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I am a bit confused on our policy for open-problems. Are we allowed to post a technical/narrow conjecture/open problem on MO?

For example, here is a type of a beautiful question that I have in mind Open problem: $\log n$ factor in Binomial empirical process with the tag open-problems. Was this question within MO-policy? I am asking because if so, I want to post some technical-open questions too from my article.

I personally enjoyed reading the above post and the updates and I imagine eventually the OP or someone from their area will just post an answer that the problem has been resolved in reference XYZ.

Q2: Is it possible to run some small experiment with "narrow open-problems" to help clarify if the community finds it valuable to have them? During that process the moderators can adjust the requirements in the tag "open problems" accordingly as they see fit.


My opinions

I understand that a similar question has been asked multiple times before eg. What should be the policy on "open problems" on MO? and What should the tag (open-problems) be used for?.

I honestly feel that it will benefit the growth of the MO website to allow the listing of technical conjectures/open problems that we find eg. in our articles.

Alternatives such as scilag.net are underused and this doesn't seem to change. Currently the process of finding open problems is still the old-school of a)talking with people, b) hopefully the authors stated them in a remark or at the end of the article or c)finding them by ourselves through experimenting.

This will also help mitigate "re-discovering" since some knowledgeable expert can just state in the answers "Oh this is already known from this Russian article X in 1962 and here is the reference.". So in that sense it can fall under the quoted answer

Most importantly, please remember that MathOverflow is a question and answer site: the prototypical question is posed under the assumption that some other user will be able to answer it.

And a question can eventually be closed once the open-problem has been resolved or proved to be ill-posed.

There would again need to be formatting guidelines to avoid stating mathematically-ambiguous open problems, but that is an issue even with regular MO-questions. I will be happy to help with clarifying OP questions from my research area.

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    $\begingroup$ Since you've mentioned the tag (open-problems), I will mention that the intended usage of this tag is unclear: What should the tag (open-problems) be used for? $\endgroup$ Aug 5, 2023 at 7:38
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    $\begingroup$ @MartinSleziak I see. Thank you. I see it is still unanswered. Do you know who can I ask about this? Should I email the moderators? Because I am genuinely wondering if I can post open problems too from my article like in that MO post. $\endgroup$ Aug 5, 2023 at 21:56
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    $\begingroup$ I’m skeptical of the value of tabulating open questions on MathOverflow. It just doesn’t play to the strengths of the platform, and would be too random and unfocused to be useful for someone looking for things to think about. That’s also why I think that other attempts at similar things on the internet have failed. The collections of problems I know about that have been influential were pretty focused, and also were not isolated problems but part of a narrative about where a field was moving. A good example of that in my field is this: math.uchicago.edu/~farb/papers/mcgbook.pdf $\endgroup$ Aug 6, 2023 at 3:40
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    $\begingroup$ @AndyPutman "too random and unfocused" is a very frequent issue with current MO questions too. And the solution is for experts to nudge the OP to clarify. I will be happy to help OPs clarify their open-problems in my area. $\endgroup$ Aug 6, 2023 at 4:17
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    $\begingroup$ Both can be available i.e. both a good well-edited long list of problems and also small technical questions thought by one person. For example, many professors carry lists of big-small technical problems in their websites. So MO can be a great place to host many of those problems regardless of the state of the initial website (i.e. website closing down). $\endgroup$ Aug 6, 2023 at 4:21
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    $\begingroup$ The versatility of MO is also its very power. A site dedicated to just collecting open-problems seems to quickly die out because there is no other source of traffic. $\endgroup$ Aug 6, 2023 at 4:23
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    $\begingroup$ I think you miss my point. MO is very good at one specific thing (getting answers to questions), and I don’t think its format adapts well to other sorts of things. I also don’t think giant collections of random open problems in different fields adds much value to the world. That format just doesn’t match up with how mathematicians come to be interested in questions. I think that’s why sites trying to do that aren’t really successful. $\endgroup$ Aug 6, 2023 at 4:25
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    $\begingroup$ Different people choose open-questions to work with in different ways. Some questions can inspire them in their own research. $\endgroup$ Aug 6, 2023 at 4:27
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    $\begingroup$ Yes, but this format accommodates a variety of types questions. I think that the open-questions will fit nicely since eventually if well-posed, they have a final answer. If not well-posed, then there will be answer too. No different than the current MO situation of giving positive answers or counterexamples or explaining why the question is not well-posed. $\endgroup$ Aug 6, 2023 at 4:28
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    $\begingroup$ For example, in the post I linked before, I imagine the OP will eventually just type an answer saying the answer got resolved by authors XYZ. I enjoyed reading the updates too. $\endgroup$ Aug 6, 2023 at 4:36
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    $\begingroup$ Can we at least experiment with some very restricted versions of "open-problems"? There is a tag already. So we can include more restrictions eg. maybe the requirement to also include some corresponding reference for those who want to read more context. Then the moderators can adjust the requirements accordingly. $\endgroup$ Aug 6, 2023 at 4:45
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    $\begingroup$ But anyhow, I am genuinely interested on whether the above post was within current MO-policy. $\endgroup$ Aug 6, 2023 at 4:46
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    $\begingroup$ At the very least, questions on open problems shouldn't be solely asking well-known open problems. Perusing the list of questions tagged open-problem reveals generally suitable and sometime very carefully and narrowly-worded queries. $\endgroup$
    – David Roberts Mod
    Aug 6, 2023 at 5:45
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    $\begingroup$ @DavidRoberts I agree, I upvote. There should be genuine effort to have a specific technical question. $\endgroup$ Aug 6, 2023 at 5:51
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    $\begingroup$ @DavidRoberts Is it within current MO policy to post narrow-open questions as the one in the post mentioned above? If possible, I would like to get an official answer below maybe mentioning some criteria to help me in writing my question. $\endgroup$ Aug 6, 2023 at 16:32

