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Example of titular activity: https://math.stackexchange.com/questions/15238/puzzle-a-strange-proof-of-the-green-tao-theorem

I was actually in the process of posting an answer, explaining both the fallacy and its relation to the correct proof, when a moderator shut down the thread as the third close vote (not the fifth and final one).

Generally, given the pre-election discussions I am surprised by how aggressive the thread closures have become.

[edit: linked question was temporarily reopened due to comments here, then closed probably in part due to its advertisement on the meta. Two answers, both upvoted, can be viewed at the original question if you want to examine whether the thread closures are precluding desirable or undesirable material.]

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    $\begingroup$ +1: Moderators should not use binding close votes except for posts that are unarguably of no value. The community should decide on all else. $\endgroup$
    – Bill Dubuque
    Dec 22, 2010 at 22:35
  • $\begingroup$ @Bill: Just for the record, I agree with your statement in principle, but see my campaign statement that you referred to so many times on why I feel justified to cast the third vote to close. In any case, T.'s argument in his comment to Moron convinced me that something can be said about the "proof" independently of the problematic sentences which I based my judgement on. So I made the fourth re-opening vote. $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 22:47
  • $\begingroup$ @Willie: I'm glad to hear that we agree in principle. I mentioned your campaign statement once. How does that count as "so many times"? $\endgroup$
    – Bill Dubuque
    Dec 23, 2010 at 0:08
  • $\begingroup$ @Bill: my apologies. I was reading/responding to the torrent of comments from you, T.., and Moron, between two different threads. The constant switching between browser tabs must have made me dizzy. You are correct to correct me on the count. $\endgroup$
    – Willie Wong
    Dec 23, 2010 at 0:43
  • $\begingroup$ As a general comment, it is helpful to post links to meta threads on the original question. $\endgroup$
    – Akhil Mathew
    Dec 23, 2010 at 3:12

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I am curious about your assessment of aggressiveness. I did state on the record that until more users earn 3000+ rep, I will take 2+ closure votes as an indication that there may be a problem with the post.

To date I've voted twice times (unless I miscounted) to close questions unilaterally.

https://math.stackexchange.com/questions/12888/is-kolmogorov-complexity-recursively-enumerable-for-some-infinite-set-of-strings is based on the OP's own admission that the question is a duplicate of a previously asked question.

https://math.stackexchange.com/questions/14881/there-are-how-many-modes-between-4-number-closed is impossible to tell what actually the question is about.

Two other votes have 2 supporting votes prior to my casting the closure. One is about whether MatLab supports object oriented programming, the other is the one linked above.

All other question closures that I am involved in otherwise have five total votes.

AFAIK Robin hasn't taken any real action yet as moderator, and Qiaochu has only closed one question with something that is not the fifth vote (and his is a fourth vote there).

So forgive me if I am taking this a bit personally. :)

I understand that you have some concern about this one question. And I can see how it is frustrating if you have written up an answer only to not be able to submit it. But I cannot see how there can be controversy on the other three times I acted without having the full five votes. Since I did promise to listen to the community's opinion (and you made a general accusation of aggressiveness), I would also like to know if there are general concern about whether I closed the other three questions (to which this issue applies) too hastily.

