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Like many people with an interest in mathematics right now, I want to get a deeper understanding where Atiyah's proof of Riemann Hypothesis might fall down. I searched and found no such question here so I asked.

Coming from a Fields medal winner this claimed proof cannot be assumed to sit in the same category as the many cranky proofs.

MathOverflow has a policy to not permit discussion of conjectured proofs of open problems, and that policy was quoted as a closure reason. There were both close and reopen votes and there was some debate in the comments defending the question's validity on the grounds:

  • MSE is fundamentally a place people come to get mathematics questions answered, and
  • this is actually a hot mathematics question right now which a lot of people want answers to,
  • unlike MO, MSE has no such policy, and
  • what really is gained by preventing people from coming here to get their questions answered?
  • If the question is closed and deleted, others wanting to learn will simply come and ask the same.

A moderator who voted to re-close the question then deleted the counterargument to the close votes but left in place the pro-close arguments, claiming that the comments are not the place to discuss whether closure is valid. I think the comments are precisely the right place to place a counterargument the question's closure - where others who might cast a vote can consider them. This left a really sour taste in my mouth and I felt it was undemocratic. Is it just me?

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    $\begingroup$ I would be in favor of closing questions like that with a link to this post on MathOverflow which explains why the question would be closed there. I have always thought that we had the same policy as MO to avoid posts about preprints that claim to prove famous conjectures. The fact that a question is "hot" that "many people want answers to" is not really an argument in favor of including the question. $\endgroup$ – Carl Mummert Sep 28 '18 at 12:27
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    $\begingroup$ At the same time, although some frustration about the seeming silence about the proof is understandable, sources such as this make it more clear what is going on. $\endgroup$ – Carl Mummert Sep 28 '18 at 12:28
  • $\begingroup$ @CarlMummert On the other hand, that article has the most "authoritative" part of it be a quote from an economist who has "studied" the Riemann hypothesis. While I largely agree with the statement made by that person, neither he nor I are really experts in this area. $\endgroup$ – Tobias Kildetoft Sep 28 '18 at 12:35
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    $\begingroup$ @Tobias Kildetoft: they did interview John Baez, as well. $\endgroup$ – Carl Mummert Sep 28 '18 at 12:36
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    $\begingroup$ @CarlMummert Ahh, good point. I had missed that part. $\endgroup$ – Tobias Kildetoft Sep 28 '18 at 12:37
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    $\begingroup$ I think the aspect that is frustrating for some people is that they want to see a bunch of experts talk about the proof, while the actual situation seems to be that few experts want to say anything about it, which leaves a kind of vacuum. I have no inside information but a little searching made the situation seem clear enough. $\endgroup$ – Carl Mummert Sep 28 '18 at 12:39
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    $\begingroup$ It's not that mse has, or should have, the same policies as mo; it's that the reasons for drastically limiting the discussion on mo also apply here. Those reasons have been explained on mo, and I urge anyone who wants to know why discussion should be restricted here to search out the discussions there. $\endgroup$ – Gerry Myerson Sep 28 '18 at 13:02
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    $\begingroup$ As for democracy, democratic societies elect leaders for a reason. $\endgroup$ – Gerry Myerson Sep 28 '18 at 13:03
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    $\begingroup$ Why is this off-topic? It's a question about moderation policy. Once again, a close vote is not a super-disagree vote. $\endgroup$ – user296602 Sep 28 '18 at 18:00
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    $\begingroup$ @T.Bongers I don't close vote on meta in lieu of a "super-disagree vote". Please don't harass dedicated users on this site, both on main and on meta, who find good reason to close a post as off topic, not because they "super-disagree" with it, but for one of many other good reasons. Usually I appreciate your input; but here I think you're under the influence of the asker's "conspiracy theory" shenanigans. $\endgroup$ – Namaste Sep 28 '18 at 18:39
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    $\begingroup$ @T.Bongers: Note that one of the question types explicitly called out as off topic is your question is just a rant in disguise: “______ sucks, am I right?” The post itself is somewhat all over the place; briefly touching a number of different issues, throwing out accusations, and an entirely different question appearing in the title. I did not vote to close/delete, but I can very certainly understand them. $\endgroup$ – Hurkyl Sep 29 '18 at 16:29
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    $\begingroup$ ... It would be better, I think, if the OP would pick a specific topic to talk about, and make a post on that topic without digressing into everything else and without making it a place to vent ill-feelings. $\endgroup$ – Hurkyl Sep 29 '18 at 16:30
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    $\begingroup$ @amWhy I don't agree with the asker's premise either, and downvoted the post. But I don't see any reason to remove this from meta. I also appreciate a lot of your input and it's unfortunate that you view my comment as "harass[ment of] dedicated users," which mentioned no particular user and pinged no one. Perhaps that's more telling of your actions than mine. $\endgroup$ – user296602 Sep 29 '18 at 21:06
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    $\begingroup$ I have voted undelete on this question not because I think there is any issue with the moderator(s) actions, but because I think the broader issue of "why don't we host questions on this proof of the Riemann Hypothesis" should have a question on meta, and because the discussion was headed back to the main question now that this one was deleted. $\endgroup$ – Carl Mummert Sep 30 '18 at 2:05
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    $\begingroup$ @CarlMummert: Maybe a better way to put that previous comment is that, if discussion on the policy question were to happen here in this post, you exclude everyone unwilling to hijack a meta thread from participating in that discussion, and you exclude everyone who doesn't follow highly downvoted complaints of moderator abuse from even being aware of discussion. $\endgroup$ – Hurkyl Oct 1 '18 at 23:48
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Yes, moderators should remove meta-comments from the main site. The suitability of a question for the site should be discussed on meta.

