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    I don't think making a philosophical comparison of Motizuki's work towards Vojta's conjecture with the Weil Conjectures is all that silly: Motizuki himself makes this comparison in "The Hodge-Arakelov Theory of Elliptic Curves", page 16, and again in "Inter-Universal Teichmueller Theory IV", page 31.

    • CommentAuthorquid
    • CommentTimeSep 8th 2012

    @Kevin Ventullo: Thank you for the information; however, I fail to see how this is directly relevant to the (meta) discussion at hand. Neither did OP say/do what you mention, nor did anybody deny it was reasonable.


    @quid: I think Kevin might have been referring to some things said earlier (by Andy among others) such as

    "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."


    "@bsteinberg : I agree that the OP has an enormous number of pretty silly questions."

    • CommentAuthorquid
    • CommentTimeSep 8th 2012

    @Todd Trimble: Thank you. I was aware of this, though. But, I should likely be more detailed regarding my view:

    OP did not make any comparison at all; for a comparison it would be necessary to know something on both sides and OP 'confessed' to total ingnorance of the one. By contrast, the story around the Weil conjectures (only, and at best) served to "define" the notion "vision". It is some pretext, detached from the actual question. The only link between 'Weil' and ABC that was invoked in the question is that two people each (it seems) worked for years towards a specific goal and since in the one case (supposedly) there was some "vision" it ought to be there in the other case as well.

    Then, it is either nonsense to make a priori this firm assumption that an analogy of the situations ought to exists, or the notion of analogy is so vague that it is useless to elaborate on the other/historic side of the analogy or to even mention it. And if in addtion the elaboration on the historic side is even imprecise, then it really makes no sense to keep it around.

    I really don't get why anyone thought to close this question. Given that Mochizuki thought his methods might be able to prove the ABC conjecture years before he came up with his (supposed) proof, it seems reasonable to think he might have an intuitive idea of a proof in his mind, and then the years of development of IUTeich were a means of putting those intuitive ideas into rigorous mathematical reality. While this could hypothetically be a question that only Mochizuki can answer, it could instead be that there is a sketch of an "intuitive proof" known to experts for years before Mochizuki's work. In that scenario, no one knew how to put those intuitive (even wishful) ideas into a rigorous foundation, and Mochizuki developed his theory in part in order to create that foundation. But that proof sketch would be both obscure enough and well-known enough to put on MO.

    In a similar vein, the lack of a suitable Weil cohomology theory over Q can be seen as a reason for a lack of proof of the RH, and I've even heard that there are fairly well-described recipes where if you can concoct a cohomology theory satisfying such and such axioms, then RH is proven (hence, obviously, no top mathematician has managed to concoct such a theory to our knowledge). If someone came up with such a theory and published a proof, I could see someone posting an analogous question on MO, and then someone would respond by explaining underlying idea behind a proof of the RH.
    • CommentAuthorquid
    • CommentTimeSep 9th 2012 edited

    @davidac897: I think I gave several reasons already why I voted to close this question, one of them minutes after the question was asked. [I can understand that they or some of them, due to their brevity, could be misunderstood and thus dislmissed as some overly formalistic approach to this matter, but it is not formalism that is the point, thus please read on.] Let me repeat what I said in reply to Tom Leinster:

    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".

    Assuming you read this already, I am given to understand that either you disagree that this particular question fails numerous criteria of 'how to ask', or you do not get why somebody would vote to close a question for this reason (or both). In any case, what you write seems more like an argument why a question of this type might be suitable for MO, than an argument why this particular question should not have been closed; and as elaborated at length this is, in my mind at least, a very different discussion.

    So, why do I vote to close a question that fails (in my opinion) too strongly criteria of 'how to ask'. Abstractly, because this means it has certain deficits discussed their that cause problems in answering it (at least this is the case in this case, for details cf below).

