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    • CommentAuthorMax Muller
    • CommentTimeMay 28th 2010 edited
    Hi there,
    I'm planning to start a question on mathoverflow posed more or less like a 'polymath' project. I would like to suggest a particular problem I'm interested in, show some methods on how I've been working on it to the mathoverflow-users and then ask people whether or not my methods would help to solve the problem.
    Is this type of question suitable for mathoverflow?

    Max Muller

    My gut feeling on this is "no". I see MO as more for questions where one expects that someone will be able to give a definite answer. In your example, you are going in with the expectation that no-one else will be able to answer your question. So I don't think that MO is the right place.


    Why don't you "preview" the question here? I mostly agree with Andrew, and think that it's likely to be extremely hard to ask a good polymath style question on MO.

    Any good polymath question immediately presents several sub-problems (in fact, hopefully a whole hierarchy of them) which are more tractable. This suggests a compromise approach: give the overview in blog format, and then farm out the minor problems to MO. The MO questions can refer back to the blog overview. If you actually announce the problem as a polymath problem, then you should also tag all the corresponding questions appropriately. Have a look at the [polymath5] tag, which already exists.

    As you've stated it though (asking whether your methods might work), it doesn't sound exactly like "polymath". A good polymath project should already have a well motivated approach, and involve other people in tackling all the resulting sub-problems that that approach entails.


    I think I agree with Andrew and Scott. My gut reaction is that a polymath question will be very regularly answered and edited so it might be getting bumped to the top too much. But I might very well be wrong. I think asking the smaller sub-problems instead, and keeping the main polymath project on a blog somewhere. But as I say, I might be wrong and perhaps the best thing to do is to ask the question, and if it doesn't work we'll learn from the experience.


    There is sort of a precedent for this; see . But that was a much more specific question. I agree that it might be a good idea to preview the question here.

    @Max Muller: the polymath thoughts you're having were pretty much similar to the ones I had when I posted that "let's compute the Fourier expansion..." question. I invited Gowers to give a colloquium at my university on the polymath stuff a couple of months ago and the idea had been kicking around in my mind ever since. But I agree with the other posters here---I don't think MO is particularly optimised for this sort of thing---it has big visibility (so e.g. if I'd just posted my question on some blog or other then it would have been even less likely to have been answered) but it has disadvantages too. Very early on junkie made it clear that he'd be able to do the problem, and the moment I realised this I just told him all I knew and then he did it. It was only a computational problem anyway---I knew the algorithm but had tried and failed to implement it and debugging was hard because my program output a plausible sequence of numbers which I knew were wrong but it was hard to pinpoint exactly why it was wrong. So it was just a case of getting someone else to do it. Not really polymath then---but I was very grateful to junkie for doing it! I'd thank him in person if I knew who he was :-) But what was tough was that when he had an idea he'd post it but it would end up as an "answer" and it wasn't really an answer and there was no real point voting for/against it, and voting just jumbled up the order of things anyway, which was hardly the best idea. Somehow perhaps my main point is: what would one vote for, and how does one stop voting from disrupting the natural flow of the argument? One can't do this. Hence for a big project I can't imagine MO working well. The advantage of what I suggested was that it was shortish so it worked---but basically one or two people were enough to nail it. If the problem had been harder it just would have been a lot more chaotic: already when I posted I knew how to do it, it was just that I didn't have the time to do it (and had already tried and failed due to making an error which I couldn't find) and someone else did!
    • CommentAuthorMax Muller
    • CommentTimeMay 29th 2010
    Hmm, thank you all for your thoughts. @ Scott Morrison and Andrew Stacey: Yes, it's true I would be going in with the expectation that no one will be able to know the answer (yet). It's a rather specific problem, but I think a lot of people would be interested in the approach(es) I could present. I think I will start the blog to present the overall problem, and pose several I approaches here on Mathoverflow, asking people if they could work. I will pose the actual question I would've like to pose initially on mathoverlfow, in the meta-section in a week or so. First, I need to get some facts straight with my mathematics teacher, so I don't make a fool of myself when put the question on this website. The sub-problems of the problem would be: how would this approaches be described rigorously? Why does(n't) this approach work? etc.
    @ (Kevin) Buzzard: I think the voting system in a polymath-style problem is a problem, too. A possible solution is (perhaps) that voting wouldn't be allowed on polymath-style questions, but I don't think that's a good solution, because voting really is a part of the identity of mathoverflow... Yes, more complicated polymath problems could result in a chaos on the answering page, but the opposite could be true as well. Perhaps I could divide the question into several different sub-questions as Scott Morison and Grétar Amazeen suggested, and the people who give the answers should adress one sub-question per answer, or something like that.
    Another question that comes to my mind now is this one: Suppose a mathematician would find a solution to the actual problem, using the methods invented by another mathematician. Then the former mathematician would be obliged to inform the latter mathematician s/he is going to write a paper on the subject, wouldn't s/he? I think the eventual paper would get quite a lot of co-authors...
    So, to conclude: I'll start the blog where I'm probably going to pose the 'big' problem and I'm going to pose the question I'd like to pose on mathovflow, here in the meta-section in about a week or so.


    please don't ask a single question (i.e. mathoverflow page) with several 'actual questions' on it. Ask separate mathoverflow questions for each sub-problem. Remember, questions should be as specific as possible (but not more so!) and you should ask every question with an earnest hope of being able to accept a single answer that you feel makes any other answers redundant.

    (You'll notice that this desideratum makes all [big-list] questions bad questions, but I think that's compatible with my view of [big-list] questions! :-)

    @ Scott Morrison and the rest: I have decided to cancel my 'polymath project'. It was largely based on methods show in <a href=""> this question </a> , the most important of which has been shown to be false in the accepted answer to the question.
    If you wonder which polymath project I'd chosen: To find the exact evaluation of Apéry's Constant. I wanted to expand on Euler's methods or find a patern of the (generalised) continued fractions of the even values of the zeta-function. I had some other 'methods' in mind as well, but they've all been rendered pretty useles.