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    This is basically a long form of the comment(s) on main.

    My impression, mainly in view of the success of the 'Thompson question' and the closure of various other questions of this form was (and this seemed very reasonable to me):

    1. In general just asking is Preprint X correct is not a suitable question (for a variety of reasons).

    2. There are certain exceptions, which perhaps can be summarized in the following way: If the question 'Is there/what is the (consensus) opinion of the math-community on this preprint?' is a reasonable/legitimate question at all, then it is reasonable/legitimate on MO.

    With the following consequences:

    a. The preprint (or closely related claims) have to be around since a significant time. b. The problem addressed has to be of fairly general interest. c. There has to be some reason to deviate from the default assumption that the preprint is correct without appearing to be needlessly 'unfriendly' (e.g., the author made similar claims before and needed to retract them; there are contradictory claims around).

    and perhaps d. The problem, while significant, is not very famous. (On the grounds that infomration on claims regarding very famous problems that are taken seriously by the community tyically can be found elsewhere.)

    My understanding was that due to something along these lines 'Thompson-question' was admissible; and that the 'Hanna Neumann-question' is very similar regarding these points. The other question all fail some or often several of these criteria (even excluding d.); most notably a.

    • CommentAuthorHJRW
    • CommentTimeJun 4th 2011 edited

    I don't see any problem with the Hanna Neumann question. Note that the question is:

    Has this attempt been verified by anyone or is [it] still under review?

    This is a question that admits a definite answer. I don't see any reason why it should lead to MO 'making enemies' (as Noah Snyder worried in comments). If someone claims that it is unverified, and then someone else does verify it, there is nothing to stop the verifier posting an answer on MO to that effect.

    Also, it's extremely useful to have this information available on the web. I can confirm from personal experience that, in the weeks after Friedman's first announcement, one needed to be in direct e-mail contact with some of the experts on the HNC if one wanted to find out whether anyone was reading his preprint. And indeed, this is the first I've heard of Mineyev's announcement, so the question has already been very useful to me.

    That said, the claim that the HNC is not famous enough for information about it to be posted elsewhere on the web is not quite correct. Danny Calegari blogged about Friedman's first preprint, and eventually publicised an error (found, I believe, by his student Steven Frankel), here.


    Henry, you have some interesting arguments, here. Which of your arguments also would apply to the "P = NP" or Collatz preprint queries mentioned above? Do we want to allow some, but not all, queries of this type?

    Henry says "Also, it's extremely useful to have this information available on the web. I can confirm from personal experience that, in the weeks after Friedman's first announcement, one needed to be in direct e-mail contact with some of the experts on the HNC if one wanted to find out whether anyone was reading his preprint."

    But let me try to draw a (in my mind, _huge_) distinction between "it's extremely useful for people working in this area to have access to the thoughts of other people working in this area, when trying to figure out whether or not this proof needs to be taken seriously", and "it's extremely useful to have the information displayed publically on the internet where people, possibly under anonymity, can post comments which can be misleading, false, hurtful...and then these comments might never ever go away".

    I have been an interested third party several times when people have announced solutions to "big" (i.e. "fairly important, in the area in which I work") questions, and ultimately have ended up in big email exchanges between interested parties who know the background involved, and, as often as not, the author of the work, where potential difficulties are raised, and then perhaps resolved or perhaps not resolved. All of this is done away from the public eye, and given that things can get quite "complex" or "heated" -- about as heated as mathematicians get perhaps (jealousy/annoyance from the people who didn't prove it, possible defensiveness from the people that do...) I think is is a VERY VERY VERY good thing that these email exchanges are never made public. I am thinking of one exchange in particular, that is filed away somewhere on my computer, and where I know for sure that some people said things that other people most definitely would not want to be made public.

    I am all for conversations between experts on "is this new preprint OK". But I think that a highly visible public forum may well be a very inappropriate place to have them.

    Another quite recent (two months) example of precisely such a question that stayed open without any discussion

    So to answer Gerald Edgar's question: "Do we want to allow some, but not all, queries of this type?" It definitely seems that this is current practise and thus what the community finds the reasonable thing to do.

    And, in view of Kevin Buzzard's 'I am all for conversations between experts on "is this new preprint OK". ' You say new and as said in my first comment I consider this to be a very important point too.

    But, this does not really answer the question at hand. To me it seems that precisely the common feature of those requests that stayed open is that they were not about new preprints, but about claims that were around for quite some while. And the Hanna-Neumann question seems to be of this form [more than two years; the most recent preprint is new, but it seems to me that this is the third installement of a specific line of attack on the conjecture by this author]. This is also a difference to the Collatz-question, which seems to be a couple of weeks old, and just now to receive more visibilty due to a brand new article (3rd June I beleive) in the New Scientist; so that one can expect that in not too long a time the situation will be clearer either way quite soon.