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  • $\begingroup$ There was also a question closed (by another moderator) without a vote, then un-closed after some discussion in the comments explaining that it was not an exact duplicate. I read only a small fraction of the material on the site and don't have the 10K tools, so I see only the effect on the material I actually read on main site and meta. I'm not suggesting that we have switched over to a police state, only that things should be kept looser without clear evidence of harm or its imminence. $\endgroup$
    – T..
    Dec 22, 2010 at 22:07
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    $\begingroup$ +1: I agree with your actions so far. $\endgroup$
    – Aryabhata
    Dec 22, 2010 at 22:07
  • $\begingroup$ @Willie: What happened to your campaign promises? (on which I based my vote for you). As I recall you stated that you would let the community close posts and would use your binding vote only for spam etc. While I agree with many of your other activities I think that it is an abuse of power for moderators to use binding votes in this manner. $\endgroup$
    – Bill Dubuque
    Dec 22, 2010 at 22:31
  • $\begingroup$ @T.. I cannot see past voting activity on a question that has been re-opened either. I assume you are talking about the one about iterated $\sin$, since that's the only question recently re-opened. Based on the comment there I'll take you word that Qiaochu closed that question prematurely by himself as duplicate and then reopened it. $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 22:32
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    $\begingroup$ @Bill: just to be clear, is that a general comment, or is that specific? For the cases where 2 votes have already been cast, I consider that, at this time, I have honoured my campaign promise. For the cases where no votes have been cast, the case of the duplicate I consider an exceptional case, since the OP agreed as such, and there should be no controversy in there. For the remaining question, if you think I shouldn't have acted unilaterally, I will refrain from doing so on such questions in the future. $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 22:37
  • $\begingroup$ @Willie: The closing system is already very unpopular here due to asymmetry etc. Please don't exacerbate the problem by abusing binding close votes. Those should be used only for posts that are clearly of no value. For all else the community should decide - not a single individual. $\endgroup$
    – Bill Dubuque
    Dec 22, 2010 at 22:40
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    $\begingroup$ @Bill: let me ask you a specific question. The question I linked to above about "modes of 4 numbers", in your opinion, does it, or does it not, have value? In my opinion, a question so poorly phrased to admit little meaning has no value. But yours may differ. Clearly we agree on the general principle of the thing. But your continued argument suggests to me that we may not be on the same page about the specifics. So help me calibrate my radar, please! $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 22:54
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    $\begingroup$ Willie, yes, it was something about iteration of sin(x). I was hoping not to "implicate" anyone that specifically or get into details, but I saw you in this case and Qiaochu in a few others as being more pro-active than expected based on election discussions. My view is that closings should be performed only in cases of obviously harmful material (spam, illegal, etc), and that generic or technological approaches such as the initiative to improve the tag space are the way to go. Qiaochu has done a great service to the site with the tags and this is a better use of time than closings, IMO. $\endgroup$
    – T..
    Dec 22, 2010 at 22:58
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    $\begingroup$ @T.. My opinion is that all moderator actions are subject to criticism. So I'd much rather you (and others) be specific so I can better gauge the community response. Can I ask for a bit of patience (before completely giving up on us) while we iron out some kinks as new moderators? Your continued feedback is of course appreciated. $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 23:09
  • $\begingroup$ Willie, "criticism" (especially any personal kind) is not really a concept that applies, since the moderators are unpaid volunteers and are obviously making good-faith efforts to improve the site. My main concern with the moderation is its existence, i.e., SE's reliance and emphasis on constant human intervention rather than upgrading the technology. Jeff Atwood said SE actually wants to increase the moderation (or policing, as he calls it). Instead of better users in control, or community policing with better control over the users, I prefer more tools to let users control what they read. $\endgroup$
    – T..
    Dec 22, 2010 at 23:26
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    $\begingroup$ @T.. point taken. Unfortunately we are stuck with what we have. Thanks for your input. $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 23:28
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    $\begingroup$ One other comment on the "criticism" subject. I assume it is understood by everyone in all these discussions, (but doesn't hurt to repeat), that moderators are beyond reproach and deserve only thanks for their time, insofar as they are just trying to improve the site, and as long as they don't undertake gratuitous negative actions such as antagonizing particular users. But there are many differences of opinion as to what is useful or strategic for the site, and these will be strongly argued on the meta, until the technology makes them irrelevant. $\endgroup$
    – T..
    Dec 22, 2010 at 23:46
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I agree with Willie Wong's action. "Harmless" is in the eye of the beholder, but this is a question about an "argument" which is not mathematical in nature and strains my credulity at being in good faith. As Moron has pointed out, someone with the same name has been active on the internet giving "proofs" of deep theorems and open problems using similar "arguments". If this person has not yet learned the fallacies inherent in such "arguments", I am not optimistic that anything we could say on math.SE will be helpful or constructive.

In fact I have myself voted to close the question.

To those that seem to think that we've agreed that the system of voting to close/reopen questions is inherently flawed: was there a referendum on this issue that I missed? I for one certainly don't feel this way. Moreover, this mechanism has been an integral part of the SE platform from the beginning. You might as well campaign against the reputation system.

