tea.mathoverflow.net - Discussion Feed (Mochizuki proof of ABC)

Kevin Ventullo comments on "Mochizuki proof of ABC" (20193)

2012-09-18T04:44:08-07:00

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: http://michaelnielsen.org/polymath1/index.php?title=ABC_conjecture. Perhaps a link could be added to the original question before locking it.

Todd Trimble comments on "Mochizuki proof of ABC" (20186)

2012-09-17T09:55:18-07:00

No, that's true here as well.

geraldedgar comments on "Mochizuki proof of ABC" (20185)

2012-09-17T06:27:14-07:00

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...

Bugs Bunny comments on "Mochizuki proof of ABC" (20184)

2012-09-17T02:05:39-07:00

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).

Alexander Woo comments on "Mochizuki proof of ABC" (20181)

2012-09-16T14:25:18-07:00

@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.

Todd Trimble comments on "Mochizuki proof of ABC" (20180)

2012-09-16T12:09:45-07:00

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).

deane.yang comments on "Mochizuki proof of ABC" (20179)

2012-09-16T11:17:39-07:00

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.

bsteinberg comments on "Mochizuki proof of ABC" (20178)

2012-09-16T08:44:59-07:00

@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.

voloch comments on "Mochizuki proof of ABC" (20177)

2012-09-16T08:35:08-07:00

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.

Tom Leinster comments on "Mochizuki proof of ABC" (20176)

2012-09-16T08:14:04-07:00

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.)

bsteinberg comments on "Mochizuki proof of ABC" (20175)

2012-09-16T05:09:05-07:00

@Alexander, look at http://tea.mathoverflow.net/discussion/1422/discussing-recent-preprints-on-mo-again/#Item_0 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.

Alexander Chervov comments on "Mochizuki proof of ABC" (20174)

2012-09-16T04:39:18-07:00

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.
PS
There were other quests discussing correctness and they were also very popular, indicating that community is pro...

bsteinberg comments on "Mochizuki proof of ABC" (20173)

2012-09-16T04:14:02-07:00

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).

Mariano comments on "Mochizuki proof of ABC" (20172)

2012-09-16T03:36:49-07:00

@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.

llIIllII comments on "Mochizuki proof of ABC" (20171)

2012-09-16T00:42:54-07:00

Propose http://michaelnielsen.org/polymath1/index.php?title=ABC_conjecture as a venue for comments and discussion on abc proof, although it has disadvantage of requiring

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 ?

Alexander Chervov comments on "Mochizuki proof of ABC" (20169)

2012-09-16T00:03:10-07:00

@bsteinberg " I don't think this is appropriate to the site" why ? " which can be held elsewhere" why ?

Will Jagy comments on "Mochizuki proof of ABC" (20168)

2012-09-15T20:56:44-07:00

Yep. It won't let me vote to close.

bsteinberg comments on "Mochizuki proof of ABC" (20167)

2012-09-15T20:38:18-07:00

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.

voloch comments on "Mochizuki proof of ABC" (20151)

2012-09-13T11:18:25-07:00

@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.

Alexander Chervov comments on "Mochizuki proof of ABC" (20149)

2012-09-13T10:40:42-07:00

Am I the only person who sees the similarities between quests ? :)

quid comments on "Mochizuki proof of ABC" (20141)

2012-09-12T05:34:32-07:00

@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 ]

Alexander Chervov comments on "Mochizuki proof of ABC" (20140)

2012-09-12T04:06:26-07:00

Ben Webster's question is nice, is not it...

what-is-the-insight-of-quillens-proof-that-all-projective-modules-over-a-polynom

http://mathoverflow.net/questions/19584/what-is-the-insight-of-quillens-proof-that-all-projective-modules-over-a-polynom

Zebedee Boing Boing comments on "Mochizuki proof of ABC" (20129)

2012-09-10T01:12:17-07:00

I was going to say the same as Asaf.

Asaf Karagila comments on "Mochizuki proof of ABC" (20128)

2012-09-10T01:06:04-07:00

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

Will Jagy comments on "Mochizuki proof of ABC" (20127)

2012-09-09T19:27:46-07:00

It's alright. I don't believe there will be any more activity or voting with respect to that question.

