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I was wondering if there are any websites out there which

  • systematically provide space for the discussion of mathematics articles (particularly those on the arXiv, though not necessarily just those), and
  • have a large enough user base to have some hope of having a good discussion (or at least have hope of attracting one in the near future).

Of course, MO is not so far from such a site, but is organized around questions, not papers, which leads to rather different discussion in practice. Similarly, some blog posts and nLab pages serve this purpose, but are not created systematically.

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Maybe the question is not appropriate for MO, but Andy Putnam's and Yemon Choi's comments don't make sense. Obviously there are innumerable forums for discussion of anything, but if it were universally known that for each arXiv paper there is an accompanying discussion page (which need not exist before someone actually decides the particular paper is worth discussing) then everyone on the planet interested in discussing a particular paper would be gathered together in the same internet forum: that particular paper's discussion page. The department tea room can't do that. –  Michael Hardy Jan 3 '11 at 22:12
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By the way, my last name is "Putman", not "Putnam" (grumble grumble grumble)... –  Andy Putman Jan 3 '11 at 22:54
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@Andy: you make a self-fulfilling prophecy. There are 100s of people who would like to participate (a handful of which are also capable), but they are forever locked out of "the community" because of location, inability to travel, intimidated by BIG NAMES. They can't become part of the community because they aren't already part of the community. –  Kevin O'Bryant Jan 3 '11 at 23:04
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Such a forum (as Michael suggests) would also serve to collect errata. –  Kevin O'Bryant Jan 3 '11 at 23:14
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@Andy: Sorry about the spelling. The number of people wishing to discuss most papers would be zero, I would think. In those cases no discussion page would be created. It's the ones that several people want to discuss that matter. You say most of those people know each other. Do you know most of the people who discuss things with you on MO? People wishing to discuss the same paper who've never heard of each other would communicate on such pages. What would happen with most pages (no discussion) is beside the point. –  Michael Hardy Jan 4 '11 at 7:39
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11 Answers

Time to mention the Selected Papers Network: https://selectedpapers.net

EDIT:

I hope that Tim does not mind me editing this to add extra links:

Introductory discussion by John Baez: http://johncarlosbaez.wordpress.com/2013/06/14/the-selected-papers-network-part-2/

Introductory discussion by Tim Gowers: http://gowers.wordpress.com/2013/06/16/the-selected-papers-network/#more-4954

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@gowers: Is a google+ account required for this website? –  Ricardo Andrade Jun 19 '13 at 12:24
    
I think you can make contributions by registering directly with the site, and anybody can read it. But Google Plus is a particularly convenient way of contributing, since all you have to do is write a normal post and add the #spnetwork hashtag. In due course other social networks will be added, but Google Plus has the advantage that public posts are genuinely public. –  gowers Jun 20 '13 at 13:18
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I'm pretty sure the answer to the question as asked is "No". At present there does not seem to exist a unique web location dedicated to discussing each individual mathematical article.

It would be technically feasible, and to my mind advantageous, to set up a "talk" page attached to each arXiv article. I have seen this suggestion on various mathematical blogs (unfortunately, I can't remember which ones, and googling doesn't turn them up; this answer, like the question, is CW, so if you know of any, please just include a link). I certainly do not know enough about web design to draft such a system, and the folks who run the arXiv do, but are horribly overworked as it is, so I doubt that they'll be writing anything anytime soon. I encourage others with massive web-fu to create some code and send it towards the arXiv administrators, but they might not even have the time to look at it. (When you are thinking about how best to set up such a site, please do keep in mind that well-working online forums tend to have fairly heavy moderation. Moderator attention is definitely not sufficient to have a well-run site, and not strictly necessary, but it helps. Since there aren't nearly enough people out there eager to moderate random columns on the arXiv, one proposal I've seen is for arXiv authors to have the option to open a talk page, with the commitment that they themselves participate and moderate.) (Another thing to think about is how to convince NSF to fully underwrite the costs at arXiv.)

