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Recently polymath projects seems to have stopped. One reason for this could be that running such a project requires a lot of effort from at least one person running it. I was thinking if it were possible to run a sort of polymath project solely on mathoverflow, i.e., without any central blog-comment form, just asking questions, giving as motivation links to the other relevant questions. Also at the end of each important question there could be some links to possible running approaches, but every question would be maintained by the person who has asked it. This decentralized structure would be a bit similar to what Gowers proposed for polymath9, but imho using TiddlySpace was not the best choice, as although it might be a great platform, it takes time to learn and not many people might be willing to put in the effort. On the other hand, mathoverflow is already used by many, and not only those would see the questions who are actively committed to participate, so it really has the potential to grow into a polymath with many participants. Note that for polymath3 and polymath5 there have been questions asked here, some quite successfully.

What do you think?

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    $\begingroup$ I think MO questions can support a polymath project well, but I don't see how they could form all of it. Keeping track of the project as a whole and then turning it into an article sounds like a feat that needs some kind of headquarters outside MO. I think such a project also requires a place for announcements that do not fit the mold of an answer or a question. (I'm not saying it's impossible. I'm just not convinced yet.) $\endgroup$ – Joonas Ilmavirta Jan 24 '15 at 22:26
  • $\begingroup$ I suppose the most important requirement for a new polymath project is that someone (or some group of people) has an interesting problem and an idea for approaching it which is suitable for polymathy collaboration. Are there such ideas out there at the moment? $\endgroup$ – Joonas Ilmavirta Jan 24 '15 at 22:34
  • $\begingroup$ @Joonas: After the problem is solved, then the article writing up part might require an outside platform, but keeping track of the progress could be possible inside the questions (or maybe not, we have to try to see). And of course a problem with an approach is also needed, if this proposal gets a positive reaction, the next meta-question will be to select a problem. $\endgroup$ – domotorp Jan 24 '15 at 22:50
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    $\begingroup$ I think a number of independent projects have started and withered or succeeded depending on the strength of the supporting community. Certainly MathOverflow the forum and the foundation can lend some support, but the basic mission of both should not be extended unless and until the community is large enough. I recommend starting a proposal (or several, why not?), and when the project is in enough of a shape to receive assistance from the MathOverflow community, place an answer to this question with a link and an invitation. Gerhard "Has Some Suggestions To Make" Paseman, 2015.01.26 $\endgroup$ – Gerhard Paseman Jan 26 '15 at 22:20
  • $\begingroup$ And don't forget we have this: Proposals for polymath projects. $\endgroup$ – Joseph O'Rourke May 22 at 10:59
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    $\begingroup$ I don't like the current trend where people suggest leeching Mathoverflow's popularity and abusing its "focused, to-the point questions and answers" format to propose their new projects. $\endgroup$ – Federico Poloni May 28 at 9:50
  • $\begingroup$ @Federico This is an absolutely reasonable objection. My only defense is that the questions related to the PolyMathOverflow project would be also very much like other questions on the site. It is anyhow quite common that a MathOverflow question inspires several other MO questions. $\endgroup$ – domotorp May 28 at 13:02
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It is, of course possible, and one does not need a big discussion to start such a project, but one needs to have a clear idea of how the problem can be approached and how to split it into cases/steps/whatever that can be handled by different people in parallel. If we just say "Hey, guys, who wants to think of ABC? Let's do it together!", we'll, most likely, just get a herd of mathematicians staring blankly at an impenetrable wall and posting off topic comments when they get utterly frustrated.

If you have a question where you just not have enough strength or abilities to handle the entire thing alone but where you have a clear plan of attack (not guaranteed, of course, but at least demonstrably plausible), by all means, go ahead. However mere wishful thinking and the hope that "there is a bigger fish in the pond that will swallow the bait" or that "if small people make a party, they'll move the mountains", or something else like that will lead nowhere.