Scott Morrison comments on "Mochizuki proof of ABC" (20126)

2012-09-09T19:14:17-07:00

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.

quid comments on "Mochizuki proof of ABC" (20121)

2012-09-09T03:51:31-07:00

@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.

davidac897 comments on "Mochizuki proof of ABC" (20120)

2012-09-09T00:33:05-07:00

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.

quid comments on "Mochizuki proof of ABC" (20119)

2012-09-08T19:57:42-07:00

@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.

Todd Trimble comments on "Mochizuki proof of ABC" (20118)

2012-09-08T18:28:47-07:00

@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."

and

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

quid comments on "Mochizuki proof of ABC" (20117)

2012-09-08T17:44:33-07:00

@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.

Kevin Ventullo comments on "Mochizuki proof of ABC" (20115)

2012-09-08T14:26:36-07:00

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.

Todd Trimble comments on "Mochizuki proof of ABC" (20114)

2012-09-08T12:16:26-07:00

Yes, thanks to Andy!

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

quid comments on "Mochizuki proof of ABC" (20113)

2012-09-08T12:13:24-07:00

@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.

Todd Trimble comments on "Mochizuki proof of ABC" (20112)

2012-09-08T12:13:08-07:00

@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.

Todd Trimble comments on "Mochizuki proof of ABC" (20111)

2012-09-08T12:01:41-07:00

@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 Yuan comments on "Mochizuki proof of ABC" (20110)

2012-09-08T11:52:06-07:00

@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.

Todd Trimble comments on "Mochizuki proof of ABC" (20109)

2012-09-08T11:31:59-07:00

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 Trimble comments on "Mochizuki proof of ABC" (20108)

2012-09-08T11:29:22-07:00

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.

Andy Putman comments on "Mochizuki proof of ABC" (20107)

2012-09-08T11:25:53-07:00

@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.

bsteinberg comments on "Mochizuki proof of ABC" (20106)

2012-09-08T11:18:55-07:00

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.

Will Jagy comments on "Mochizuki proof of ABC" (20105)

2012-09-08T11:16:40-07:00

Plus, the question no longer uses the word behooves.

HJRW comments on "Mochizuki proof of ABC" (20104)

2012-09-08T11:02:39-07:00

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.

Andy Putman comments on "Mochizuki proof of ABC" (20103)

2012-09-08T11:02:04-07:00

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.

Todd Trimble comments on "Mochizuki proof of ABC" (20102)

2012-09-08T10:53:15-07:00

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

Giuseppe comments on "Mochizuki proof of ABC" (20101)

2012-09-08T10:12:19-07:00

I agree with Andy, Henry and Henry.

HJRW comments on "Mochizuki proof of ABC" (20100)

2012-09-08T09:51:15-07:00

Yes, +1 Andy.

Henry Cohn comments on "Mochizuki proof of ABC" (20099)

2012-09-08T09:42:52-07:00

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

Andy Putman comments on "Mochizuki proof of ABC" (20098)

2012-09-08T09:01:12-07:00

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?"

quid comments on "Mochizuki proof of ABC" (20097)

2012-09-08T08:19:06-07:00

@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.

Footnote:

(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.

Donu Arapura comments on "Mochizuki proof of ABC" (20096)

2012-09-08T07:43:21-07:00

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.

Tom Leinster comments on "Mochizuki proof of ABC" (20095)

2012-09-08T06:14:34-07:00

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.

quid comments on "Mochizuki proof of ABC" (20094)

2012-09-08T04:23:11-07:00

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).

velnias comments on "Mochizuki proof of ABC" (20093)

2012-09-08T01:04:20-07:00

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.

@quid

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.

Andy Putman comments on "Mochizuki proof of ABC" (20092)

2012-09-07T22:03:29-07:00

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.

Marty comments on "Mochizuki proof of ABC" (20091)

2012-09-07T21:43:56-07:00

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!

James Borger comments on "Mochizuki proof of ABC" (20090)

2012-09-07T19:45:48-07:00

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.

quid comments on "Mochizuki proof of ABC" (20089)

2012-09-07T16:59:56-07:00

@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?

