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Jan 13, 2011 at 17:48 comment added Łukasz Grabowski Terry: I completely agree. I think that one of the most important moments in one's mathematical career is when the number of people which are interested in one's paper enough to actually read it more-or-less completely becomes bigger than 1 (1 corresponds to the advisor). I'm still waiting for this moment, and I suspect it might be that suprisingly large percentage of mathematicians is still waiting for this moment.
Jan 13, 2011 at 16:04 comment added Terry Tao 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.
Jan 5, 2011 at 23:39 comment added Ryan Budney 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.
Jan 5, 2011 at 21:09 comment added Kevin O'Bryant If commenting was restricted to those who can already post to the arXiv (i.e., authors), that eliminates 99.99% of the nonsense "on most web forums", and 95% of the nonsense on "math forums". The quality on MO is quite high, and there is absolutely no barrier to posting here.
Jan 5, 2011 at 3:41 comment added Theo Johnson-Freyd @Yemon (2nd comment): I hope to emphasize that I don't think that Math Reviews are what the original question was after. I did want to bring them up to say that there are things not too distant from a "talk" page that definitely do exist, and are worth reading. @Michael and Yemon: Absolutely, it would be easy to set up a horrible system, and hard to set up a good one. MathOverflow could also "fill up with the mathematical equivalent of yes-men" or "allow anyone to criticize a paper ... and a lot of people would even stop using it". I can't guarantee these won't happen, but they haven't yet.
Jan 4, 2011 at 20:11 comment added Michael Hardy 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.
Jan 4, 2011 at 7:20 comment added Andy Putman @Michael : I feel exactly the same way.
Jan 4, 2011 at 7:04 comment added Michael Greenblatt 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.
Jan 4, 2011 at 6:52 comment added Yemon Choi Also, Theo, I find your last para somewhat puzzling. The whole point of invited/commissioned reviews is that they are not talk pages; there is a deliberate barrier to commentary, and a deliberate avoidance of open discussion with all and sundry. Now these reviews are of course not the be all and end all, and in many cases are of less use to interested parties than a well-moderated blog discussion; but they have, and always intended to have, a different aim.
Jan 4, 2011 at 6:48 comment added Yemon Choi 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
Jan 4, 2011 at 6:14 history answered Theo Johnson-Freyd CC BY-SA 2.5