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    I was wondering how it happened that a question about the validity of Mochizuki's papers on ABC was shut down, and another related question was closed temporarily, even though these questions are as interesting as anything else that has been on MO lately. So I saw the other thread here in the meta about closing the discussion of a crackpot paper. I agree that if the paper itself is not plausibly interesting, then neither is a question about whether it is correct. However, this is clearly not the case for Mochizuki's work.

    First, it's not really consistent to be able to ask about the ideas of a paper, without also being able to ask about whether it's correct. (Nor vice versa! The two issues always go together.) In fact, there are already a lot of questions along the lines of "where is the mistake", where either the poster has a mistake or sometimes his source has a mistake. Second, no other web site has proved to do a better job of critiquing dramatic announcements. It's a service to the community to have the discussion on MO. If you prevent these discussions here, then it's a waste; it's pursuit of rules just for the sake of rules.

    Again, if the paper in question is "a short and concise proof of Fermat's Last Theorem", then you can simply say that alternative mathematics is off-topic for MO. It's not the same situation.

    I don't know what I think about this. Maybe I agree with you, Greg. But I think you might have expressed "it's pursuit of rules just for the sake of rules" more diplomatically. As I remember, the principle that MO isn't for discussion of the correctness of preprints has evolved through conversations here and at MO itself. The people who've argued for this principle have had their reasons (even if you and maybe I disagree with them) and surely care about the direction of MO. I don't think it's fair to suggest that the principle has arisen through sheer pettiness.

    Incidentally, another case in point is the discussion of the amenability of Thompson's group F. There we were in the unusual situation that two papers made directly contradictory claims, and the question asked which if either was correct. It shares with the Mochizuki question the feature that one of the answers — if itself correct — describes a genuinely important mathematical advance.

    • CommentAuthorquid
    • CommentTimeSep 30th 2012

    @Greg Kuperberg: there is plenty of information available (both for the specific question as well as the abstract matter) in the meta thread of the question itself and the threads linked to in the thread HW mentioned. From your contribution it seems to me you did not yet read them. In order to avoid repeating old arguments over and over again, may I thus ask you to do so and then (if still wondering) to express your disagreement with something specific as opposed to some abstract 'I was wondering...' while several people already said very clearly why they do not want this or also this type of question (while one should not confound the two matters both were adressed).



    I think it would be helpful if you were more specific about what questions you think have been wrongly closed. There were several Mochizuki questions; personally, I think the most popular one was OK, though I respect the arguments for closing. But that question got good answers because it wasn't asking for evaluation, but about the underlying motivation for the proof, whether the details are right or not. I remain completely unconvinced that anything productive comes from just asking whether a paper is right or not without providing any specific concerns. It's hard for me to tell from your post whether that's what you mean or not.


    I'm generally quite apprehensive of MO as a place to evaluate correctness of large works of mathematics. Mostly this is because some aspects of these kinds of discussions should be handled more privately. But also, I think that MO just isn't the right infrastructure for working through substantial amounts of mathematics, you want a seminar, or a giant wiki. Furthermore, in the case of ABC, my impression is that any discussion of correctness on MO would be premature because people just don't understand the techniques well enough yet. Nonetheless, I could imagine sufficiently specific questions about the ABC proof that would be excellent questions to have here. But it seems to me like a general "Is the proof correct" discussion is at least as likely to do harm as good.


    I agree with Noah. An additional problem with MO serving to evaluate papers is the upvoting/downvoting, which has the potential to seriously mislead. In other words, in cases where there is a lot of voting by people not in a position to deeply understand the answers, a totally wrong impression about a paper might be received.

    I don't think any real harm was done in the case of the popular ABC thread, but I do suspect that there was a lot of voting by people who didn't understand the (what I myself suppose were excellent) answers given.

    I don't have a strong opinion either way, but it's easy to see how a discussion on correctness of a new paper could backfire. On the same day that some concern has been raised, you could have grad students all over the world gossiping at department tea "So, I heard that so-and-so's proof might not be correct after all...". Especially if these concerns turned out to be unfounded this would obviously be a bad thing.
    • CommentAuthorHJRW
    • CommentTimeOct 1st 2012

    quid has it spot on. It seems that it's a good moment to have another discussion about this issue, but it would help if it could build on previous discussions.

