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    • CommentAuthordavidac897
    • CommentTimeSep 5th 2012 edited
    This is less of "is this question acceptable" but more "could and if so how would one make this acceptable?"

    I'm wondering whether it would make sense to have some kind of discussion on Mochizuki's recent purported proof of the ABC conjecture. Maybe something so that experts could give ideas about what ideas are in the proof? A discussion of when people might know enough to seriously judge the proof? Some other kind of discussion?

    Discussion per se is not really well-suited for the MO software.

    On the other hand, I would really be interested if a discussion is held somewhere publicly on the internet (someone´s blog, perhaps?) so I can follow along and perhaps be lucky enough to learn some trickle-down insight.


    Which Mochizuki is being referred to?

    • CommentAuthorWill Jagy
    • CommentTimeSep 5th 2012


    As with P vs. NP, we would rather allow some time for the early returns from those who actually know what is going on. Note that nobody is asking now on MO for tutorials on P-NP.

    someone’s blog, perhaps?

    Try the comments on Jordan Ellenberg's post.

    • CommentAuthorvoloch
    • CommentTimeSep 5th 2012
    Feel free to discuss it in the blogosphere. There are already ongoing discussions on Jordan Ellenberg's (JSE here) blog and on the Secret Blogging Seminar (which is ran by several people connected with MO). Here is off-topic unless maybe you have a specific question about a specific point in the paper.

    Links for the lazy:

    Discussion is of course not really what MO does, but there are probably a mess of really good questions people could ask (if not answer immediately!) about "Inter-universal" things.

    Yeah, I agree with stankewicz.

    @stankewicz: and yes, such question(s) has already been asked before. At least one was asked three years ago when MO was just started! Link.

    • CommentAuthorHJRW
    • CommentTimeSep 6th 2012

    This is a great example of a question about Mochizuki's work that is acceptable. (It also appeared just after Mochizuki's paper.)

    • CommentAuthorWill Jagy
    • CommentTimeSep 6th 2012
    Recent question

    which currently has five upvotes and four votes to close, as will generally happen for this sort of thing. To me, it is one of many possible well-meaning questions which amount to "Isn't this exciting! I'd like to hear more." I think we can wait.
    • CommentAuthorquid
    • CommentTimeSep 6th 2012 edited

    EDIT (to address complaints, hope the thing below now works for everybody):

    The question does not ask a specific question but makes a very generic request for elightenment, and tries to hide this behind this some analogy that is presented at length (for no intrinsic reason).

    Hundreds of people might have asked a similar question. If any question of this type stays open, I would at least hope it is one where OP made some actual prior effort.

    I cannot see in what sense this question is 'well-meaning' either.

    I must quietly protest. Here is a small list of questions in this spirit that I have asked in the past that have been greatly encouraged on this forum:

    My question is well defined, and questions of this type are routinely answered with great enthusiasm on this website. Since I'm not asking about the proof itself, but only about its sketch (which, supposedly, people have known for years), others are in a position to be illuminating. The argument that I must read the mathematics before I ask the question is ad hoc. On many occasions I have seen people preface their question with "Before I start reading on _______, I would like to get some motivation" (and about much less complicated mathematics), and have gotten enthusiastic support.

    I feel that the people who have closed this question are trying to discourage frivolous questions regarding a new fad. But that is misleading -- my question is well defined, easy to answer for experts, and interesting to many members of this forum. I see no good reason to close the question.

    I agree that it might be too early for a good answer, but the question itself doesn't seem unreasonable. Maybe we need to get BC out of retirement, to provide a good comment, even if answers will have to wait.

    • CommentAuthorquid
    • CommentTimeSep 7th 2012

    As ever so often reopened without any of the reopeners commenting...

    Well, I can understand you might not have cared about my opinion in particular as it was not articulated too well. But, the fact that JSE who blogged about this (positively) voted to close it did not give you any pause for thought either?

    @Scott Morrison: if BC wanted to comment substantially he could have done/can do so on JSE blog where he left a comment.


    Regarding (my emphasize)

    my question is well defined, easy to answer for experts, and interesting to many members of this forum. I see no good reason to close the question.

    Yeah, right. Depends on your notion of expert, I guesss. I do not know what a 'well-defined question' should be in this context. But since yours is based on some premises of yours for which you only provide most anecdotal evidence, I doubt even that. (But this last part is besides the point.)

