Polymath projects on StackExchange/mathoverflow?

I’ve been thinking a bit about whether the StackExchange software (which mathoverflow is running on) could be used to host a polymath project.

I’d imagine it involving many many questions and answers, with links between them, modelling the division of the “big question” into its constituent chunks.

There are some big advantages — in particular, it’s easier to pay attention to individual parts, because there’s more structure than in blog comments.

As a first approximation, you might start out like this: Terry asks the polymath7 problem, linking elsewhere for motivation and background. Tim posts a first ‘answer’: “Could we attack this by proving Lemmas X, Y and then generalising the approach of Theorem Z?” and at the same time creates questions corresponding the Lemmas X and Y and a more open question about Theorem Z. Other participants can then go to those questions to give their thoughts. Answers don’t have to be “answers” in the convention sense — they’re just meant to correspond to “ideas”, and should often link to a new question if it’s obvious that the idea needs further development. The StackExchange software allows for comments on answers, which would allow short responses to previous answers.

The big disadvantages of StackExchange are that
* at this point, there’s no LaTeX support, although this will hopefully change.
* the reputation system inhibits new participants, at least at first (they can still ask and answer questions, but commenting and upvoting are limited).
* it may end up harder to understand the “big picture” than in a blog thread.

The solution to the first two of these may be to try a polymath project at mathoverflow.net itself, rather than a new installation. Many participants will already have reputation (and on an established site it’s very easy to gain enough reputation to comment and upvote, because any decent question will quickly garner reputation). It’s easy to filter questions by tags, so I think you could ignore everything else happening on mathoverflow.net if you wanted to.

The last problem might be addressed by having a “community wiki” answer at the top of each question, summarising progress so far, as well as regular progress reports on blogs.

8 thoughts on “Polymath projects on StackExchange/mathoverflow?

  1. I think this model might be suited for a project which can split naturally into a large number of loosely interacting parts. A good example might be a reading seminar on a paper; one could have different threads based on specific questions in specific sections, and one might be able to accommodate lots of readers who are at varying stages of working their way through the paper.

    For projects which require a big picture, it may be sub-optimal though, even with some blog oversight, unless one had some dedicated moderators who were willing to invest a fair amount of time in organising the chaos. But it’s worth a shot, perhaps for a mini-polymath project at first; it should yield useful data even if it doesn’t fully achieve its ostensible aim.

  2. The StackExchange software is promising as far as its ability to keep the barrier to entry low. You don’t have to wade through a ton of past comments to see one clearly stated question at the top of the page which you might have something to say about. But I agree that some big-picture stuff is needed (and of course I’m going to posit this big-picture thing should, eventually, just be a Wave organizing all the relevant questions).

  3. The more I think about this idea, the more I like it. But for me, the barrier still remains coming up with good Polymath problems; I have plenty of research problems, but they’re not good for much of anyone else (which is, in part, why I’m working on them).

  4. I think there’s even more interesting question — suppose MathOverflow had a special type of tags, like ‘research-polymath’, that would prevent question from appearing on a front page. Then people could post these questions on a regular MO site, and see all of them by searching for this tag. There would be then some question balance between the convenience of not having to set up a separate site and inconvenience for others who might occasionally see the research-polymath posts. It’s not clear for me into what direction the balance would point out. What do you think?

  5. Eh, I read half of your post, then posted the comment #5, then read the other half and noticed that you’re essentially thinking about the same idea. I would say it now deserves to be publicized.

    Also, “For projects which require a big picture” probably the right technical things is a combination of wiki + MO (perhaps a “research-polymath” tag search could automatically display some text from a predefined wiki page?)

    I agree though that the problem of “the reputation system inhibits new participants, at least at first (they can still ask and answer questions, but commenting and upvoting are limited).” is not easy to solve. It appears that activities under standard MO and special research tag are simply different, so it’s suboptimal to try to force the equality of “somebody becoming proficiant on MO” and “somebody becoming proficient in polymath” by technical means.

  6. the reputation system inhibits new participants, at least at first (they can still ask and answer questions, but commenting and upvoting are limited).

    beta 6 of SE will include “bootstrap mode” where the various reputation thresholds are lowered.

    I like the Polymath5 approach of outsourcing subquestions to MO, but having it’s central hub elsewhere. It effectively taps people who aren’t otherwise following the polymath without disrupting the normal functioning of MO and without giving up any of the benefits of threaded discussions.

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