Certain polymath-flavor questions appear on MO, and are not really appropriate for the forum. Such questions are probably posted (I can only be sure for my own such posts) because MO captures a huge "mathematical experience footprint" that is unlikely to be harnessed by a blog, for example.

The present post does not so much contain a question, but contains a suggestion for better handling (and/or preventing?) such posts. Here's the suggestion: There is a plugin available that will add Q/A functionality to a WordPress blog. If someone is interested in starting a "mini polymath" project that is intended to collect the community's ideas on a particular question, he or she can start such a blog dedicated to that question...forming a "Local MO" for that question. A single question on MO (viewed as global MO) can be dedicated to collecting links to all of these local MO "polymath" sites dedicated to the more speculative or collaborative efforts surrounding a given question.

The up/down voting for a local site will not signify "reputation" of a user, but instead evaluate a given idea for its "promise". The Q/A functionality will then allow the most promising ideas and strategies to bubble to the top for a question and it's associated answers.

I'm interested in the community's thoughts on this idea.

Of course, I'm posting this on mathoverflow.meta because the single big-list question pointing to these local polymath projects needs to be suitable for MO, and the post on MO pointing to these projects would probably be the main way the local projects can be found.

  • $\begingroup$ I've been chided elsewhere for irrelevant/frivolous comments, but I couldn't resist the following link since "Local MO" instinctively reminded me of "Local 24" youtube.com/watch?v=EvsG67DYVLk Silliness aside, I'm slightly concerned: are the MO posts going to be generated automatically, and do we still have the power to close ones which are, erm, unsuitable? $\endgroup$ – Yemon Choi Aug 26 '13 at 16:33
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    $\begingroup$ @Yemon: I was going for minimally invasive. MO won't change at all, but there will be a single MO question containing, as answers, links to the "local MO" sites...which will be taken care of by those who created them. The links to the local sites would be posted as usual by any MO user. Most likely a link to a local MO site would be posted by that site's creator. Nonsense sites of this kind will probably be violently downvoted... $\endgroup$ – Jon Bannon Aug 26 '13 at 17:01
  • $\begingroup$ Also, the local 24 thing was funny...I hadn't seen that. $\endgroup$ – Jon Bannon Aug 26 '13 at 17:05
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    $\begingroup$ Here is an idea of Scott Morrison, 3 years ago ! $\endgroup$ – Sebastien Palcoux Sep 9 '13 at 12:10
  • $\begingroup$ suggest new proposal on area51 for polymath type projects. all that is needed is critical mass of users. it can be helped by "high profile" or "celebrity" type endorsers. anyone game? put further discussion on theory-salon chat $\endgroup$ – vzn Nov 26 '13 at 22:04

The problem with large collaborative projects like the Polymath Projects is that they are not Q&A structured. Instead, they are branching discussions with moving hotspots. What you need to host such a project is a platform like Discourse, Disqus, Vanilla, etc.

The reason why these posts appear here is because of MO's main asset — a large community of highly knowledgeable mathematicians. It turns out you can have that if you're creative enough to take advantage of MO's main weakness — an insatiable appetite for fresh mathematical questions. For example, when an interesting problem pops up in your project, post it on MO with a link to the project and reel in the goodness. It doesn't matter whether you catch users or answers, it's a win for your project and a win for MO!

On a technical note, I would recommend creating a special tag to use on questions associated with the project. This way, you can have your own custom MO page that to facilitate back & forth flow. If this catches on, we should request an event tag mechanism so that these special tags don't pollute the tag ecosystem.

In another note, there is a position available at MathOverflow for creating manageable side projects and other features for MO's public relations side. A decent place for community announcements would be a very desirable feature, for example. Sadly, nobody has shown much interest in that position yet...