James Cranch comments on "Mochizuki proof of ABC" (20088)

2012-09-07T16:17:28-07:00

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.

Will Jagy comments on "Mochizuki proof of ABC" (20087)

2012-09-07T14:21:36-07:00

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.

quid comments on "Mochizuki proof of ABC" (20086)

2012-09-07T13:52:10-07:00

@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.

Giuseppe comments on "Mochizuki proof of ABC" (20084)

2012-09-07T13:11:35-07:00

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.

Will Jagy comments on "Mochizuki proof of ABC" (20083)

2012-09-07T12:13:34-07:00

James, is there some reason you almost never answer questions on MO?

JamesDTaylor comments on "Mochizuki proof of ABC" (20081)

2012-09-07T08:51:19-07:00

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."

Henry Cohn comments on "Mochizuki proof of ABC" (20078)

2012-09-07T06:10:13-07:00

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.

quid comments on "Mochizuki proof of ABC" (20076)

2012-09-07T01:54:32-07:00

@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?

evgeniamerkulova comments on "Mochizuki proof of ABC" (20075)

2012-09-07T01:36:49-07:00

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.

quid comments on "Mochizuki proof of ABC" (20074)

2012-09-07T01:15:00-07:00

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.

@JamesDTaylor:

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:

http://tea.mathoverflow.net/discussion/1109/posting-questions-without-adequate-thought/

Scott Morrison comments on "Mochizuki proof of ABC" (20073)

2012-09-06T21:54:36-07:00

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.

JamesDTaylor comments on "Mochizuki proof of ABC" (20072)

2012-09-06T20:09:14-07:00

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:
http://mathoverflow.net/questions/78696/is-there-an-intuitive-reason-for-zariskis-main-theorem
http://mathoverflow.net/questions/75335/what-is-the-reason-for-modularity-results
http://mathoverflow.net/questions/67595/why-was-it-reasonable-to-ask-what-the-higher-k-groups-are
http://mathoverflow.net/questions/80786/did-grothendieck-have-a-plan-for-proving-riemann-existence-algebraically

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.

quid comments on "Mochizuki proof of ABC" (20071)

2012-09-06T19:38:43-07:00

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.

Will Jagy comments on "Mochizuki proof of ABC" (20070)

2012-09-06T19:23:21-07:00

Recent question

http://mathoverflow.net/questions/106560/what-is-the-underlying-vision-that-mochizuki-pursued-when-trying-to-prove-the-abc

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.

HJRW comments on "Mochizuki proof of ABC" (20067)

2012-09-06T05:08:08-07:00

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

WillieWong comments on "Mochizuki proof of ABC" (20066)

2012-09-06T02:05:03-07:00

@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.

davidac897 comments on "Mochizuki proof of ABC" (20062)

2012-09-05T11:18:37-07:00

Yeah, I agree with stankewicz.

stankewicz comments on "Mochizuki proof of ABC" (20061)

2012-09-05T10:31:59-07:00

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.

voloch comments on "Mochizuki proof of ABC" (20060)

2012-09-05T10:27:43-07:00

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:

http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/#comments

http://sbseminar.wordpress.com/2012/06/12/abc-conjecture-rumor-2/

Dylan Moreland comments on "Mochizuki proof of ABC" (20059)

2012-09-05T10:27:09-07:00

someone’s blog, perhaps?

Try the comments on Jordan Ellenberg's post.

Will Jagy comments on "Mochizuki proof of ABC" (20058)

2012-09-05T10:25:50-07:00

http://sbseminar.wordpress.com/2012/06/12/abc-conjecture-rumor-2/

and

http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html

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.

Ryan Budney comments on "Mochizuki proof of ABC" (20057)

2012-09-05T10:10:04-07:00

Which Mochizuki is being referred to?

WillieWong comments on "Mochizuki proof of ABC" (20056)

2012-09-05T08:54:33-07:00

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.

davidac897 comments on "Mochizuki proof of ABC" (20054)

2012-09-05T08:42:37-07:00

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?