    Regarding your other questions that were so well received, guess you missed that thread:

    quid writes "The question is completely void of any actual question, and tries to hide this behind pompous lyric" and "this is not even a well-meaning but a self-important question" . This is insulting and not tolerrable. Specially by anonymous user.
    • CommentAuthorquid
    • CommentTimeSep 7th 2012 edited

    @evgeniamerkulova: I changed it, hope it works now. [For the record the second phrase that is quoted from me had a a sort off disclaimer attached to it that made it less strong than the quoted form suggests.]

    But calling me "stubborn" (on main even) is tolerable?


    my question is ... easy to answer for experts

    This is actually what makes me a little uneasy about the question (I don't agree it is easy to answer for experts). Maybe I'm off base about this, but my impression is that there are only a handful of people in the world who could give a really compelling answer beyond simply repeating things from Mochizuki's recent papers. I'm not fond of the idea of questions aimed at a very small set of people, since it feels too much like a personal request for information. On the other hand, the broader interpretation would be a request for one of the people currently reading these papers to summarize their understanding of the motivation in the form of an MO answer, which doesn't seem all that constructive to me (this already has a natural home on blogs).

    questions of this type are routinely answered with great enthusiasm on this website

    I see them as questions of a somewhat different type, namely about folklore intuition that is definitely known to many experts but may be written down only in places a non-expert wouldn't be aware of.

    Henry, you mischaracterize my question! I am not asking for an explanation of the new papers by Mochizuki. I'm asking for the motivation for their existence. An example of a good answer is: "it's true for function fields, and here is the rough argument... Therefore what we need is a number theoretic analogue of _____. Mochizuki's papers aim at filling that gap in the theory."
    • CommentAuthorWill Jagy
    • CommentTimeSep 7th 2012 edited
    James, is there some reason you almost never answer questions on MO?
    • CommentAuthorGiuseppe
    • CommentTimeSep 7th 2012
    Will, I don't see why your question is relevant to the discussion at hand. (Even if James had such reasons, he is under no obligation to share those in this public forum.) I'd like to request people not to get too personal here.
    • CommentAuthorquid
    • CommentTimeSep 7th 2012

    @Giuseppe: I could tell you plenty of reasons why it is relavant. Just deleted a ten lines explanation tough, since perhaps I said already enough.

    • CommentAuthorWill Jagy
    • CommentTimeSep 7th 2012
    Giuseppe, perhaps I can make this seem less personal. When I began on this site, I answered questions for a week or two before posting my first question. I have often asked that there be a minimum number of good (upvoted?) answers before a person gets to ask any questions. That never flew. I have also asked for some milder thing keeping answers somewhere near comparable to questions.

    Now, part of why these will never go anywhere is the great importance placed on anonymity. The dream of the creators of the site is that the next Fields medalist could post a question without registering or doing much of anything else. The phrase "minimal barriers" seems about right.

    Meanwhile, there is no requirement to actually have a Ph.D. or be in a math Ph.D. program. Enough people are mathematically competent who are in something else (I guess you are in Physics), in a few cases some very strong math undergrads, or are simply outside the traditional chain of study. I like people to answer questions, partly for them to learn the manners of the site, what makes a good question. But I also want people to answer questions to demonstrate core competence in some area of mathematics, possibly not the one about which they are asking. But something. There is a supposition, or at least a desire, that people on the site are involved in research and wish for help in something that has them blocked, perhaps something basic outside their area.

    That seems enough. It would take a while, but searching my posts on Meta, back two and a half years, would show that these really have been concerns of mine over the years.
    I was quite miserable when it looked like there was a lobby to close the question; now I am very glad indeed that it remained open. It has produced a beautiful and thought-provoking answer.
    • CommentAuthorquid
    • CommentTimeSep 7th 2012

    @James Cranch (but also more generally): I do not know what you mean by 'a lobby to close the question'. Anyway, it is a completely standard thing that individual user based on their judgement express their opinion that a question is unsuitable for MO (for any number of reasons) via a vote to close or just by saying so.

    Sorry to have made you temporarily feel miserable.

    Let us see how we all feel if ever somebody should answer that the vision was this but it is flawed for that rason, accompanied by some argument that does not seem nonsensical and is not easy to refute. Then, what?