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  • $\begingroup$ What Navier-Stokes and other stuff are you talking about? I've never mentioned any of these... I agree with the rest of your answer, adding only that having a handful other enthusiastic, committed users is also needed, which is why I've proposed this thing. Also note that this was more than four years ago, right now my own enthusiasm and time is less to manage such a project, though I would be happy to participate to some extent. $\endgroup$ – domotorp May 23 at 9:21
  • $\begingroup$ @domotorp Ah, sorry, I didn't realize that was by you and not by Thomas. My apologies, should be more attentive. Deleting that part. :-) $\endgroup$ – fedja May 23 at 13:01
  • $\begingroup$ @fedja Most of the time mathematicians spend their time being stuck. The SE version of OpenGarden will serve as a years-long record of various comments and approaches. The post of a problem might be open long after the original author has retired. $\endgroup$ – Thomas Kojar May 24 at 14:54
  • $\begingroup$ @fedja Also, we agree that good posts should be about concrete subproblems accessible by specialists (as opposed to general big problems), but also by other area mathematicians who might notice some similarities with their body of results. $\endgroup$ – Thomas Kojar May 24 at 14:55
  • $\begingroup$ There is a clear demand for such a record of open problems and approaches that is not stuffed inside papers. So sooner or later we will create this. $\endgroup$ – Thomas Kojar May 24 at 14:57
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So we put a proposal in the spirit of this idea in here and described in Stack-exchange devoted to research problems, the suggested approaches and updates. The proposal was closed for various reasons.

This is in the spirit of Polymath where individual problems are tackled by numerous people. Each post is devoted to a research problem and we post approaches and updates to the problem.

Contrary to Polymath where people are coordinated and usually meet in conferences, in this SE version users will post approaches and updates independently and interact through the comment sections or chats. So it at least tries to get close to the level of interaction in a Polymath event.

But for now we encourage you to help with the growth of OpenProblems and OpenGarden, where in a sense we are collaboratively working on particular problems by posting the updates. In their comments section we can even suggest approaches.

We welcome any comments or feedback on this answer. I will try to improve it.

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    $\begingroup$ Why do you think it was closed because it was too close to MO? It looks to me as though it was closed on the grounds that it wasn’t suitable for the SE platform. $\endgroup$ – Jeremy Rickard May 21 at 19:06
  • $\begingroup$ @Rickard there are already many questions of this form in MO eg. "ABC conjectures updates?". In these questions there is no "one right answer" but many of them. It will be the SE version of OpenGarden, where we clarify research problems and propose approaches. $\endgroup$ – Thomas Kojar May 21 at 20:27
  • $\begingroup$ Why the downvotes? I will try to improve the answer. $\endgroup$ – Thomas Kojar May 21 at 20:27
  • $\begingroup$ @Rickard Originally the proposal was closed due to being too close to MO. I agree with this reason to some extent. My main issue with using MO is that these research posts are not answerable in the short term and so they would crowd the answerable posts. $\endgroup$ – Thomas Kojar May 21 at 20:32
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    $\begingroup$ I think that your proposal is entirely different from mine. While your goal seems to be to collect many open problems, I've suggested to pick one, and attack it by communicating over MathOverflow instead of a linear blog. $\endgroup$ – domotorp May 21 at 21:48
  • $\begingroup$ @Domotorp Each research post is devoted to only one problem and we attack it by communicating our approaches and updates as answers to that post. $\endgroup$ – Thomas Kojar May 21 at 22:32
  • $\begingroup$ This would result result in a linear (or almost linear, as their can be several answers) research, which is not that different from a blog. My proposal's structure would be a tree. Also, it would benefit from using mathoverflow, as it would involve automatically any user of the site. $\endgroup$ – domotorp May 22 at 9:03
  • $\begingroup$ Not the mention the brilliant name PolyMathOverflow! $\endgroup$ – domotorp May 22 at 9:04
  • $\begingroup$ @domotorp Each answer-approach will be visible to many and so multiple people will work on the same approach. Every answer has a comment section below it. Also, it will have multiple answers on the same approach but each one with updates or distinct flavours. $\endgroup$ – Thomas Kojar May 22 at 15:59
  • $\begingroup$ @domotorp As an intermediate step we can do something in this spirit inside MO, by creating a special tag for this eg. "Polymath" or "open problems database" (the post on the tag for "open problems database"). $\endgroup$ – Thomas Kojar May 22 at 16:03
  • $\begingroup$ Yeah, I've also imagined that a tag would be created for each PolyMathOverflow that we would append to each related question. $\endgroup$ – domotorp May 22 at 18:43
  • $\begingroup$ @domotorp please feel free to post your ideas at the post we created about this tag: meta.mathoverflow.net/questions/4230/… $\endgroup$ – Thomas Kojar May 22 at 22:40

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