    Now, some might think that is not a good enough reason to close a question but then there seems to be a very widespread misunderstanding what it actually means to close a question on MO (or at least it is a persepective on it other than mine, but I believe that mine is the correct one, in the sense that this is how the mechanism was conceived, AFAIK). So here, what it means (to me):

    If there are significant deficits in a question (for example, that make it impossible to answer properly), then it is closed. Then problems can be fixed and if/after that has happened the question gets reopened. (Only if problems are never fixed or they turn out to be unfixable does the question stay closed forever.)

    If ever you disagree that this is the (theoretically) standard interpretation of how things (should) work, explain why editing, including the consequence of bumping, stays possible after closure just like when it is open, and why one can still comment on closed things.

    And, to stay in the house-analogy of main. If there is significant construction to be done in a building, it can make sense to (temporarily) close it for the general public while the work is under way.

    So, where does the question have problems. One example. This is how "how to ask" starts (basically).

    Ask a focused question that has a specific goal.

    What is the specific goal of the question? Isn't the goal obvious, you might reply. Or perhaps, who cares about the goal.

    However, the lack of specifiying the actual goal has the consequence that it is not clear "what constitues an answer." To wit, cf David Speyer's first comments (he asks whether this info is relevant) and the reply of grp (on main) saying basically that's old stuff surely this not what is meant, but then OP clarified that of course it was relevant to him. [Edit: Deleted further imprecise and tangential elaboration.]

    To sum up one reason:

    The question was unclear, so it is closed at least until things are clarified.

    If you still do not get why somebody thought to close the question, please point to a precise point in my explanation where you disagree. Else, I will assume it is clear now.


    Oh dear; I foolishly hit the entire post with the wiki hammer, while meaning to only do the question. This is a bit of a screw-up, primarily because it now makes it quite hard to see who wrote what. I'm really sorry about this, but I'm also not sure what can be done to fix it.

    • CommentAuthorWill Jagy
    • CommentTimeSep 9th 2012
    It's alright. I don't believe there will be any more activity or voting with respect to that question.

    Scott, you can wait until the transition to SE 2.0 and then cancel that... :-)

    I was going to say the same as Asaf.
    Ben Webster's question is nice, is not it...

    • CommentAuthorquid
    • CommentTimeSep 12th 2012

    @Alexander Chervov: yes, it is quite nice. But, in case you should want to imply that this is similar to the situation at hand. This is really not the case. [(almost) sucessfully supressing the urge to write a climax of 'really's ]

    Am I the only person who sees the similarities between quests ? :)
    • CommentAuthorvoloch
    • CommentTimeSep 13th 2012
    @Alexander Chervov: A fundamental difference between the two questions is that the Quillen-Suslin theorem was proved in the '70s and there has been ample time for the proofs to be understood and digested. Mochizuki's work has just been announced and nobody (really!) has had a chance to understand, let alone digest, the proof. It's very premature to ask the question, although I must say the answers were pretty good, considering.
    • CommentAuthorbsteinberg
    • CommentTimeSep 15th 2012
    The latest addition to the famous ABC conjecture question is the first of what may be many comments on the correctness of the proof. I don't think this is appropriate to the site (and in fact several questions to this effect have been closed). I can no longer vote to close because I already did, but perhaps it is time to close the question before it becomes an argument about correctness, which can be held elsewhere.
    • CommentAuthorWill Jagy
    • CommentTimeSep 15th 2012
    Yep. It won't let me vote to close.
    @bsteinberg " I don't think this is appropriate to the site" why ? " which can be held elsewhere" why ?
    • CommentAuthorllIIllII
    • CommentTimeSep 16th 2012
    Propose as a venue for comments and discussion on abc proof, although it has disadvantage of requiring <math></math> tags, which is more cumbersome to type than dollar signs. Nor does it have voting.

    Alternatively Google+ has voting, but does it have TeX ?

    Where else can you have TeX-enabled or MathJax-enabled discussion ?
    • CommentAuthorMariano
    • CommentTimeSep 16th 2012

    @Alexander, it has long been an accepted policy of the site not to discuss the correctness of papers —at least this recent.