    To wit, on some blog (sbseminar, incidentally, if I remember well) there was already some jokster claiming an error, in a naive form, which is no problem as easy to refute. But somebody might do it in a sophisticated form or in good faith (while being wrong), or also [it is not exclude, though I certainly have not heard anything like this so far] while being right. In some sense while globally very unfortunate the last would be the least problem for MO in such a scenario.

    But do you personally want to take responsibilty for potentially spreading some (false) rumor on the incorrectness of this result?

    Now, you can say you have no influence on this. However, if one has the ability to vote on the open/closeness of a question then one shares this responsibility personally (in a certain sense; not fully as the moderators could always overrule any decision, but then it seems almost unfair to me to leave them alone in these decision).

    So, you might think all these people that vote to close are just some wet-blankets (or worse). But, perhaps, just perhaps, some of them actually thought about what they are doing when they press that button (in abstract and concrete situations).

    Now, you are of course free to disagree with their judgement in this case. Yet, if you would like to do so it would seem apt to me if you could answer the question I asked. 'Then, what?'

    It is honestly not so clear to me how to proceed then, if the question is open. (What would be the argument to outlaw this answer we do not want? The others are not so narrowly on-topic either to make an argument based on this aspct for instance).

    So, how would you proceed in this scenario?

    I personally don't see any harm in leaving this question open. There are only a small number of people in the world whose opinion would be taken seriously if they said there was a problem with the proof. So I think there's not much risk of spreading false rumors that anyone would believe.

    On the rare occasion I think about voting to close or re-open a question, I ask myself whether the question is likely to make MO better or worse. (Some people have more objective criteria, but I don't find such codifications very useful.) In the case of this question, I think it's most likely to make MO better. I learned a new point of view from Marty's answer. Further, nothing embarrassing has been posted, nor do I think it's likely.

    I also don't really care about the OP, whether he was just fishing for enlightenment, and so on. I'd rather see more discussion about Mochizuki's argument than less. The number of people in the world who can say anything at all about his recent papers is so small, I prefer to err on the side of openness.
    • CommentAuthorMarty
    • CommentTimeSep 7th 2012
    I second James Borger's comment here on meta. Another argument for reopening is given by Minhyong Kim's comment -- he wishes to submit an answer if it is reopened. I would greatly appreciate his insights!
    OK, I was one of the recent voters to close. But Minhyong's promise to answer is good enough that I voted to reopen, and it is now open.
    • CommentAuthorvelnias
    • CommentTimeSep 8th 2012
    Full disclosure: I have not voted on the question being debated here, either for closing or re-opening.

    @Will Jagy:

    since MO is a question and answer site, curtailing the questions also holds back the answers. Moreover, it is clear that some subfields of math are highly over-represented on MO, and so anyone coming in from outside these fields would immediately face an immensely annoying barrier to entry and participation under your hypothetical rules. It seems from your profile that you work in number theory, which also happens to have the second-highest frequency (in excess of 3000 at the time of writing). If you worked on Schur functions, you would have had to wait 8 months (from the date of your current first answer here) before even seeing a question in your field. And of course, one wonders who would possibly have asked this question on Schur functions to give you an opportunity to demonstrate your core competence, since that person would also have had to answer... well, hopefully you get the idea. Unless you are prepared to institute policies that will actively keep out experts in under-represented fields, I honestly can't see the point of requiring n answers from newcomers before a question can be asked.


    If closing the question results in an existing gap NOT being found, will you accept personal responsibility for your negative contribution to the understanding of mathematics? There are many good reasons to close this question, and you have previously mentioned some of them here. However, the "what-if-this-hypothetical-disaster-happens-if-we-don't-close" line of reasoning lies on a steep gradient path to complete absurdity.
    • CommentAuthorquid
    • CommentTimeSep 8th 2012 edited

    Some direct replies and then some more general comments:

    @velnias: yes, I do admit to overdramatizing a bit and it seems too much so. Thus, in view of your elegant formulation let us agree I should not go for long in this direction ;) Your analogy with the responsibilty if a gap were not to be found is however not so good in my opinion; looking for one is completely out of the mandate of MO, thus there is simply no responsibilty regarding this, so I can easily accept my share of it.

