# How to treat `polymath' questions?

W. Kuperberg asked a question about plane geometry, which invites contributions to solving a research problem which he has worked on.

Small quadrilaterals containing a given convex region

Given that we're a questions and answers platform, I'm not positive than MathOverflow is the optimal place for such a question: but the project he is proposing seems worthwhile, and it seems a fairly decent polymath-like request as such things go. Can this and similar questions be usefully migrated to a polymath-suitable platform, in which people can post little comments, share knowledge, and make progress together? E.g. to some sort of linked blog?

Any ideas? For this and for similar questions, which do come up from time to time.

• I think this is related to the discussion on open problems: meta.mathoverflow.net/questions/360/… In this case, the OP posted an open problem without including all the relevant background. – François G. Dorais Jul 11 '13 at 5:46
• Except that the OP phrased this question as a contest, which I read as an invitation for a polymath project or suchlike, given that he is an expert on the topic. He obviously thinks it's tractable and we should take a whack at it- but I am skeptical that MO is the right platform for this. – Daniel Moskovich Jul 11 '13 at 9:49
• This case seems still different (and in fact this view seems confirmed by an comment of OP on main meanwhile): namely, it was to rather present a problem as some sort of challenge/game. This is AFAIK perfectly alright on other places but not on MO, so that a new user does not know this is not a big deal, but I think this also could be made more explicit. Indeed, indpendently of this event I had planned to include this issue in the second round of discussion of the post linked by @FrançoisG.Dorais I did not yet since I wanted to let time pass for people to comment and vote on 1st round. – user9072 Jul 11 '13 at 14:27

I'm perfectly happy with the current culture that sees this type of question as not-for-MO. But challenges and games (and, indeed, poly-style open problems) are, I think, welcome on other SE sites. (I say this without a lot of experience on other SE sites, so I'm happy to be contradicted.) So I don't see any technical reason not to allow this type of question — the software doesn't seem to be the reason that this question isn't appropriate.

Perhaps it's time to start explicitly allowing well-posed open challenge questions. If we do, we should have some way of marking them as such, and some guidance on the help pages about what makes a good or bad question of this type.

Or perhaps we should continue to send these questions elsewhere — they're not, at least not yet, the primary goal of MathOverflow. I don't have much of a preference.

• What is an "open challenge question"? – user9072 Jul 11 '13 at 22:39
• @quid: I didn't mean anything completely precise, but a question of the type linked --- an open problem, but one that seems like it could be quickly solved if you pose it as a problem-solving challenge. You know, if IMO or Putnam started putting open problems on the test... – Theo Johnson-Freyd Jul 11 '13 at 22:51
• If somebody seeks input for a res.problem and is very clear about what they know and intend, I might very hesitantly consider allowing this. (For actual collabortaion the site is unsuitable for one thing as this was way to noisy; this was one of the last disc. on the old meta, conclusion no. I see not reason to already revisit this.) The orig. question is absolute no-go for me; it was not clear it is a question where the OP knew a lot more about it then said. This is a considerable problem as it potentially wastes other peoples time. I answer here to help people, not for challenges. – user9072 Jul 11 '13 at 23:04
• Even if it were clear, it has nothing to do with research to refind things others did before when being prompted to do so. If enough people want a site specifically for math challenges and puzzles, it is easy enough to set one up on SE. (But I think such places exist already on the internet AoPS for example, AFAIK) – user9072 Jul 11 '13 at 23:07
• To add to this it is true there are SE sites for challenges and puzzles, in programming, for example codegolf.stackexchange.com But of course this is a site separate from say Stack Overflow or Programmers and so on. – user9072 Jul 11 '13 at 23:18
• @quid: All sounds great, and as I said, I have no complaints about the current mores. – Theo Johnson-Freyd Jul 12 '13 at 3:16

Why should there be a difference between a question “It is known that this constant $x$ is between $1$ and $2$, but for some ugly calculations I need better estimates. There are some simple optimisations to get a smaller value of it. Are there sharp results? Do you know any better estimates?” and “The value of this constant is unknown, but between $1$ and $2$ and it is easy to do some optimizations. Contest: Find an estimate, the smaller the better”. I think the real difference is not the funny word “contest” (it is not bad to use some funny words), but that in the second case it is known to be an open problem. Thus this is just a special case of the open-problem issue in my opinion.

• I think these are totally different. The first one is "Tell me about some relevant research I might not have heard of." The second one is "Solve my open problem." – arsmath Jan 10 '14 at 21:27
• @arsmath That is exactly what I tried to say. It is not about the word “contest”, but about the meaning “solve my open problem”. – The User Jan 16 '14 at 21:45

Local vs. Global MO in relation to "Polymath" efforts

The above discussion post contains a suggestion for handling these.

It may be time for a shift in behavioral culture. Instead of asking the original poster to improve the question, have a "boilerplate header" placed at the top of the question, which can be removed when the question has been properly changed. For the question at hand I suggest the "Reference-Request": "In keeping with the goals of this forum, the community encourages the question to be seen as (and further edited to increase emphasis on) a request for references. Please help by editing appropriately and answering in kind.", followed by clarifying text such as "This forum is not appropriate for placing challenge or contest problems; it is appropriate to ask for references to such problems." The current edit by another member is commendable, but could go further.

• Change is never good. Look at all the horrible things that have happened only because protein molecules began to change and formed protective membranes around themselves! – Asaf Karagila Jul 11 '13 at 21:59
• Of course change is never good. Nor is the status quo. The above is proposed as an energy-minimizing tactic. Long Live Entropy! – The Masked Avenger Jul 11 '13 at 22:23