  • $\begingroup$ Thank you François! I wasn't aware of the platforms you mentioned. These are very interesting ideas. $\endgroup$ – Jon Bannon Aug 26 '13 at 23:25
  • $\begingroup$ Regarding the other note: is there a link to the description of the position? $\endgroup$ – Jon Bannon Aug 26 '13 at 23:26
  • $\begingroup$ @Jon: There is no official description, we're hoping the candidate will come with their vision for the position. (Unfortunately, this is an unpaid position though there are options for funding some projects.) $\endgroup$ – François G. Dorais Aug 26 '13 at 23:35
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    $\begingroup$ Interesting. I hope the candidate has a sharp idea of how to interface MO in the way you describe above. A vision of a healthy online organism for collaborative mathematics with MO as one of its organs is a very promising vision to sharpen. Perhaps some ideas for how this might look could appear as comments to this question. If something manageable crystallizes, someone is bound to take it on. $\endgroup$ – Jon Bannon Aug 26 '13 at 23:40
  • $\begingroup$ Actually, it may be a good idea for someone to start a thread on meta to try to provide an initial sharpening of the community's vision for the broader role of MO. A discussion of some possible directions for branching out might provide focus that might draw someone into taking on the unfilled position. Just a thought. $\endgroup$ – Jon Bannon Aug 27 '13 at 0:00
  • $\begingroup$ In fact, if it is already clear how MO fits into the grand scheme of online mathematical collaboration, something in the FAQ might help stave off inappropriate questions for the forum and redirect such content to a better place. Is this already known? $\endgroup$ – Jon Bannon Aug 27 '13 at 0:05
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    $\begingroup$ @JonBannon the FAQs since a long time contained (and contains) suggestions for other places than MO for certain content inappropriate here. Unfortunately, all too often they are ignored. $\endgroup$ – user9072 Aug 27 '13 at 12:50
  • $\begingroup$ @quid: I should have been more specific with my comment. The FAQ should point to specific resources of quality commensurate with MO, complete with links to as many of these as possible, for other valid yet MO-unsuitable content. $\endgroup$ – Jon Bannon Aug 27 '13 at 15:08
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    $\begingroup$ @JonBannon this is impossible (or will be empty) as of course no other resource is of quality comensurate with MO ;-) But leaving this aside this is/was done to some extent, for example for open problems. See the relevant section of what question can I ask here in the help-center and my proposed rewrite meta.mathoverflow.net/a/540/9072 $\endgroup$ – user9072 Aug 27 '13 at 16:59
  • $\begingroup$ @quid: A valid point! (But I'm an MO groupie...) :) $\endgroup$ – Jon Bannon Aug 27 '13 at 17:04
  • $\begingroup$ If the questions about collaborative works on open-problems are almost non-accepted on MO, and if there is no polymath-type site of quality commensurate with MO, then this issue has its purpose for creating all together here a site (or many sites) complementary to MO, for massive collaborative works on famous open-problems, of quality commensurate with MO. $\endgroup$ – Sebastien Palcoux Aug 27 '13 at 19:11
  • $\begingroup$ @Francois: you give the impression of being sad about nobody coming forward with interest in a position that has seemingly never been publicly communicated. That seems kind of odd. Why not tell people about it? $\endgroup$ – Ryan Budney Aug 28 '13 at 20:59
  • $\begingroup$ @Ryan: We did but then we realized we had no good place to put the announcement... Vicious circle? Nah, we could try harder... but none of us is any good at... Dang! $\endgroup$ – François G. Dorais Aug 28 '13 at 21:04
  • $\begingroup$ disagree that polymath prjs cannot fit into stackexchange model somehow, think there is very strong potential to use stackexchange software as a polymath type tool. but as a separate site, not inside math overflow $\endgroup$ – vzn Nov 26 '13 at 22:16

If in addition references to the literature (especially when made freely available online or at least indicated when it is behind a paywall) are collected on such a blog, so that not just ideas are presented but a summary of published ideas has also been collated, that would serve as a reference worthy of being pointed out by MO. Somehow a polymath wiki before it achieves results is not quite as deserving, in my opinion.

(Even if the references are loosely formed, yet firm enough that later scholars can provide exact citations, that would still make an acceptable resource, again in my opinion.)


Praise to collaborative work :

Here is a list of abilities for mathematicians :

  • Creativity: have lots of new ideas
  • Curiosity: be interested in what is unknown, new
  • Organization: provide a framework, a space 'privileged' to what has not yet
  • Discrimination: distinguish between a good and a bad idea
  • Development: do the first works, the first steps
  • Communication: talk the works to other people.
  • Discipline: identify errors quickly
  • Performance: quickly assimilate a large amount of information and work very hard.

The activity of mathematician requires to have developed a little each of these abilities. Nevertheless, every being is naturally gifted in some of them, and much less in others. Therefore, the mathematician lose a lot of time and energy into certain aspects of his work, while these aspects would be dealt much more easily by others.

Solve an open problem, is an entire business, but in a real business they are many people, boss, accountants, salesmen, secretaries, security guards, workers, people of households ... Imagine if one person should play all these roles, this would be very laborious and exhausting, and the business did not work well, or else it would be a very small structure. Solve great open problems, it is a great business, and for being effective and fluid, it needs a lot of people, well-coordinated.

