that are receptive to this kind of this ("Mathematics of Computation" and "Experimental Mathematics" spring to mind).
If it concerns elementary mathematics and is relevant to a wide enough audience you can try a popular journal such as "American Mathematical Monthly".
Other than that, you can

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*put in on your website, if you have one.

*share it with experts, as they have the highest chance of solving it, and at the very least of assessing its importance and difficulty and possibly guiding you towards relevant literature or a proof.

*share it in the problem session of a relevant conference. Problems from such sessions tend to be published in the form of conference proceedings.

A: For open problems in group theory: https://arxiv.org/abs/1401.0300
A: Open Problem Garden
I occasionally stumble across this in my search results. It's currently skewed heavily to graph theory, which suggests that the user base also skews that way. Con: it doesn't appear to be very active; the most recent addition is from 2020, although there are comments from 2022.