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  • $\begingroup$ I agree meta comments in general should eventually be removed, but in the first few minutes while close and reopen votes are being cast, is it really that urgent a matter that a moderator should vote and remove one side of the argument from the comments? $\endgroup$ – samerivertwice Sep 28 '18 at 12:53
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    $\begingroup$ @RobertFrost: You keep saying "remove one side", as if there is another side of discussion appearing in comments that is allowed to stand. $\endgroup$ – Hurkyl Sep 28 '18 at 13:04
  • $\begingroup$ @Hurkyl pretty sure that was removed later after I raised the one-sidedness as an issue but I cannot confirm that now. $\endgroup$ – samerivertwice Sep 28 '18 at 13:06
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    $\begingroup$ @Robert: I can post the deleted comments here if you want, including deletion times. There was no one-sidedness. I only left the comments of Prezmo as it was pertaining to your question, and of Arnuad which pointed towards previous meta discussions (so when someone does come to meta to discuss meta issues, there is a reference to the past discussions for them to use). Let me also say that part of my decision to delete the comments was because several of them generated flags as unfriendly and unkind. $\endgroup$ – Asaf Karagila Sep 28 '18 at 13:14
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    $\begingroup$ @AsafKaragila several of them generating flags sounds implausible. My one unkind comment (thoroughly deserved) came only after you deleted my comments as a point-scoring exercise and accompanied by a sarcastic comment which was mildly funny to be fair. $\endgroup$ – samerivertwice Sep 28 '18 at 14:33
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    $\begingroup$ @Robert: You seem to be calling me a liar in a way that, how did you put it? "basically the same effect, with the added strength of giving you deniability." $\endgroup$ – Asaf Karagila Sep 28 '18 at 14:35
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    $\begingroup$ @AsafKaragila except in this case my motivation is that I can't see any of the history in order to check the facts while you hold all the aces by virtue of being a moderator and I feel like my status is being manipulated downwards by a person in a position of power and I've never had a problem before with how any other mod has wielded the diamond. $\endgroup$ – samerivertwice Sep 28 '18 at 14:36
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    $\begingroup$ @Robert: What motivation I have for this, really? I could have deleted your question, I could have suspended you after that comment of yours, and every time I am giving you seemingly undeserved leeway. $\endgroup$ – Asaf Karagila Sep 28 '18 at 14:43
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    $\begingroup$ @AsafKaragila at first I thought, you know what, kudos to Asaf not giving me a penalty for my unkind comment but in the back of my mind there was feeling... or on the other hand maybe that's just been put in the kit bag to hold over me for later. And now here we are, sure enough it's come out with the threat of revealing my comment. Really, it was wrong of you to grant me undeserved leeway and now hold it against me, you should have given the penalty and let that be the end of it. Some people enjoy the feeling of being in a position of power over others & this is exactly what's going on here. $\endgroup$ – samerivertwice Sep 28 '18 at 14:45
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    $\begingroup$ @Robert: So first you call me names, then you call me a liar. What would be next? Call me a ruthless incompetent dictator? If you're escalating, why are you surprised that at some point I might have enough? Seriously. Stop for a minute. Step back. Think it through. Yelling "HELP HELP I'M BEING REPRESSED" helps nobody... $\endgroup$ – Asaf Karagila Sep 28 '18 at 14:47
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    $\begingroup$ @Robert: Oh, wait. You already called me a dictator by claiming that I only deleted the comments that supported your question being reopened. How silly of me to forget. It's right there, on the top part of my screen... $\endgroup$ – Asaf Karagila Sep 28 '18 at 14:49
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    $\begingroup$ "several of them generating flags sounds implausible." @Robert, I think you owe Asaf an apology. $\endgroup$ – Gerry Myerson Sep 29 '18 at 7:44
  • $\begingroup$ @GerryMyerson why's that? $\endgroup$ – samerivertwice Sep 29 '18 at 12:40
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    $\begingroup$ I didn't think I'd need to spell it out for you, Robert, but here goes. Asaf wrote, "Let me also say that part of my decision to delete the comments was because several of them generated flags as unfriendly and unkind." When you write, "several of them generating flags sounds implausible," you are suggesting Asaf is a liar, and that's way over the line. Please, Robert, if your reputation here means anything to you, apologize. $\endgroup$ – Gerry Myerson Sep 29 '18 at 13:05
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    $\begingroup$ @GerryMyerson I'm at the disadvantage of no longer being able to see the comment thread and this leaves me to rely upon my (pretty unreliable) memory. I have no problem putting my hands up and saying "you know what, I shouldn't have called you that name" but I genuinely have no recollection of saying anything other than one comment which would have generated any flag. Since you think it a matter of integrity and reputation I think the only course of action is to take up Asaf's offer fo reinstating the comments and times and I will be more than willing to apologise accordingly. $\endgroup$ – samerivertwice Sep 29 '18 at 17:48
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Your question should have been closed; there is something like a policy:

Proof Verification of Open Problems

The point is questions like this fall into at least one of two categories:

  • The questions is too broad.
  • The paper is not worth the consideration.

You can pick which one you prefer to assume in this case.

On the removal of comments, just to repeat another answer, meta comments do not belong on the main site.

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  • $\begingroup$ I like this answer because it's more or less the comment left on the question which led to the two or three comments, which initially led to the question being retained / reopened (I can't see the history, nor can I see the comments but I guess we just have to repeat the process here). My response was something like... $\endgroup$ – samerivertwice Sep 30 '18 at 14:42
  • $\begingroup$ ...most proofs of famous conjectures are wrong, even those by leading mathematicians. Andrew Wiles' first proof of Fermat's last theorem is a prime example. While MO has an explicit and strict policy to disallow these, MSE's policy to close questions about such proofs has been established entirely in the context of discussing proofs which did not come from a Field's medal winner. Given that this claimed proof originates where it does, it's a MATHS QUESTION and probably the most compelling one around right now.... $\endgroup$ – samerivertwice Sep 30 '18 at 14:48
  • $\begingroup$ ...and given that this site is fundamentally and above all other things, a place where people come to get maths questions answered, this should be a place where people can come to get this question answered. Now I wasn't at the time of asking aware of various related sensitivities, but as it happens in my opinion for everybody to treat these as the emperor's new clothes and look at each other shiftily and say nothing, is actually insensistive, and it's misguided. I strongly believe the most respectful treatment of the proof is to discuss its mathematical merit openly. $\endgroup$ – samerivertwice Sep 30 '18 at 14:52
  • $\begingroup$ Incidentally, it seems to me that your linked meta question holds up the "this question is permitted" argument more than it does the "question should be closed". The linked meta question suggests short proofs which can be quickly assessed will result in answers which are meritous for the site. Sir Michael Atiyah's proof is actually very compact because it stays at quite a high level. There is next to no effort required for a MSE user, having considered the clained proof to digest the question, and the answer will actually be quite revealing for most users. $\endgroup$ – samerivertwice Sep 30 '18 at 14:59
  • $\begingroup$ The answer, I believe, is that the merit of the proof will depend upon whether the Todd function is well-defined. From what I can discern, it appears that if it is a complex analytic function then one can quickly deduce the function cannot have the properties claimed, and the proof quickly reduces to the Todd function being zero everywhere. But there is perhaps doubt as to whether the function is indeed complex analytic. There is also further doubt as to whether it is fundamentally ill-defined as related work yields a fine structure constant which differs from the known value. $\endgroup$ – samerivertwice Sep 30 '18 at 15:03
  • $\begingroup$ An accurate assessment is beyond me but I have no doubt it would be of interest to users, and I am also resolute that it would be the most respectful thing to Sir Atiyah for the site to afford him the dignity of hosting it. For me there's absolutely no shame in reaching for the stars, soaring higher than most of us ever dream, and falling flat on ones face every now and then. $\endgroup$ – samerivertwice Sep 30 '18 at 15:04
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    $\begingroup$ I think you misunderstand the situation. To me it was a virtual certainty once I heard the news that it's wrong and likely so in a non relevant way. You say " it's a MATHS QUESTION and probably the most compelling one around right now and probably the most compelling one around right now" Not at all. It's pretty much irrelevant. Move on. $\endgroup$ – quid Sep 30 '18 at 15:25
  • $\begingroup$ I expected a comment like this (that doesn't mean I'm critical of it). Yours is an expert's position and I wouldn't dispute it on a site frequented by experts. Some are heard muttering "not even wrong" but the reality for many of us (the non-experts), which I think you fail to appreciate is that even if fundamentally flawed, the conjectured proof almost certainly contains insightful fragments of genius which we'd like to understand better. Perhaps it is hard work to give an exposition of them. It would indeed be sad if there were none. $\endgroup$ – samerivertwice Sep 30 '18 at 15:36
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    $\begingroup$ @RobertFrost It's in a way pretty funny how you bring up the emperor's new cloth etc for others and then are all keen on this paper. Why exactly? Did you already read a book on analytic number theory? If not, then maybe do that. There are great ideas in there that actually work. If yes, then maybe read a more advanced one. If you did that too. Then there are many interesting papers out there to study that are actually correct and relevant. Or maybe read one of those papers of Atiyah for which he got the Fields medal. $\endgroup$ – quid Sep 30 '18 at 15:43
  • $\begingroup$ Why do I take interest in this paper? Because a man who raised the ceiling of human understanding before claimed to have done so again and that idea sparked something in my imagination. Did I read a book on analytic number theory? No, I never even knew what it was until I Googled it after your comment and would never have had a reason to do so before. Maybe it would be better if mathematicians of my level stuck to reading about it in the newspaper. $\endgroup$ – samerivertwice Sep 30 '18 at 16:19
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As you've come to Meta to argue the merits of asking a Question on the main site, let's leave aside the issue of whether similar argument through Comments on the Question should be removed, though I hope in the future you will appreciate the virtue of having a polite discussion here as opposed to a heated discussion there. Entertain instead a discussion about for this particular Question.