    For the record, my attitude towards the discussion of recent preprints on MO is (by the standards of earlier discussions) quite liberal. I have no problem with such questions as long as they are focussed, admit a definite (not necessarily unique) answer, and are respectful of the preprint's author. But I'm opposed to broad questions of the form 'Are there any problems with Mochizuki's work on the ABC conjecture [say]?', for reasons similar to Noah's and Todd's. Vesselin Dimitrov's answer to question 106560 threatened to move the question in that direction.

    On the other hand, I think Dimitrov's answer would have been a great for a question like 'Does the literature already provide a counterexample to Mochizuki's Theorem 1.10?', and indeed Dimitrov could have asked such a question himself and then answered it.

    Greg, along with others voices in previous threads, argues that there's a clear, bright line between crankish behaviour and serious attempts to solve major problems. I think this is wrong (as are most forms of essentialism). I have in mind a naive attempt by an excellent mathematician to solve a major problem - which mathematician and which problem specifically I'd rather not mention. Anyway, this attempt ended up attracting considerable scorn from parts of the mathematical community, which filtered through to the popular literature. This was before the days of MO, but I think MO has the potential to make that sort of occurrence much, much worse. See also Kevin Buzzard's comments here.

    I agree with Greg completely.
    • CommentAuthorDL
    • CommentTimeOct 2nd 2012
    > It's a service to the community to have the discussion on MO.

    +1 Greg. These discussions are already going on in private--I see no reason why they shouldn't happen in public. And if one concedes that, I think it's hard to come up with a better venue than MO.
    • CommentAuthorquid
    • CommentTimeOct 3rd 2012 edited

    @DL: It is fine that you see no reason, but others, for instance Kevin Buzzard, do see reasons. Isn't it somewhat rude to simply ingnore their concerns by trying to have such discussions regardless?

    By the way, are you in favor of referee reports of papers being made public? I would find it interesting and a service to the comuunity, too (this is not a joke). If so, perhaps you could start posting the ones on your papers.

    ADDED: while I replied to DL this was mainly to have a link into the discussion. The question(s) are meant for everybody in favor of discussion. Perhaps let us make a deal: everybody being so much in favor of discssions post some of the referee reports on their papers (bad ones/rejections preferably).


    I disagree with Greg completely.

    I feel I ought to leave it there, but I'll reiterate what others have said. It's not that I don't want this sort of discussion, it's that I don't want it on a question-and-answer site where voting takes place (regardless of how seriously we take them), where threading is next to impossible, and where it is very difficult to find out if someone has replied to you or not. This is what blogs, forums, and wikis are for. The famous SO diagram puts SO as the intersection of blogs, forums, and wikis. But that means that it misses out on those features that each of them has that makes them what they are.

    It is lazy to think: "MO has a high profile so let's dump everything vaguely of interest to research mathematicians there." but it just makes it even harder to find the good pieces of MO amongst the dross.


    I think Kevin Buzzard's comments on the linked thread make the argument that I would like to make better than I could.

    • CommentAuthorDL
    • CommentTimeOct 3rd 2012
    @quid: I think what Kevin Buzzard says is quite reasonable--of course we don't want vitriol on MO. But we do have the ability to flag that sort of thing for deletion, so this seems to me to be a minor objection.

    And I think there's a weird conflation between public and private discourse that this argument makes, which is also present in your suggestion that I and others post referee reports. Namely, referee reports, and the private emails to which Kevin Buzzard refers, were written with the *expectation* of privacy, and so are sometimes not couched in the diplomatic terms that make civil disagreement possible. On the other hand, MO is public, so I think there's an expectation that less unpleasantness will occur; I think that expectation can be turned into reality with some vigilance.

    **In any case, if the concern is that people evaluating a result will be rude, hurtful, etc. then it makes sense to police that behavior, rather than the discussion itself.**

    @Andrew Stacey: I agree that MO isn't the best possible option for this sort of discussion. But it is the best existing option, as far as I know--and as far as I know, discussions in the other natural places (e.g. various blogs) haven't really taken off. So if you agree it's a good idea to have the discussion, I think it's hard to argue that it shouldn't be here.

    So if you agree it's a good idea to have the discussion, I think it's hard to argue that it shouldn't be here.

    It's very easy to argue that it shouldn't be here. If it were done here, it would be done really badly. I think it's actually better that it not be done at all than that it be done here.

    But I have an opinion on why it hasn't really taken off. It's because, actually, not many people are really interested in properly discussing papers like this. There are a small number of papers a year where lots of people are interested in seeing such a discussion happen, although the majority of those people are not really able to follow or contribute to such a discussion. They just want to sit in the room while others discuss it and feel like they're a part of it. But most papers aren't read by many people and most papers aren't suitable candidates for discussion.