    So, yes, new preprints should be first discussed by the experts in a non-public way, but to arrive from this at the conclusion that question regarding each preprint should be closed (in case this was the intention, but it seems so) seems non-obvious to me. As the intention of the questions regarding these old preprints seems to be not to make the dicussion of the experts public, but merely to get the conclusion of the discussion. (Sort-of like a press-conference after a meeting that was closed to the public and/or press.) It seems to me that it is quite typical that consensus that a significant conjecture is solved arrives many months (sometimes even years) before an official publication. And, for the very famous ones it is typically easy to find out this semi-official consensus somehow, but for the not very famous ones this can be tricky, and hence these things get asked.

    I do not want to write too long, so only briefly. By completely standard criteria 'too localized' [the results of the preprint is only of interest to a relatively small subset of the community, as are the majority of all papers], 'not research level' [the preprint seems obviously 'strange'; not that it applies to any of the ones mentioned here, but there are enough out there on RH, Goldbach and so on], 'subjective and argumentative' [the clain is so recent that even the experts cannot have a firm opinion yet] one can (and I think should) argue directly for the closure of various preprint-related questions one might envision, yet some preprint related questions 'survive' this obvious test, and for them at least a closer inspection (as opposed to instant closure) seems suitable to me.

    One salient difference (to me, at least) is that certain open questions (eg the Riemann hypothesis, the Collatz conjecture, P vs NP, etc) have the following two characteristics.

    1. They are serious crank magnets.
    2. They are famous enough that once the experts agree they are solved, basically everyone will know about it not too long thereafter.

    Point (1) seems like a strong reason to avoid discussing purported solutions here on MO. Keeping the cranks at bay is vital for the health of this website. And point (2) implies that there is really no pressing reason to talk about them here.

    The Hanna Neumann conjecture is not of this form, though it is one of the highest profile open questions in infinite group theory.

    This doesn't mean I think that we should talk about purported solution to the HN conjecture here. I have the same concerns that Kevin does, and I really don't know what I think the right answer should be.
    • CommentAuthorfedja
    • CommentTimeJun 4th 2011
    I think that once something is put in a public domain, it is open for the discussion. There is no need for the expert review behind curtains. If line 3 is wrong, it is wrong. If it is right, it is right. If it is unclear, it is unclear. On the other hand, verifying a proof is not something everyone is willing or even competent to do. It is a hard job and if there is an interest in going over the proof line by line together, I see nothing wrong with doing it on MO or on any other public forum. But more often than not the question means "I have no idea whether it is correct, no desire to put any decent amount of my own time and effort into verification, but would love to hear the latest rumors". Such type of questions should certainly be closed IMHO.
    @fedja: your post strikes me as "logically correct", but here are two points. Firstly, whilst it is perhaps fine for experts to go over a proof line by line on MO, I myself would definitely not want to put the credibility of someone else's proof online with publically viewable posts of the form "Do you think Lemma is OK? I think I have a counterexample". I would far rather email the author or an expert with a worry of this form. This way, if I have made a mistake, then there is no possibility that the fact I made a mistake is interpreted as a possibility that I "don't believe the proof" or whatever. People sometimes aren't very good readers, especially if I write "is there a mistake here?" and then, 20 comments later, I write "you're right, there's no mistake", by which time my first comment had been voted up 5 times. Conversely, if I haven't made a mistake and Lemma destroys the paper, then the author can quietly go about retracting the paper with less public humiliation than were it to be splashed all over MO.

    And secondly, whilst you say there's nothing wrong with a bunch of experts meeting at MO and taking a proof apart -- do you really think this is likely to happen? What is far more likely is that most experts aren't reading and either nothing happens or you get more noise than signal, which again can't be good for the site. I really cannot imagine that e.g. Jeff Lagarias, who knows a lot about $3n+1$, is suddenly going to appear on MO and organise a working group on going through the proof. He's far more likely to read it in private and discuss issues with other experts via email.

    So in summary, you might be saying something like "wouldn't it be great if experts come along and take new preprints apart carefully and give an in-depth look at them, leading to an evaluation of the correctness of the MS", I think my response is "yes it would be great -- but it ain't going to happen, and so leaving a question of this form open is unlikely to do any good and might do some harm".
    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.

    Conjecture: It's hard to find an example of a good MO question where, if the question were to turn into a discussion, the OP would have absolutely nothing to add to it. My exaggerated example above is perhaps a case of this.

