I think there are a lot of good conjectures out there that don't get as much publicity as they should.

I think it would be useful for the research community if there was a centralized repository for all open conjectures much like: http://www.openproblemgarden.org/ I think was intended to function.

The most difficult factor preventing this from happening in my opinion is getting users to actually submit their conjectures and getting readers to visit the site to explore conjectures.

MO is not purely intended for this (and some users believe it is off topic while others believe its on topic) but the point is that A LOT of open problems probably do get asked here and this is the closest humanity has had to a crowd sourced open problems repository.

If there existed an "open problem", "formerly-open-problem" tag that was appropriately added to questions containing a mathematical question that is not known to be solvable and have generated interest but not generated any resolution then it would be very easy to filter through all of MO and find the set of all open problems.

I think that there are people (well at least myself) who would be interested in further structuring and organizing this data and then making it publicly available so that the state of research in math becomes a least a little bit clearer.

Would MathOverflow be interested in something like this?

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    $\begingroup$ Probably it's worth mentioning that there is a tag called (open-problems). However, it's a bit unclear what the tag is intended for - whether it should be used for post about a specific open problem or whether it's intended for lists/collection of open problems. See a related conversation in chat, in particular this message from one of the moderators. $\endgroup$ – Martin Sleziak Sep 6 at 22:40
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    $\begingroup$ I have added the (tags) tag to your question - well, since it's about tags. It seems that - to some extent - this is also about discussion whether such questions are suitable for MO. So perhaps the (on-topic) tag would be suitable too. (But as this is less clear, I did not edit the post myself.) $\endgroup$ – Martin Sleziak Sep 6 at 23:07
  • $\begingroup$ @MartinSleziak, I find the tag description for open-problems to be pretty clear, and applicable in both of the situations you mention. $\endgroup$ – Matt F. Sep 6 at 23:22
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    $\begingroup$ @MattF. That's true. OTOH, maintenance of the tag-wikis on MathOverflow is relatively poor, so it's not necessarily up-to-date. In the linked chat conversation, a MO moderator mentioned that they merged (open-problems-list) with (open-problems) and that the usage of the tag (open-problems) for a single open shouldn't be encouraged. Although the moderator did not update the tag-info in any way when they merged the tags. In any case, the intended usage of this tag would be probably a topic for a separate discussion. (But there are certainly bigger problems with the tag system on MO than this.) $\endgroup$ – Martin Sleziak Sep 6 at 23:30
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    $\begingroup$ FWIW, I would be against using MO as a "centralized repository for all open conjectures", mainly because I think MO works best when we can get answers by leveraging known expertise. Most open conjectures require more than known expertise, otherwise they wouldn't be open conjectures ;-) $\endgroup$ – Yemon Choi Sep 7 at 16:04
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    $\begingroup$ I will just point out that the question Stack-exchange devoted to research problems, the suggested approaches and updates is - to some extent - related. The question also links to Tag for "open problems database" and other ideas for collecting open problems their approaches and updates - however that question has been deleted since then. (Of course, it is still visible to 10k+ users.) $\endgroup$ – Martin Sleziak Sep 9 at 11:29

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