    What would be better would be a place where folks could store their "notes" in plain view that they take when reading a paper. Then others could benefit from reading them, and maybe add their own notes or correct misconceptions. This sounds a bit like a wiki to me. If a discussion arises, there could be a forum attached where regular note-takers could discuss topics of interest and note their contributions. Discussions would arise naturally from time to time, but naturally not "top down" as would happen here.

    Sounds like a good idea, to me. What do you think?


    Asking for evaluations of papers on MO seems like a disaster. MO may be the most active on-line forum for serious mathematical research but expecting it to do everything well is silly. This isn't what the forum is designed for.

    • CommentAuthorquid
    • CommentTimeOct 3rd 2012

    @DL: I agree that there is a difference whether something is written for public or private. However, too much couching also creates imprecision and confusion; it is also a problem if people do not feel comfortable to say what they actually think on a paper. And, some things that are nothing but the objective truth formulate in a neutral way can and will be offensive to some in such contexts. Recently a paper on MO was referred to as 'not a serious paper' this was in my firm opinion a completely accurate description of the paper in question and not overly aggresively formualted either. Still some found this problematic. But, how should one say in a nice way that in some paper there is nothing whatsoever that is of any scientific value. Now, Greg Kuperberg seems to try to make some argument that those preprints should not be discussed as they are not interesting enough for discussion. However, I am certain that the question will still be asked as if the person asking would be capable themselves to judge it is not interesting they would never ask. So then we close some of the preprint discussion with the argument the preprint is obviously not interesting enough to merit discussion on MO (for obviously dubious papers). But then we might also face situations were the preprint itself is still a reasonable preprint but some might think it is still not relevant enough. So do you want to allow a question on each and every preprint, or how will you decide which to admit. And in particular how will you do so without being offensive. (Not such a nice experience if you'd see a question somebody asked on your prerprint being closed with the rational the paper is too irrelevant in some peoples opinion to merit discussion on MO.)

    Regarding your reply to Andrew Stacey: this is also a bit of a chicken-and-egg issue. I doubt that Vesselin Dimitrov would have kept his observation to himself if it were not for MO (and regarding actual discussion of the preprint, this is the only contribution here too AFAIK). Things might be moving slightly slower without MO. But actually in my opinion this would be a good thing.

    For example AFAIK somewhat recently a detailed PvsNP preprint discussion happened on some blog(s). One additional advantage to me here is that I think for discussion that can easily get out of hand it is better if there are few people in charge that can decide what is an is not appropriate and else are sort of responsible for it. As opposed to community moderation, where also people far outside the field or even the scientific community proper have some say.

    Alos, it can happen that too much publicity in the end creates the effect that people will be more secretive and thus lead to less openness. If you cannot post a preprint on your website anymore without 'the world' instantly doing some chatting about it, you might choose to make it public only later (and keep it longer to just a group of trusted peers). In that sense I am not so sold on the fact that all this is such a big service to the community. In particular not for the (at least at first) relevant one. Look, voloch for example wanted the question closed, while definitely having an interest and competence in the matter that far exceeds that of the typical user here.

    Sometimes I really wonder what all this real names thing is about when in cases of decisions where exprience and competence is relevant, who says what is completely ingnored and mainly votes count.

    If this were a matter of envisioning some new use of MathOverflow, then I might agree that it's debatable. But that's not what's going on here. Mochizuki's work is serious mathematics, and an interesting thread on his work appeared because people wanted it. Nonetheless, a strong sentiment arose among purists that the posting defies "the purpose" of MO and should be closed. That sentiment appears all over the posting, but in this case the posting survived. With a trick that is. The trick was to ask about the ideas of Mochizuki's proof. That is an interesting question in its own right, but one that cannot be separated from the question of whether the ideas are actaully likely to prove the ABC conjecture. For a lot of people (including at least three serious number theorists who I spoke to directly), the most interesting answer posted was the one by Dimitrov --- which is replete with apologies and comments that it's off-topic. It isn't *vaguely* of interest, it's of clear, massive interest.

    Also to address Noah's comment: Obviously the way that many people critique a difficult paper is to look for some other theorem or conjecture that it contradicts. It isn't premature. I agree that that's not a full evaluation, but I'm not asking for any standard of full evaluations.