    Kevin Buzzard, regarding your last comment: I think nobody so far argued for keeping this type of preprint-question open. Indeed, Andy Putman and me (for slightly different but closely related reasons) explictly said that of course this type of question should be closed. And this is also current practise. The two PvsNP questions linked to above that were precisely of this form were closed. By contrast, some other preprint-related questions stayed open, because they were apparently judged to be of a way more reasonable form, for example because they did not ask about it a day after the preprint appeared.

    And to make a general point: I remember in 2005 attending a fairly large AMS-co-organized conference (all kinds of subjects). One of the plenary speakers was Hamilton, more or less on the (then) current status of the verfication of Perelman's proof of Poincaré. So, if talks to a couple hundred non-experts can be given I guess one could also have considered a question for it to be a legitimate MO question [and I mean legitimate in 2005, the day after the posting of the preprints to the arXiv it is not a legitimate question].

    I guess we're agreeing about the lazy questions. What I'm worried about with the second para is that Hamilton is clearly an expert so has every right to stand up and say what he thinks about Perelman's work to an audience of many. If one could be assured that an expert would come to MO and offer their wisdom as a result of someone asking a question about a preprint then this would be great. My worry is that this is unlikely to happen and that you'll end up with far more noise than signal, which is not ideal.

    We also agree on the fact that 'noise' can be a big problem on this type of question. However, to me it does not seem so likely that too much noise happens except for certain types of the most famous problems (which actually was a secondary reason, I did not state as I did not really find a good way to way to formulate it, for me suggesting in the first comment to perhaps not allow such questions on (certain types) of the most famous problems). But, for anything but a handful of super-famous problems, who but a knowledgable person will consider commenting? I simply do not see all kinds of non-knowledgable people commenting on the merits of one or different approaches towards resolving the HN conjecture. I mean, what does one say (without instantly revealing ones own ignorance)?

    And, the density of experts on MO seems high enough to me that there is a fair chance to get an expert answer. Or, and this seems also important, the extend expertise of somebody might at least include the problem to a sufficient extend that s/he can signal if somebody makes a nonsensical statements and/or draw the awareness of an expert to the question [if I understand the first sentence of Mark Sapir's answer to the thompson-question correctly, he came to MO specifically to answer that question as somebody told him about it].

    Finally, I would say that an answer of the form: 'there is not yet a consensus on the preprint and it might not be the right time to discuss this preprint publically' (followed by closure) is also an answer of some use if it comes from somebody knowledagble on the subject matter. The only thing I would find unfortunate is (and it seems to me there were some tendencies in this direction) if anything 'containing the forbidden word preprint' was closed automatically without further consideration.

    • CommentAuthorHJRW
    • CommentTimeJun 5th 2011

    Gerald - similar arguments could be used to justify 34953 - but it's such a lazy question I'm delighted it was closed.

    A special feature of the Hanna Neumann Conjecture question (66828), as has been observed above, is the amount of time that has elapsed since Friedman's first attempt. The current preprint is his third, and I know for a fact that many of the experts who read his first closely won't read this one. So it's genuinely unclear whether anyone is making an attempt to verify it.

    Kevin - I'm not for a moment advocating that MO should be used as a forum for the active discussion of recent preprints. But I don't think that's what 66828 asks for.

    I think 66828 contains an instance of precisely what I'm worried about. Mark Sapir's witty comment is of course funny, but could also be interpreted as insulting (especially if you're at the end of it). If that question weren't there, then we wouldn't have Mark's comment. I'm sure Mark would leap to defend his right to make the comment and whatever, but I think it's a shame that we now have up on MO what is arguably an insult. If the question weren't there, then there would be no place for the insult to sit, so Sapir would take it somewhere else -- e.g. perhaps he could trade insults with one or both authors by email, which is of course fine by me. But I find this sort of thing far from what I perceive MO to be good at.
    • CommentAuthorfedja
    • CommentTimeJun 5th 2011
    @Kevin "And secondly, whilst you say there's nothing wrong with a bunch of experts meeting at MO and taking a proof apart -- do you really think this is likely to happen?" If you've read the second part of my post, you could easily see that I place the chance at 0.00...1. Nevertheless, Tao and Gowers are here and if somebody posts a question in the form: "I have difficulty understanding the proof of Lemma 2.3 because it seems to me that, and so on", there may be a meaningful response. Of course the "pure noise" should be deleted on the spot but I still maintain that a reasonable and civilized discussion of proofs on public sites is possible. It just requires a real desire to figure things out (which includes a good will effort to clarify everything and to correct whatever is or seems wrong) and a certain level of maturity from the audience. Whether any of those conditions is satisfied is a completely different issue.