    @James Borger: Did you consider that the existence of this question, makes it unlikely (basically impossible) that a much better question of this type will ever be asked (and survive) and even if it would be asked not receive the same level of attention. This is mentioned in my very first comment here on meta; I would have some reservations for any question of this form at this time, but if there is to be one, it should better be a good question. I find the idea that some non-MO mathematician searches on the net for information on the recent ABC developments and then this question (containing blatant falsehoods, for instance) is the first they see of MO simply a bit embarassing. Okay, the answers do make up for it, but this question even more so with that level of approval is in my opinion a disgrace [added: is 'disgrace' too strong a word? if so replace by 'unfortunate']; if at least the question had a negative score, one could think community moderation works.

    @General: Of course I do agree that now Minhyong Kim should have the opportunity to answer (and this already happened), however I would like to highlight his very first half-sentence (cf Henry Cohn's contribution in this thread):

    I would have preferred not to comment seriously on Mochizuki's work before much more thought had gone into the very basics [...]

    not to quote this out of context though I add that he gives this a positive twist for example by saying

    [...] the current sense of urgency to understand something seems generally a good thing.

    So, I really hope all those that were so keen to know about this in near real-time will make some effort to actually understand something relate to this. In that sense I liked Marty's suggestion.

    Added a bit later: I forgot, somehow in reply to velnias but also James Borger, to clarify that while the precise scenario I mentioned is admittedly not that likely (to cause a real problem) I however do think that (in particular over time, and if this stays open in the end, answers can come in in months) there can be a slippery slope and grey area from 'vision' to 'outline' to 'commenting on correctnes/feasibilty'. And, there were lengthy discussions on discussing recent preprints on MO. Indeed, on this matter I am/was personally rather towards the soft/open end of the spectrum of opinions expressed (with some caveats and reservations). Yet, some others basically said this should never happen. In any case, I do maintain that the vague and openended nature of this question over time has the potential to lead to problems (albeit not disasters).


    I think I cast the first vote to reopen in the current round, so I should probably give a reason, though for the most part the reasons have already been explained by other people. Simply: having this question open makes the world, and MO, a better place.

    As far as I can tell, the main objection has to do with whether the question could have any good answer at this stage. I think the superbly informative answers that have now appeared lay that doubt to rest.

    I haven't really followed the number of open/close cycles that this has gone through, but it is open now, and I hope it stays that way. The way the question is phrased doesn't strike me as bad (e.g. it is not explicitly asking for opinions about correctness), and the answers are of course great.
    • CommentAuthorquid
    • CommentTimeSep 8th 2012

    @Tom Leinster: in some sense it is too late for this occassion, but just to clarify my point of view, since this might or might not become relevant on other occassion.

    My first objection to this particular question is simply that in my opinion it is a terrible question, and for example fails numerous criteria laid out under "how to ask". (It is true I also have some reservation regarding this type of question, but this is a different matter; and my oppoisition to this type of question is not at all absolute, it is mainly a question of timing.)
    Now, there is something to be said that one sometimes can allow 'bad questions' to get the 'good answers', but in this case I see (I should say saw) very little reason for doing so, since there are many people suceptible of creating an instance of this type of question that would be much better.

    To further ilustrate what I mean: in retrospect I think it was a mistake that I opposed "Has-the-abc-conjecture-been-solved?" ; except for the title (but this is easy to change), this is in my opinion the relatively better question in that it at least does not pretend to want something specific (and does not force upon the reader some drivel around the Weil conjectures). It then could have served as some sort of container for texts on the subject (because this is what we are actually talking about here, not answers to some formulated question).

    You say:

    having this question open makes the world, and MO, a better place

    However, I think there is a potential fallacy here. Namely, you(1) conflate the existence of a question of this type on MO, and the existence of texts of the type given as answers in the world, with the existence of this particular question. But this is not realistic; except perhaps on a very narrow timeline. But then if this is so important we should have encouraged davidac897 and his idea to have all this possibly still some hours earlier, or allowed the first questtion of about this type.

    Personally, I consider it, as said, as unfortunate that this particular question got the interesting texts as so-called answers, as opposed to them or close cognates of them living under a nicer roof (on MO, or elsewhere).