    This case is not like Kevin Buzzard's examples. I agree that there is no rigorous gap between crackpot and non-crackpot work --- of course with my involvement in the arXiv I know about those issues. Nonetheless, they are different. Buzzard's examples might in the extreme diminish MO's reputation. Dimitrov's post about Mochizuki's work has achieved the opposite.

    I stand by my comment that this has become, I admit unintentionally, rules for the sake of rules. As well as trying to too hard to define MO by what it isn't. It would be better to just let interesting MO questions and answers be what they are. That is, to take an organic view of how MO can be useful to the mathematics community.
    Finally to address Ben Webster's question, which is a good one. There is a non-rigorous, general principle of MO that thoughtless, off-the-cuff MO questions are a problem. If someone just asks whether someone's new proof is valid, particularly in a cheeky tone, then any smart-aleck who doesn't know anything can ask a question like that and it doesn't deserve anyone's time. So I agree that a posting related to a claimed proof should be more respectful and respectable than just that. Asking about the ideas in the proof is not a bad way to start.

    However, after that, it bothers me when a respectable critique of a claimed proof is weighed down by remarks that it's off-topic. Or if people vote against a question because it turned into that. I will say that part of the problem is the encoded StackExchange procedure, whereby votes to close a question are unstoppable until the question gets closed, and then you switch to votes to reopen. Obviously that voting system favors restrictionists in the initial round.
    • CommentAuthorRyan Budney
    • CommentTimeOct 3rd 2012 edited

    Hi Greg. It sounds like you're blurring the distinction brought up in Ben Webster's comment. There's a big difference between threads specifically for the purpose of evaluating a paper (public refereeing) and asking for a big-picture context for someone's efforts. The former seems to not be a good idea, and that's what people were worried about in the original version of the Mochizuki-topic thread. I think people are much happier with the latter topic, and that's what the Mochizuki-topic thread turned into.

    edit: whoops, I posted just as you replied to Ben's comment! Ah well...

    • CommentAuthorquid
    • CommentTimeOct 3rd 2012 edited

    @Greg Kuperberg: The question matches exactly a case Kevin Buzzard's described, as one for instant closure; let me quote for you Kevin Buzzard from that thread:

    I guess one thing that should be independently noted is that a question of the form "Hey -- I just noticed a new proof of RH in my daily ArXiv summary email and, despite the fact that hundreds if not thousands of people will also have noted this, I just thought I'd post on MO despite not having looked at the preprint -- and it's not in my area anyway -- to see whether all the experts here have already got well-formed opinions on the correctness of the preprint?" should be closed. I'm exaggerating a bit with the example, but we've seen several milder versions of such posts and they still strike me as being very lazy.

    ADDED: I just saw your second comment. But I am now quite surprised you still are in favor of this question. (Also, do you know it's original version?)


    Have been a bit too snowed under (metaphorically) to formulate a coherent contribution to this thread (though I incline more towards the views set out by Andrew, Ryan and quid). I did enjoy Andrew's most recent comment although I kept being distracted by the pink elephant that he was emphatically not mentioning...

    • CommentAuthorDL
    • CommentTimeOct 3rd 2012
    @Andrew Stacey: I think that such a site, if it had the same user-base as MO, would be great.

    As for your evaluation of the Mochizuki discussion -- I think it has taken off to some extent, via Vesselin Dimitrov's excellent answers and the comments therein. This doesn't seem to be the disaster which you predict. Also, re:

    > They just want to sit in the room while others discuss it and feel like they're a part of it.

    I don't see anything wrong with this desire. But in any case, I know many people (myself included) who have been trying to get some tiny handle on some of Mochizuki's earlier papers. Such people have a legitimate interest in the ongoing evaluation of the correctness of the papers (if only to save themselves time). So I don't think the evaluation is really the spectator sport you suggest--rather it is of actual public interest.

    @quid: I essentially agree with everything you've written. I don't think that MO is a good place to evaluate every paper, or even most papers. But this is an extreme case.

    I agree with Greg that it would be good to have a more flexible attitude when deciding which sorts of questions should be allowed on MO. I see no harm in experimenting, either. Why not tolerate questions which fall into grey areas until actual problems arise? Predictions that certain classes of questions would wreak havoc and ruin MO are not very convincing in the absence of actual experience with those types of questions. Allowing (provisionally) other types of questions would not be the start of an irreversible slide down a slippery slope. As has often been noted in this forum, the standards for what's allowed on MO have changed in the past, and these standards can continue to change in the future in response to our experience with actual questions.