Today, a high-level collaborative structure, where each plays its role according to its intrinsic abilities, would advance very quickly on problems on which mathematicians block for so many years. Why this blocking ? Because everyone separately, or in small group, try to solve the problem, while the problem is a larger business that would require a massive collaboration well-coordinated.

I invite each user who read theses lines, to express their views, their ideas for a new site, complementary of MO, for a massive collaboration of very high-level, for solving all the great open problems.

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    $\begingroup$ "Today, a high-level collaborative structure, where each plays its role according to its intrinsic abilities, would advance very quickly on problems on which mathematicians block for so many years." I fail to see the evidence for this. Look at the amenability problem for Thompson F, for instance $\endgroup$ – Yemon Choi Aug 28 '13 at 17:58
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    $\begingroup$ Also, en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect seems pertinent $\endgroup$ – Yemon Choi Aug 28 '13 at 17:59
  • $\begingroup$ @YemonChoi : You have no evidence for this, but we have no evidence for the opposite. One example is not a proof, I could cite the classification of finite simple groups etc... I'm not sure to well-understand your analogy with Dunning–Kruger effect, but perhaps it's interesting, so could you please be more precise ? $\endgroup$ – Sebastien Palcoux Aug 28 '13 at 18:24
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    $\begingroup$ I sense that solving the great open problems is a poor use of such collective power. $\endgroup$ – The Masked Avenger Aug 28 '13 at 18:26
  • $\begingroup$ @TheMaskedAvenger I guess it depends if you are the traveller who gets to drink the stone soup, or one of the people who actually has ingredients $\endgroup$ – Yemon Choi Aug 28 '13 at 18:27
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    $\begingroup$ @Yemon's comment on Dunning-Kruger: This could be a MAJOR obstacle to productive large-scale collaborative effort in mathematics. $\endgroup$ – Jon Bannon Aug 28 '13 at 19:25
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    $\begingroup$ The effect could also be a tool, as the less competent could generate ideas. A central problem to this will still be managing communication. $\endgroup$ – The Masked Avenger Aug 28 '13 at 19:36
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    $\begingroup$ @MaskedAvenger: Perhaps this is where the focus should be...somehow sifting the right amount of crazy. I don't have a clear idea of how to do this... $\endgroup$ – Jon Bannon Aug 28 '13 at 20:23
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    $\begingroup$ @Sébastien Palcoux: The Dunning-Kruger phenomenon seems to suggest that a large number of less-than-qualified individuals may form a very loud voice on a badly designed collaborative site. I don't think an Area 51 proposal would be harmful, but I think that math.se and mathoverflow are perceived as having exhausted the Q/A needs of the mathematics community. $\endgroup$ – Jon Bannon Aug 29 '13 at 0:17
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    $\begingroup$ Something different is needed. I'm not sure what, if anything, will work. $\endgroup$ – Jon Bannon Aug 29 '13 at 0:19
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    $\begingroup$ I think quality control is more important than a large number of people eager to share their intuition and "creative" ideas. That is what I meant by my reference to the Dunning-Kruger effect $\endgroup$ – Yemon Choi Aug 29 '13 at 8:43
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    $\begingroup$ Moreover, near the start of this comment thread, you claimed I have no evidence for the opposite (of what you claim). I could reel off a long list of hard problems that are either still open or were open for a long time and not solved by some communal work by the non-experts and dilletants, but by focused work by the experts $\endgroup$ – Yemon Choi Aug 29 '13 at 8:46
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    $\begingroup$ I have a problem with those who feel that those of us who want exactitude and careful thought are stifling creativity. People being "creative" can turn out to be people talking rubbish. Yet again: I refer you to Dunning-Kruger. Let me be even more blunt: in my view, ideas are cheap. $\endgroup$ – Yemon Choi Aug 29 '13 at 9:02
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    $\begingroup$ I'm not sure we do. I meant that it is easy for someone to spout off half-baked or ill-informed ideas, and it is hard for someone else to come along and fix them, or create order and value. Why encourage people in the former if they cannot or will not do the latter? (I have to go now, I'm afraid.) $\endgroup$ – Yemon Choi Aug 29 '13 at 9:09
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    $\begingroup$ let us continue this discussion in chat $\endgroup$ – Sebastien Palcoux Aug 29 '13 at 9:17

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