    In all likelihood, this will continue if the question is not closed.

    • CommentAuthorbsteinberg
    • CommentTimeSep 16th 2012
    The question is not asking about correctness of the proof and therefore any such comments are off-topic. 2 previous questions asking about correctness have already been closed if memory serves (in fact this thread was opened to address those questions and not the popular which survived by avoiding asking correctness).
    I am not sure that words "long accepted policy", "FAQ says..." are correct. FAQ says site is "community driven". So we set rules and polices for ourselves. Voting is democratic way to do it.
    There were other quests discussing correctness and they were also very popular, indicating that community is pro...
    • CommentAuthorbsteinberg
    • CommentTimeSep 16th 2012
    @Alexander, look at and the threads therein. The popular questions predate the long policy (at least 1 year) of not discussing correctness. Also note that popularity is by no means a good way to judge merit or appropriateness.

    Aren't these arguments to delete Vesselin's answer rather than close the question? (Or perhaps there are more collegiate options than forcibly deleting it, e.g. politely asking him and the other commenters on his answer to halt their discussion.)

    • CommentAuthorvoloch
    • CommentTimeSep 16th 2012
    It would be a pity to delete Vesselin's answer since it is actually quite interesting, even though it's not an answer to the question. Maybe we should close the question instead.
    • CommentAuthorbsteinberg
    • CommentTimeSep 16th 2012
    @Tom, my fear is that if the question remains open, it will attract more comments on the proof, maybe not all from people as reputable as Vesselin. Perhaps a new question should be opened on particular points of the proof if someone has a question on some lemma.
    • CommentAuthordeane.yang
    • CommentTimeSep 16th 2012
    Although I understand why Dimitrov's answer and comments contradict the letter of MathOverflow policies (and clearly he should be encouraged to set up a blog and continue to post his thoughts on it), I vote for some flexibility on this.

    Yes, it would be very good for people to blog about this (and particularly for VD to do this, with a link to a blog post under his answer). But I share Benjamin's concerns about noise. So far those who have answered have done so about as well as could be expected, but the fact of the matter is that it's an open and unfocused question (and perhaps idle as well, since the OP has yet to engage with any of the respondents who put hard work into their answers), and the highest-rated answers start with frank admissions that the posters don't understand the recent work of Mochizuki.

    I strongly back those like quid and Gerhard who counsel patience. No doubt seminars are being organized around the world to have top-flight people take a hard committed look at this work (and no doubt Mochizuki is already very busy answering questions). In six months or a year, I imagine some dust will have settled, and then people will be in a better position to give much more informed answers to questions. So why all the clamor? (I also wonder, maybe a little unkindly: how many celebrants of this question have attempted to thoroughly digest the answers which have been given so far? all appearances suggest they are not for the innocent!)

    It would be great to have people write focused and engaged questions about this work. Meanwhile, I second (or third...) voloch's call to close this question (and have voted to do so).

    @Alexander Chevrov: All societies need mechanisms to make sure they do not make Socrates drink hemlock. As the Athenians demonstrated, one person one vote (much less one account one vote) is not sufficient for this purpose.
    • CommentAuthorBugs Bunny
    • CommentTimeSep 17th 2012
    I voted to close (1st time) but I am not going to go into the close war and vote again. I think that the arguments of the opponents are overwhelming. The arguments of the proponents are basically that it is interesting (math behind it and some of the answers).

    Isn't it true, if you voted to close before, and then the question is re-opened, that you are not allowed to vote to close again? Or is that just on 2.0 sites...


    No, that's true here as well.


    As someone who upvoted the question originally, I agree that it should be closed now. Minhyong has written an essentially optimal answer given the time frame, and it seems to be degenerating now.

    I like the idea of people writing their own blog posts and adding links to this page: Perhaps a link could be added to the original question before locking it.