    Kevin, I think that'll lead to some amount of frustration. A common perception of math overflow is it's a place where fancypants established mathematicians live by different rules than the ones they apply to newcomers. If you want to have any kind of community consensus, people will have to make some effort towards being consistent.


    Ryan, I don't understand your objection. Perhaps I didn't successfully communicate what I was proposing, so I'll try to be more specific. Step 1: We stop closing/discouraging the sort of question Greg described. Step 2a: After a few such questions are asked, we observe that they don't cause much problem, and we continue to allow them. Alternatively, Step 2b: After a few such questions are asked, we observe that they cause too many problems and we decide to discourage them in the future. I don't see any consistency problems here. Also, I think the MO consensus toward other types of questions has evolved over time in a way similar to what I sketch above, so I'm not really proposing anything radically new.

    Independently of the above, I think that MO should be a place where the rules for "fancypants established mathematicians" are different than the rules for non-mathematicians. More specifically, I think questions from fancypants mathematicians should be given the benefit of the doubt, while questions that appear to be from non-mathematicians should be subjected to greater scrutiny. I'll refrain from writing more, since this is off-topic in this thread. But if you disagree then I'm interested to hear why, so feel free to start another thread or email me privately.


    I certainly respect Greg and Kevin's opinions quite a bit, but I must say I don't find anything in this thread as convincing as what Kevin Buzzard said in the other thread. Discussions of the correctness of major results should be done in private until a consensus among experts emerges and the author has a chance to reply to any concerns in private. Having these discussions in public in front of a bunch of interested but completely uninformed bystanders is counterproductive. There's too much opportunity for politics and for people's feelings getting hurt. I think MO already allows too many questions along these lines (87310, 87674, 108631).

    Furthermore, if one were to design a site for discussions like this it would look very very different from MO. There would be no anonymous users, comments from non-experts and new contributors would be moderated before being posted, there would certainly not be upvoting by non-experts.

    • CommentAuthorWillieWong
    • CommentTimeOct 4th 2012 edited

    Andrew Stacey wrote:

    What would be better would be a place where folks could store their "notes" in plain view that they take when reading a paper. Then others could benefit from reading them, and maybe add their own notes or correct misconceptions. This sounds a bit like a wiki to me. If a discussion arises, there could be a forum attached where regular note-takers could discuss topics of interest and note their contributions. Discussions would arise naturally from time to time, but naturally not "top down" as would happen here.

    I like that. I would pitch in to help in ways I can if such a site were to be born.

    Noah Snyder wrote:

    Furthermore, if one were to design a site for discussions like this it would look very very different from MO. There would be no anonymous users, comments from non-experts and new contributors would be moderated before being posted, there would certainly not be upvoting by non-experts.

    Why not just require all anonymous contribution be regarded as "non-expert" and moderated; a "no anonymous user" stance seems a bit extreme? Another problem is how we decide who to call "expert": we certainly cannot base it upon "votes", as the traffic volume of MO already indicates, for certain subfields if votes were used as a notion of expertise we would hardly ever get new experts beside the seeding few.

    I'd think instead we would just have no MO-style voting at all, but with proper threading support. Real-name users will be staking their reputation on what they write, so I don't see why any moderation should be necessary. Moderation of anonymous and pseudonymous users should be done by real-name users (a post from anon comes in, it becomes only visible to real-name users but not public at large; some X number of seconding votes releases the post for public consumption, with the names of those who approved the post displayed for accountability).

    The difficulty in such a system would be for moderators (more like a sysad) to verify the real names when users register. But that can be done by requiring first registrations to use a verifiable institutional e-mail address or something like that.

    It may be good/interesting to also have a Slashdot-like "post as anonymous coward" option....

    Anyway, just my random two cents. Feel free to tear a hole into my scheme.


    I would pitch in to help in ways I can if such a site were to be born.

    See Yemon's comment about the "pink elephant". I'm not sure about "pink", but at 7,000 pages then "elephant" is justified. Interestingly, its largest baby is my list of "papers that caught my eye". I've even made notes on a couple of them.

    Although it will spoil the joke, let me quote from the pink elephant:

    The purpose of the nLab is to provide a public place where people can make notes about stuff. The purpose is not to make polished expositions of material; that is a happy by-product.

    We all make notes as we read papers, read books and doodle on pads of paper. The nLab is somewhere to put all those notes, and, incidentally, to make them available to others. Others might read them and add or polish them. But even if they don’t, it is still easier to link from them to other notes that you’ve made.