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There are clearly cases when the tag has been used a perfectly acceptable way, for instance asking questions about open problems as a class of problems, or in meta-discussion about a specific open problem. I believe the intended off-topic use-case is to so tag questions that are basically famous open problems, or mild variations on them. If a user is putting in a decent amount of background work into their question, delineating it carefully, and being very tight and focused on what their question is intended to cover, then there is more leeway as to what is allowed. As a counter-example, I recall a question Is the Riemann Hypothesis equivalent to a $\Pi_1$ sentence?, which is not tagged , though it is about an open problem (the RH) but actually on a very specific question that in the end itself wasn't an open problem. Tagging the above question as an open problem might indicate that the "is it equivalent to a $\Pi_1$ sentence?" question was open, when it was not.

As discussed in the comments, there is a sense in which many, if not most questions on MO are open problems: unless someone is asking for something in the literature, it is probably a problem no one has thought about before, or if so, very few. I have a couple of questions that ultimately led to more than one paper being published by others, because what I was asking about just didn't exist before. But I wouldn't consider tagging such a question as .

The example given by the OP is in some sense a reasonable example, and would have been even if not such a success story. It is a very narrow technical question that had a chance of being answered, or at least prompting people to think about it. As originally asked, the question didn't mention how the question had been presented as an open problem. What should be avoided is questions that it's clear have no hope of getting an answer either on MO or by people thinking hard about it and subsequently writing a paper answering the question (this has happened due to space constraints: you can't post a 20-page paper as an MO answer!).

Above all, the point of MO is to get answers to specific questions. The original mental image of MO was of being able to ask one's colleague down the hall, or at morning/afternoon tea. Telling people about an interesting open problem and asking a specific technical question about it, to an expert on that area, or a related one is useful if you think you'll get some kind of helpful answer. Bugging a colleague with a difficult, well-known open problem they cannot really say anything about is not productive.

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  • $\begingroup$ You have mentioned a few times the tag (open-problem). Such tag currently does not exists - there is a tag called (open-problems). The moderator who changed the name mentioned that he does not see this as a suitable tag for a single open problems - it seems to be closer to (open-problems-list), which existed in the past. See also: What should the tag (open-problems) be used for? $\endgroup$ Aug 19, 2023 at 4:29
  • $\begingroup$ @MartinSleziak gosh, silly me, that was an accident $\endgroup$
    – David Roberts Mod
    Aug 19, 2023 at 10:18
  • $\begingroup$ However, @Martin, let me point out eg ra.rings-and-algebras, ds.dynamical-systems,... are plural by name, but can be used for the singular. The use of open-problems is very much edge-case territory, and aside from some general examples that are on- or off-topic, it might beta case of "I know it when I see it" $\endgroup$
    – David Roberts Mod
    Aug 19, 2023 at 10:33

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