Note that although most mathematics papers are available on arXiv, it is not the only database of papers. I could imagine adding a talk page to each bibliographic entry at Numdam, for example, or to each article at Web of Science.

Something like a "talk" page does exist for (almost) every (published) mathematical article, but I don't think it's what the question is after. MathSciNet and Zentralblatt include reviews of every (almost) article in their databases, written by experts. This does not accomplish the goal of "systematically provid[ing] space for the discussion of mathematics articles", but it is something.

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I am probably too cynical, but I am not convinced that everyone who wants to comment has something of substance to offer. Not to mentioned papers churned out by people who are just turning the handle; I envision comment threads filling up with the mathematical equivalent of yes-men –  Yemon Choi Jan 4 '11 at 6:48
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If arxiv papers had to have a talk page, it would allow anyone to criticize a paper and the author would likely feel compelled to respond. Given the type of "commentary" you see on most web forums, including math forums, I think this would just drag down the arxiv and a lot of people would even stop using it. I can see myself stop putting papers on the arxiv if I had to deal with random internet people with an opinion and arxiv access. And even if it were made optional, many people would still voluntarily use it and the same type of thing would still go on. –  Michael Greenblatt Jan 4 '11 at 7:04
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I think Michael Greenblatt's and Andy Putman's fears are exaggerated. The same objections could far more easily be adduced to prove that Wikipedia could never work, since the pages "would" just get filled with graffiti. But it works. –  Michael Hardy Jan 4 '11 at 20:11
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In a sense the arXiv does have a way for users to comment on papers, as there is a "track-back" feature where any time an arXiv paper is mentioned on a specific family of blogs and webpages, the arXiv keeps track of it. For example, this forum is one such location that that arXiv tracks back to. –  Ryan Budney Jan 5 '11 at 23:39
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One side effect of having an automatic talk page for every paper is that it will make authors realise just how tiny the audience for their papers really is. I post about my own papers on my blog and these are reliably the least viewed and least commented upon articles on my site. This is fine with me - the comments that I do get are often of extremely high quality (and also supply some valuable corrections and references) - but it is likely that many authors may overestimate, at least initially, the magnitude of impact that any of their papers will have. –  Terry Tao Jan 13 '11 at 16:04
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http://arxaliv.org/comments

http://arxaliv.org

Ralph Furmaniak created a site based or reditt where people can leave comments and up-vote the arXiv papers. See discussions at

http://publishing.mathforge.org/discussion/83/frontend-to-the-arxiv-httparxalivorg-based-on-reddit/

http://arxaliv.org/r/help/comments/12hd/welcome_to_arxaliv/is

I think this is great, unfortunately not so many contributors, let us contribute ?

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I think this is a very reasonable question. It comes up often enough and deserves an answer. In fact, I see not one but two potential forums. Here is my take.

1) Rumors, followup ideas, small errors, minor comments and remarks on the paper. This is all worth doing on your own blog space. I see no need to make this kind of discussion "official". In fact, the diversity of blogs and opinions is a plus here: less "intimidation by experts", fewer worries about "degeneration" of the discussion, etc. Finally, typos and mistakes in the paper are responsibilities of the author - when you find them, email them to her/him and stop worrying about other readers. In short, I see no need for a single forum for a discussion of this kind.

2) Serious comments, substantial remarks, delicate technical problems with the paper, etc. I think a blog or wiki type discussion forum is a too informal/unserious for contributions of this kind. On a positive side, there is a perfect forum for this kind of discussions: it's called the arXiv! Remember, the arXiv was never meant to be a only a "free storage" of published papers. It has moderators, calls uploaded papers "submissions", and once approved, calls them "publications". A great feature of arXiv is that you can store and advertise there the kind of work that you don't intend to publish in traditional journals. So if you have something important to say to everyone, don't be shy, follow Mnёv's example and post it on the arXiv (here are some other examples). Make sure to add hyperlinks to older arXiv papers if you want it to look more webby. Finally, there is already a great tool to explore forward arXiv citations. So why bother inventing a new forum when the one we have works fine, if only people used it more often for this purpose.