    • CommentAuthorquid
    • CommentTimeOct 4th 2012

    @DL: There might have been some misunderstanding what Greg Kuperberg and (thus) you actually suggest; I took it initially as a quite general suggestion, after all the title of the discussion is "evaluation of potentially credible papers should be allowed". I agree ABC is an extreme case. However, as Andy Putman and me (under my old name an_mo_user) abstractly said one can also make an argument that for very famous problems there is less need to (ab)use MO for such things as the information will appear elsewhere. In addition, while I for example find it a good thing that MO got linked on the AMS website I do not find it a good thing that MO got mentioned on, say, slashdot in the context of ABC; mainly this has the potential to bring contributions of dubious quality. For example I was already anoyed when I found one question asking how ABC implies FLT, but then there came a second one...argh (first it does not, second it is easy to find what follows, and one might even prove this on the spot, if one has some minimal familiarity with the subject, but great we have this twice, and once even with a slightly wrong answer, which reminds me I should point this out there too). In the end it is certainly a balancing between somewhat contradicting interests of different parties. In any case, as I said in the other thread I would have been more sympathetic to a question of this type if say you or davidac had asked it. But that particular OP was not even willing or able to follow up on the CW matter.

    @General: It might be true that some (including me) sometimes are perhaps overly cautious. However, I am a bit puzzled why Greg Kuperberg, Kevin Walker, Deane Yang and likely existing likeminded senior members on MO did not support the idea of davidac, who explictly asked about asking such a question on meta before the current one, when apparently they find this such a good idea. What to me is mainly an unfortunate developpment of MO is that those that follow proper procedures and ask in case of doubt first on meta often are told not to ask something, while then if somebody simply does ask it is tolerate. I consider this as problematic. Thus, regarding the general idea of experiments it would seem like a good idea to me if some discussion could happen first on meta; but in exchange this discussion is rather permissive and open-minded (for lack of better word).

    But, regarding what Kevn Walker said: I am still convinced tha without any experiment some things can be judged in advance as not feasible. Simply for technical reasons by the sheer size and number of the necessary contributions, it does not seem feasible to have an indepth discussion of a long and complicated paper on MO. Okay, one might use MO as a link collection to whereever but then we also get close to what I was always in favor of, namely that after a reasonable amount of time one can ask about preprints on MO to collect the consensus opinion/information that accumalted already (as opposed to trying to create this info on the fly on MO).

    Also, some of these things can go well multiple times but then fail horribly. For example, I do not have the habit of jumping over a running chainsaw installed at one meter height, while I am sure most of the time it would not cause any harm and might be fun.


    @Andrew: How much does nLab actually stick to the nPOV? I've always been somewhat intimidated by that and so my use of it has been largely that of a leech.


    @WillieWong - you are free not to stick to the nPOV, it's just that if it is possible to add, people who are au fait with n-categories will likely add it. There is definitely material in there that is quite resistant to being interpreted as abstract nonsense in infinity-categories...


    Willie, the thing to hold on to is that people will generally add but rarely subtract.

    Here's a discussion we had on the nForum about a year ago that's quite related:


    Willie, the articles on "fundamental theorem of algebra", "composition algebra", "valuation ring", and "Lagrange multiplier", just to name a few off the top of my head, are as currently written pretty light on the nPOV.

    You and anyone else with mathematical expertise are invited to contribute. You just have to not mind not "owning" the page you start, in the sense that people are likely to add something to it. In practice, something is subtracted only if there is an error or spam or crackpottishness, or if something is better placed on another page. Such things, among many others, are discussed at the nForum.


    @DR, AS, TT: thanks for the clarifications, and especially for the link to nforum.


    Noah wrote this, and I think this summarizes one point of view very concisely.

    Discussions of the correctness of major results should be done in private until a consensus among experts emerges and the author has a chance to reply to any concerns in private. Having these discussions in public in front of a bunch of interested but completely uninformed bystanders is counterproductive. There's too much opportunity for politics and for people's feelings getting hurt.

    I agree with some underlying ideas here but I think this is not the right way to think about this. I sometimes wonder "Is this correct?" when reading a paper. This is certainly a valid question when looking at Mochizuki's work. But, leaving that very special case aside for a moment, this is not really what I ask myself when reading a paper. Either the results contradict my expectations or there is a step in the argument that I don't follow (and some variants). In any case, clarifying that is a perfectly valid use of MO. There is a proper way to ask such questions though: "Does this result contradict so-and-so's result?" and "Is this part of this paper wrong?" are not proper.