    As said it now seems to late anyway, but still I wanted to summarize my point of view and in particular highlight that I consider the question whether this particular question was one suitable for MO and the question whether a question of this type can be suitable for MO as quite orthogonal. For the former in my opinion the answer is very clearly "no" (and this opinion stays, independent of all answers), for the later this is more tricky but this is somehow obsolete now and already having writeen too much I will leave it here.


    (1) Actually from what you write alone I can not be sure you personally do, so this is rather an abstract you. But I am quite convinced that not too few people are (at least to a certain degree and/or subconsiously) victim to this falllacy.

    • CommentAuthorAndy Putman
    • CommentTimeSep 8th 2012 edited
    I agree that the question is terribly written and historically/philosophically dubious. Why doesn't one of us edit it to remove the bs about the Weil conjectures? That would, I think, greatly improve it.

    Here's my suggested edit:

    "Mochizuki has recently announced a proof of the ABC conjecture. It is far too early to judge its correctness, but it builds on many years of work by him. Can someone briefly explain the philosophy behind his work and comment on why it might be expected to shed light on questions like the ABC conjecture?"

    I think that edit would be great and would really help clarify the question and make more users happy with it.

    • CommentAuthorHJRW
    • CommentTimeSep 8th 2012

    Yes, +1 Andy.

    • CommentAuthorGiuseppe
    • CommentTimeSep 8th 2012
    I agree with Andy, Henry and Henry.

    Yes, please edit away; thanks. It really should have been made community wiki anyway, IMO.

    OK, I just made the edit. I also changed the title.

    Like Todd, I also request that the moderators hit the question with the wiki-hammer.
    • CommentAuthorHJRW
    • CommentTimeSep 8th 2012

    Todd - I thought that too, but considering the fantastic amount of work that the likes of Minhyong Kim have put into their answers, I think they deserve credit.

    • CommentAuthorWill Jagy
    • CommentTimeSep 8th 2012
    Plus, the question no longer uses the word behooves.
    Those who gave nice answers do deserve credit. I do find it disturbing that one can obtain 500 rep for asking what is the intuition behind a recently announced solution to a big problem. It takes no great originality to ask this and in some sense the original question is not much better than the previous questions asking for comments on the preprints that were closed. Ok we don't care about rep, but one can observe that this OP had asked nearly 100 "what is the intuition about famous result or notion X" questions and has obtained sufficient rep to open/close questions without ever answering a question (other than his own and a big list question) and without asking about a single specific research question. This I think was Quid and Will's point above.

    Anyway, all is well that ends well and the answers were nice.
    @bsteinberg : I agree that the OP has an enormous number of pretty silly questions. But it's worth noting that after the migration, his reputation will be cut in half.

    As a technical point -- is credit that has already been acquired erased once a question is struck by the wiki-hammer? I'm asking with regard to both questions and answers.


    What I don't understand, behaviorally, is all this wildly celebratory upvoting of a question which seemed sort of off-hand and casual. MO is so weird, sometimes. The upvoting of great answers I do of course understand.


    @Todd: my interpretation is that those upvotes more or less mean "I would also like to see an answer to this question!"

    Let me also note that on StackExchange there is a moderator message template part of which concerns users who answer few questions. This isn't bad enough behavior to warrant a suspension but it is somewhat contrary to the spirit of the enterprise.


    @Qiaochu: after about 50 upvotes and several thousand views and several good answers , it seems further expression of such a wish is pretty redundant, unnecessary, superfluous. "Your wish has been granted, already. Calm down."

    Anyway, can anyone answer the question I asked a few comments ago?


    @Qiaochu, again: I can't say I'm particularly bothered by people who mostly ask rather than answer questions, per se. (Thus, I don't particularly approve of mechanisms which try to get people to give more answers, if that's not their inclination.) I am bothered though if there is little indication that they are truly engaged with the question, or engaged with the people who try to provide thoughtful answers. Depth of thought and research behind a question is generally highly appreciated. I guess those are obvious points.

    • CommentAuthorquid
    • CommentTimeSep 8th 2012

    @Andy Putman: Thanks for the edit.

    Regarding CW mode: credit is not erased retroactively. It would be possible to only turn the question into CW mode; existing answers would then not be CW; new ones however would be CW.


    Yes, thanks to Andy!

    @quid: thanks; that's what I suspected.