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Suppose that someone on Math.SE posts a questions that is, shall we say, difficult. After spending a lot of time on the problem, seeking help from both Math.SE and MathOverflow, I find out that no one knows the solution to it- in fact, there is a well-known conjecture such that the proof of the original question would follow from it, but this conjecture is just that- a conjecture, with no proof.

So I go back to the OP where the question came from. Despite getting a lot of views, and a handful of small comments, there is not a single response in the form of an answer. Should I write an answer, not exactly answering the original question, but rather explaining that there is no known solution yet, but that there is a conjecture that could address the question directly?

Normally I'd just be inclined to comment, but such a comment would be pretty long; I'd have quite a bit of commentary to put down.

What do you think?

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    $\begingroup$ Showing that the question posed is a form of an open problem is a good answer. $\endgroup$ – user147263 Nov 3 '14 at 21:38
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    $\begingroup$ When they prove that a Hilbert Problem is undecidable, do they publish a paper? or do they just add it as a comment on the next edition of the Hilbert Problems? $\endgroup$ – Gerry Myerson Nov 3 '14 at 21:38
  • $\begingroup$ @GerryMyerson I didn't (and no one to my knowledge did either) prove that the question is necessarily undecidable or unsolvable, but only that there is no (currently) known solution. I feel that proving a statement is undecidable is much more significant than saying "hey, we're unsure of any solution." But if you still think it's in line with MSE policy for me to answer accordingly to that problem, I totally will. $\endgroup$ – daOnlyBG Nov 4 '14 at 0:19
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    $\begingroup$ Sorry, I just meant to point out that sometimes a perfectly good answer to a question doesn't answer the question in the sense in which the questioner was expecting it to be answered. And in this case, if you're contributing good and significant content to the website, who can complain? $\endgroup$ – Gerry Myerson Nov 4 '14 at 3:07
  • $\begingroup$ @GerryMyerson No need to be sorry- I understand what you're saying, and I think I agree. I just wanted to make sure I wasn't giving off the impression that I proved the OP was unprovable or unsolvable. That would definitely be an answer! Thanks for your advice $\endgroup$ – daOnlyBG Nov 4 '14 at 3:09
  • $\begingroup$ They don't mention answering the unanswerable question, not sure why en.wikiquote.org/wiki/Man_of_La_Mancha $\endgroup$ – Will Jagy Nov 7 '14 at 21:49
  • $\begingroup$ Here's an example of an open question that I posed on mathoverflow mathoverflow.net/questions/182338/… I felt that the "answer", though it's not an answer or even part of the solution to the answer, appropriate though. I don't know why the question got closed down though. $\endgroup$ – Doug Spoonwood Nov 15 '14 at 3:21
  • $\begingroup$ Tiny niggle: the original question might in fact be much easier than the famous conjecture. Supposing it is just as hard, then proving it is (that is, showing that from an answer to the original question, the famous conjecture can be decided), would be an even better answer. $\endgroup$ – Steve Jessop Nov 16 '14 at 13:28
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I'm in a similar situation in that I've posted a difficult question, and thusfar, no answer has been submitted.

As an asker, I would very much like to read what you have attempted and, if possible, a clear concise statement of the reasons you did not arrive at the answer. It is beneficial to hear other people's initial ideas on methods of solution, especially if the problem requires extensive specific knowledge that the asker may not currently possess.

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Why not state an answer, stating that this is not a solution because you know of none, and state your thoughts? What's the worst that could happen?

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    $\begingroup$ Make sure to give a good argument. $\endgroup$ – Ali Caglayan Nov 3 '14 at 22:50
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    $\begingroup$ What's the worst that could happen? - Famous last words$\ldots$ $\endgroup$ – Lucian Nov 4 '14 at 22:49
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    $\begingroup$ In the worst case scenario your words will summon Gauss's ghost who will haunt you in your dreams telling you every night that the answer was in one of his unpublished papers of his drawer. $\endgroup$ – Cure Nov 4 '14 at 23:39
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    $\begingroup$ @Cure, if he'll also answer other questions I'll agree to that arrangement. $\endgroup$ – Daniel McLaury Nov 6 '14 at 9:13
  • $\begingroup$ also to prevent a comment to be cut up over multiple comments (because of the number of characters) , it is better to make it an answer $\endgroup$ – Willemien Nov 6 '14 at 11:01
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    $\begingroup$ @Lucian: Reminds me of "Hold my beer, I'm gonna try something" ;) $\endgroup$ – MPW Nov 6 '14 at 15:25
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    $\begingroup$ @MPW: "What duck?" $\endgroup$ – RghtHndSd Nov 6 '14 at 21:24
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    $\begingroup$ Worst that could happen? Infinity down votes seems spot on. $\endgroup$ – User Nov 10 '14 at 7:02
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Definitely post it as an answer. Even thought you do not solve the original problem, you provide a piece of information which is precisely what anyone interested in the problem wants to read.

Apart from the obvious advantage of making the answer appropriately visible, it also makes it possible for OP to accept, and thus remove the question from the "Unanswered" list.

If you feel inclined to do so (I wouldn't), you can always make the answer CW.

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  • $\begingroup$ Just checking, is it definitely desirable to remove open problems from the "unanswered list"? How much more accurate can the description "unanswered" possibly be ;-) $\endgroup$ – Steve Jessop Nov 16 '14 at 13:28
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    $\begingroup$ @SteveJessop: The way I see it, "unanswered list" is the place where one would look for a question to answer. Since known open problems are not likely to be solved here, I don't think there is much use in having problems like that on the list. $\endgroup$ – Jakub Konieczny Nov 16 '14 at 17:40

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