Yes, I too am curious about what substance there is to Atiyah's proposed approach to proving the Riemann Hypothesis. It would be great if there were a source I could turn to for a more incisive presentation than what I've seen in the media (see Phys.org, New Scientist, and Gizmodo, among others that present some amount of skeptical assessment).

But the mission of Math.SE is limited as to the size of a reply that can be conjured and the scope of material that can be given a fairly dispositive Answer. We should presumably await at least a preprint of the proposed proof. When Atiyah posted a different unsolved problem claim to arXiv.org in 2016, it became possible for various MathOverflow threads to provide analysis.

Connecting the Riemann Hypothesis to the determination of the fine-structure constant of theoretical physics sounds to me like a topic that few experts will be able to evaluate in the early days of such a preprint, so I'm resigned to being patient. All the more reason to avoid accusations of bad motives in the meantime.

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  • $\begingroup$ Some hints as to the problems exist - I saw a claim that a theorem he relies upon to define the fine structure constant, when evaluated computationally yields a totally different number to the constant. Then there are a few very technical comments in a MO post hinting at a) the composite Todd function is not well-defined, and b) it is just a constant function. Then there seem to be other suggestions (as per John Baez's comment) that really to join the dots there is a vast amount of detail and work missing... $\endgroup$ – samerivertwice Sep 28 '18 at 15:40
  • $\begingroup$ ...So on the face of it, people seem to be jumping pretty quickly to the conclusion that it's quite a naive attempt, albeit subject to seeing the full detail. But I don't see any issue with people coming out and stating that as a tentative initial assessment on here as an answer to a question. $\endgroup$ – samerivertwice Sep 28 '18 at 15:40
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    $\begingroup$ I don't think "naive" is the right word. People often make very subtle mistakes in mathematics, ones that require sophistication. I think Math.SE eschews providing mere conjecture about "a vast amount of detail and work missing", though that may turn out in perspective to be true of Atiyah's remarks. $\endgroup$ – hardmath Sep 28 '18 at 15:48
  • $\begingroup$ When I suggest naive I refer to mathoverflow.net/questions/311280/… and mathoverflow.net/questions/311280/… and mathoverflow.net/questions/311280/… so only naive in a relative sense $\endgroup$ – samerivertwice Sep 28 '18 at 15:52
  • $\begingroup$ I edited your title to be more focused on the allowed-questions issue and to remove in part the tone of accusation. I think further editing on your part of the body of the Question might result in reopening the Question on that basis, if it interests you. $\endgroup$ – hardmath Sep 29 '18 at 2:48
  • $\begingroup$ I was never asking about whether the question was on topic. There were maybe 7 upvotes and 5 downvotes on the original question, and as many reopen votes as close votes. A closer had kindly given their reasons and I gave my counterargument, which I still believe to be a legitimate use of the comments. The question was probably destined to stay and be answered. Then a diamond mod came along, deleted my counterargument and decided the matter. This meta question asks whether it's legitimate use of the diamond to decide a matter against the democratic will of the users. $\endgroup$ – samerivertwice Sep 29 '18 at 3:00
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    $\begingroup$ Okay, rolled back. You are the expert on what you want to ask here. Accusing the moderators of abusing you is not the way I'd approach this. Voting is not indicative of whether an off-topic Question is "destined to stay and be answered." $\endgroup$ – hardmath Sep 29 '18 at 3:04

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