    For larger beasts like Mochizuki's work there are quite a few more traps... Questions are more likely to be overly broad, subjective, discussiony, spammy or offensive. It's the nature of the beast to steer in these directions, but these are valid reasons to close any question on MO, not just questions of that type. Again, however, there are productive ways to use MO with the goal to ultimately answer the question: "Is this a valid argument?" The trick is always the same: turn it into a mathematical question about a specific aspect or part of the argument.

    I don't see why "[d]iscussions of the correctness of major results should be done in private." It's perfectly fine for experts going through the argument to use MO to ask questions and clarify certain points. I think MO is actually well suited for this since the format helps prevent useless political digressions. I would be very happy if a loose group of experts decided to use MO this way while working through a long winded solution to a major problem.


    That's a reasonable point. I think that sufficiently politic phrasings of specific mathematical questions concerning Mochizuki's work would be on topic for the site and might be worth having. I think one indication that a questions was sufficiently politic and specific is that the title would not make it clear that it was about Mochizuki's work and so the questions and answers wouldn't get 80 upvotes from people who don't understand the questions or answers.


    @quid: "What to me is mainly an unfortunate developpment of MO is that those that follow proper procedures and ask in case of doubt first on meta often are told not to ask something, while then if somebody simply does ask it is tolerate[d]."

    Are you sure about this? I think I see "yeah, this is fine" more often than anything else. In any case, asking on meta whether a question is suitable should be deprecated. In case of doubt, it's often better to post anyway but be mentally prepared for closing than to ask on meta first.


    I mostly (maybe entirely) agree with Francois in his next-to-last comment. I certainly agree with the entirety of the paragraph beginning "For larger beasts". A big problem is that MO is horribly adapted to discussions, and that's really what a work like Mochizuki's needs: basically, working seminars with experts who can freely get into all the discussions they need to be having.

    In principle, it would be possible for a group of experts to use MO as described in his last paragraph -- but it would take an awful lot of skill and discipline to do it well, for example a divide-and-conquer approach with question like "I have been studying lemma 4.1.2, and there is this point that I don't understand... can someone clarify?" But I think there are better and more efficient alternatives I think than MO. Such as, for example, the seminar room, or perhaps closed video-conferencing. (And I'm not even factoring in the noise level from the crowd of (typically non-expert) bystanders watching and voting up/down.)

    • CommentAuthorquid
    • CommentTimeOct 4th 2012

    @François G. Dorais: it might depend on the precise meaning of 'often', and I did not say in the majority of cases, so it could still be compatible with your observation ;) I will, however, not insist on 'often' and it is perhaps an overstatement.
    But, it definitely happened in this case. Do you agree? In combination with later developments, I do find this unfortunate.

    And, more generally, I do believe (but it is really just a believe) that the phenomenon that some users (in particular young ones) that try to be 'good MO citizens' are at a considerable disadvantage regarding the question they can/dare to ask relative to some others that simply do as they please. IMO this sends a wrong message. But that this is so is more a believe or feeling that will be hard to back up. However, in this spirit the above comment arose that in a word-by-word sense might as said be an overstatement.

    Regarding your general remark: this is fine for me, but since some are so against closures it could be a problem for them.

    I have to emphasize again that it is way too difficult to prevent a question from getting closed, which in the long run skews the discussion of which questions should be closed --- in favor of restrictionists who have natural voting power. The software is stupid. You should be able to vote against closing a question, instead of having to wait to vote to reopen a question after it's closed. There are so many questions that get 3 or 4 votes to close and then comments that say "no, don't close!" And then the extra votes to close show up and the more restrictive side looks like it has been proven right.

    It's a lot like votes to raise local taxes in California. People who vote against a tax only need 1/3. People get tired of pointing out that the system is skewed, they learn to live with it, and in the long run the system grants tax cut opponents an extra perception of rectitude, because they prevail. In other words, a measure that failed by 60% in favor is "wrong" and its backers are "wrong" because it's their responsibility to come up with something that gets 2/3. It really does change people's thinking, insidiously.

    The same thing happens with votes to close MO questions, in a voting system that allows no votes against closure, only a later vote to reopen.
    • CommentAuthormarkvs
    • CommentTimeOct 5th 2012
    @Greg: I do not know much about voting system in CA. But from what I heard should the majority
    always have the way, everybody there would be smoking pot and married to his/her refrigerator by now. I think the voting system in MO is just fine. I do not like some votes but I suspect that other people may not like how I vote too.