    "If the question weren't there, then there would be no place for the insult to sit". If MO weren't there, there would be no question. And if a few well-known people weren't there, there would be no MO. Should we go after our moderators now? Mark's comments are just what they are: Mark's comments. Our reaction to them (from applauding to reporting) is just what it is: our reaction. Everyone is responsible for his own behavior and it ends there. To hold the question poster responsible for everything that is written in the answers is a bit illogical, isn't it?
    A good question to think about when discussing whether questions should be closed or deleted (or indeed whether they should have been asked in the first place) is:

    "If this question along with its answers and comments were the first thing a mathematician knew about MO, would they be likely to immediately form a negative opinion of MO."
    • CommentAuthoran_mo_user
    • CommentTimeJun 5th 2011 edited

    To continue a bit on the last part of Fedja's comment: to avoid insulting others is certainly a good idea (though not always easy in practise, e.g., as things can get read differently than how they were written/intended). And, it might be true that for this type of question we are discussing here the risk of insulting somebody is a bit higher than normal (though for the specific instance in the interpretation I assume, I'd say, if there are people that doubt the validty of a preprint, which is anyway often the default assumption of many regarding claims of establishing important results [though it might not be said directly], then I doubt the authors are completely unaware of this and then totally shocked to find this out, expressed in a quite mild and indirect form, by reading MO; but one can certainly see this differently).

    However -- while I tried so far to avoid bringing this up not to derail the discussion I now can't help, as this 'insulting' comes up basically for the third time -- in view of certain incidences in the recent past I think it is justified to assume that this non-insulting-goal cannot be such a priority as to warrant a rule or policy that implies the direct closure of various questions of essentially purely mathematical content just on the grounds that it makes it somewhat more likely that somebody might get (mildly) insulted; and I would maintain that questioning the validity of a result is not an insult in itself, but simply a critical opinion, and one could even consider it ones professional duty to voice such an opinion (if one is convinced of it).

    Just to recall, we recently had a question whose explicit purpose was to 'name and shame' (fine institutions not people, but institutions are represented by people and some of them are/might be mathematicians, in case that distinction is relevant to somebody) and whose usefullness is still totally unclear to me, as a sequel to a question where at least it was clear to me that it might be useful to some but equally clear that it is very likely insulting for others; and the handling in practise -- completely needlesly -- in fact resulted in grave insults in particular towards one mathematician (to whom I have no relation whatsoever, in fact I never heard of him before) directly, milder insults towards some others, and most likely to a couple more indirectly (the worst one was eventually deleted, but what remains is bad enough).

    And, I could attribute this discrepancy in worry over insults then and now to imprecissions of community moderation and alike, but if now the, if I rememeber well, literally first person to take a strong position in favor of said question (the latter one), supported by another one that also massively supported said question, are so worried about insulting somebody on MO then, I am sorry, but I cannot understand this.

    ADDED: this was written before I saw Noah Snyder's comment; it is not a response to him.

    • CommentAuthorHJRW
    • CommentTimeJun 5th 2011


    Mark's comments are just what they are: Mark's comments. Our reaction to them (from applauding to reporting) is just what it is: our reaction. Everyone is responsible for his own behavior and it ends there. To hold the question poster responsible for everything that is written in the answers is a bit illogical, isn't it?

    Hear, hear.

    I'm not 100 percent convinced, but I think we can agree to disagree. Whilst it is of course clear that the questioner isn't responsible for any comments which can be perceived to be inappropriate made by an answerer, it is also clear (to me at least) that some questions lead themselves far more easily to the temptation to be snarky (is that the US English word I'm looking for? I want to say sarky (=sarcastic) and I know Henry will understand but I'm scared no-one else will!) than others. As has been pointed out, if seeing derogatory comments being thrown around is by chance someone's introduction to the site, what are they going to think?

    I guess the bottom line is that I'll continue to play the odds as I see them (i.e. voting to close questions I think look like trouble) and others might play a different game, and probably we muddle through to some sufficiently satisfactory outcome.

    @Kevin: for what it's worth, "snarky" is indeed well known in American English. I'm pretty sure that we Yanks (and Canadians too) would understand 'sarky' as well.


    Wikipedia claims "snark" is a portmanteau of "snide" and "remark." I can attest that it is quite commonly known amongst Americans of my aquaintance.


    Wikipedia might claim that, but the OED differs. Either it goes back to Lewis Carroll (the noun) or is an old Germanic/Norse word (the verb) meaning "to snore or to snort, or to nag". Given the lack of sources on the Wikipedia page, I'm inclined to go with the OED on this one.