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Igor, you make some interesting points, but it seems to me that your (1) and (2) are two opposite extremes and there's a broad class of things between the two that could be dealt with in discussion pages. –  Michael Hardy Jan 4 '11 at 20:08
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Although no such system exists formally (as far as I know) there is an informal way to do this. Namely make some comments on a blog or web page and then add a trackback to the arXiv page. If this happened on a regular basis then it could be developed into something more systematic along the lines you are suggesting. My feeling is that only a small percentage of papers would attract any discussion.

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Right. Haven't there been posts dedicated to discussing particular papers on the n-category cafe? –  Qiaochu Yuan Jan 4 '11 at 11:23
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My experience is that this paper arxiv.org/abs/math/0601209 has a blog link linking to this discussion on the n-category cafe golem.ph.utexas.edu/category/2007/09/… Similarly this paper arxiv.org/abs/hep-th/9310164 has five blog links. –  Bruce Westbury Jan 4 '11 at 13:01
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You can try SciRate (http://scirate.com/), a site that allows you to rate and comment papers from Arxiv (it updates the list of papers automatically). It doesn't seem to be very popular, though (lack of critical mass?).

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+1 for mentioning this site. But somehow scirate's interface makes it very unappealing to use. –  Suvrit Jan 4 '11 at 12:54
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I'm shocked by the lack of professionalism of many of the comments on scirate (eg, see scirate.com/user.php?user=Rezn&what=comments). I'm very glad it has not caught on in math. –  Andy Putman Jan 4 '11 at 22:10
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Yeah, it definitely lacks moderation. –  Marcin Kotowski Jan 4 '11 at 23:02
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Slightly facetiously, I'm mildly tempted to vote to close as a duplicate. However, I shan't and shall merely point out that most of the answers to the question: Is a free alternative to MathSciNet possible? are relevant to this question, particularly mine. The question Errata database? which covers similar ground.

(The rForum mentioned in the latter has stalled a little. It could be revived if sufficient interest is shown.)

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I just found http://math-arch.org/, which seems to be exactly what is needed. I've created an account, but I don't yet have experience the site, so I can't comment on usability or comment quality.

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A quick perusal of the comments indicates that basically all of them are spam. –  Andy Putman Jan 6 '11 at 2:19
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A quick perusal of my own confirms the validity of Andy's observation. –  Kevin O'Bryant Jan 6 '11 at 4:27
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I remember seeing the site back in the days when I was trying (and failing) to understand Shavgulidze's claims about Thompson's F. math-arch.org/node/216 It seems that after some on topic discussion from Brin and Sapir, the spam has rolled in... –  Yemon Choi Jan 8 '11 at 3:04
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(This should be put in the thread right below the original question as it does not provide any answer, but I can't leave comments). Yan LeCun wrote down some ideas for a new publishing model/system for Computer Science, also talking about discussing/commenting papers. Reading the comments to this question, his suggestions seem quite relevant.

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It seems appropriate to mention Gowers's "Modest Proposal" from fall of 2011. Here is his original post, and then his "more modest proposal." This came about after the OP asked this question and seems very related, since a big benefit of his recommended mathoverflow-like system of submitting papers was the ability to have discussions of those papers. As others have pointed out, this also allows the community to quickly correct errors in the papers and also would reduce the lag-time between when new results are finished and when others can start to build on those results. I'm not sure what ever happened to Gowers's idea, except that there was a lot of discussion at the time and problems were pointed out. If someone knows, I hope he/she will edit this and fill in the details. This also seems related to Alex Chernov's recent answer; maybe Furmaniak's site was based on Gowers's ideas. I'm not really familiar with Reddit, so I don't know how similar it is to what Gowers envisioned.

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