    I certainly agree with you that you should be able to vote against closing before the question closes. Sadly I don't think SE is ever going to give us that feature. As far as I know they've never really explained why, but they seem pretty sure about it.


    I think there's a strong counter-argument to Greg's critique of the "no don't close!" mechanism. Since people tend not to similarly post accounts of intended votes to override the "no don't close!" comments, there's no accounting mechanism. So if you don't want to waste time attempting to account for all the repressed votes to close vs. keep open, the only real option you have it to actually cast a vote to close (or reopen once its closed). If you're impatient this mechanism could seem frustrating but it seems to work, even with the open-close cycles. IMO the main flaw in this voting process is the original poster gets to vote to re-open.

    I agree with Greg when it comes to the voting mechanism (not about paper evaluation). While still not satisfying, SE allows to speed up the process of closure votes rotting away a bit:
    • CommentAuthorgilkalai
    • CommentTimeOct 5th 2012
    Let me make the following mild suggestion about occasional cases of not following rules. If a question is closed and reopened twice then it stays open.
    • CommentAuthorptrnz
    • CommentTimeOct 5th 2012 edited
    Regarding the phrase "pink elephant" that was emphatically not being mentioned. Some might think it a reference to the phrase "elephant in the room", but I think it was the meaning as used in the book "Drop the Pink Elephant: 15 Ways to Say What You Mean... and Mean What You Say".
    • CommentAuthorquid
    • CommentTimeOct 5th 2012

    A couple of quick remarks.

    1. I agree with Greg Kuperberg that things being as they are has the unfortuante psychological effect that there is a lot more talk on that a question is not a good than that a question is good.

    2. However, leaving psycholgy aside though it might be important, I would still like to make explict that closers need a majority against openers to close a question permanently. And the question starts open after all. Not sure if Greg Kuperberg would be in favor of switching the open/close roles completely (question starts closed, and 5 to open) in order to instead skew the situation for anti-restrictionists with voting power. Would you?

    3. I am not quite sure what (hypothetical) change of voting mechanism with 'anti-close' votes people envison. Yet, the 'obvious' idea is IMO flawed and I do not see a good alternative right away. (What I mean by 'obvious' idea is to look at the difference of close and anti-close votes and only if this passes a threshold of say again 5 the question is closed. But what then if it is closed with difference 5. It seems bad to reopen if it just drops to 4, and then reclose at 5 again, since this open/close with a single vote would be a major annoyance IMO. But if you only reopen if it drops to 0 (matching current situation) then the system gets considerably more random regarding timing; think of 5 people wanting to close and 1 not, if the anti-vote gets in in time it stays open if not it is closed.)

    4. It might be true that closing is too easy. But then reopening is likewise too easy. Even more so, IMO. Reopening should be relatively more difficult than closing. If five qualified (in the sense of points and thus with some experience on MO) users think a question is unsuitable (in its current form) then this is a considerably stronger statement than just whoever posting a question. To override there opinion should take more than just a matching vote. In general, I think appropriateness of MO questions should not be a majority decision, by contrast if enough people 'veto' a question it should stay closed. I understand that Gil Kalai just formulated the opposing view that if enough people 'endorse' a question it should stay open, but I disagree, in particular for controversial question like the current one. If enough people see a problem, it is a problem (at least for these people) and the others should have a very good reason to ignore the concerns of these MO colleagues.

    Perhaps the discussion has moved on, but to return to the original topic, I'm among those who feel that evaluation of correctness of a preprint on Mathoverflow is generally not a good idea. (I am willing to concede there are exceptions.) It takes a lot less effort to post here than it does to really study and evaluate a paper. While I'm sure that most people would be cautious about posting premature assessments and opinions, it's not clear that everyone will be. And if you happen to be anonymous and untraceable, then what have got to lose by posting carelessly? A few points.
    To tie my two points together, MO hasn't been a system that concedes exceptions very well, partly (or maybe entirely) because of its protocol to close questions. Sometimes you're better off following the letter than the spirit of the rules.

    I agree/concede that it takes an exceptional reason to expect an appropriate discussion on MO about the status of a claimed proof. It clearly wouldn't make sense to use MO as a system of peer review. However, common sense says that Dimitrov's answer about Mochizuki's proof is one of those exceptional cases. The answer is interesting, even influential, and it wasn't going to be posted to some other web site. What's the point of harassing a discussion like that with objections that it doesn't belong?