We can certainly (if not necessarily usefully!) debate where the line should be drawn, but in principle participation in any community implies some degree of acceptance of and obedience to its basic structures and norms. Socrates felt that he had participated in Athenian society too much and for too long to slip away quietly into the night when things got bad. But it would be relatively easy for someone to start up a new math Q&A site with a very different policy on closing questions. It actually sounds like a good idea to me -- competition is healthy, and variety is...well, you get the idea.

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    $\begingroup$ +1: Without knowing any of the alleged history of the user, the failure to take into account the thoughtful answers he had received suffice to strain my credulity. $\endgroup$
    – Jonas Meyer
    Dec 23, 2010 at 2:43
  • $\begingroup$ re: "was there a referendum I missed" -- well, the following meta thread stands at +11 and no downvotes: meta.math.stackexchange.com/questions/871/… . The analogous discussions on meta.SO also were, judging from votes and comments, strongly against the one-sided vote to close process. For this posting the vote did not reach five before closure, and of the three voters one changed his mind later. Some of the commenters here would have voted to open had that been possible initially. $\endgroup$
    – T..
    Dec 23, 2010 at 4:16
  • $\begingroup$ @T: the meta thread you link to proposes a change in the closure process, not that we should ignore or do away with it entirely. In other words, what you suggested in the thread is in order. But of course it is not a referendum. As I mentioned in my answer above, every user who participates in a site and does not complain about the site mechanics is at least tacitly supporting them. $\endgroup$
    – Pete L. Clark
    Dec 23, 2010 at 5:03
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    $\begingroup$ Pete, it seems clear from the multiple opinion samples represented by the various meta and meta.SO discussions that a symmetrical vote-to-close procedure would defeat the asymmetrical one in a referendum. (It was also ranked #6 out of 150 suggestions on UserVoice, the precursor of meta.SO). As you say, this is a separate matter from chucking the concept of closure entirely, but the question and title of this thread refer not to a hypothetical new system, but "pro-active" short circuiting of the status quo, i.e., moderators casting a close vote after fewer than four users have done so. $\endgroup$
    – T..
    Dec 23, 2010 at 5:43
  • $\begingroup$ @T..:Okay, I think I agree with all of that. $\endgroup$
    – Pete L. Clark
    Dec 23, 2010 at 12:48
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I don't have a strong opinion on Willie's particular action, since as he observes there were already two votes to close on the original question, but I am fond of a quote of Andrew Stacey:

A good answer does not a good question make.

The original question was not mathematics; the key offending quotation was

Notice that we have determined that a-(k-1)b is not prime without having any information about the factors of a-(k-1)b. This is impossible. (Note that even though it is possible to determine whether or not an integer is prime without factoring the integer, it is still impossible to determine whether or not an integer is prime without having any information about the factors of the integer, since the factors of an integer are what determine whether an integer is prime or not.)

As stated, I don't see any evidence that the OP is acting in bad faith, simply that his question is mathematically meaningless. The fact that T.. was able to post an interesting and useful answer on the Green-Tao theorem does not change the fact that bad questions should be discouraged. It would be undesirable to have a website littered with bad questions having good answers.

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    $\begingroup$ What's wrong with downvotes and tags (e.g., [fake-proofs] should have been applied here, and still can be added)? Some people may find it interesting to distill the valid and invalid material from vague arguments and others may want to read the results. Restricting discussion to some nebulous standard of "meaningful" questions is a major change of site purpose and should be articulated (and debated) in advance. The main content here is the answers, so "good" is whatever the respondents make of things. They can't do this if silenced. $\endgroup$
    – T..
    Dec 23, 2010 at 4:06
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    $\begingroup$ @T..: I think that, in general, the point of closing anything is that simply downvoting is not a strong enough disincentive for people to ask such questions. Answers to poorly formulated questions may be of interest to others, but likely not to the OP. $\endgroup$
    – Akhil Mathew
    Dec 23, 2010 at 6:38
  • $\begingroup$ If you look at arxiv.org, a percent or so of the papers (maybe higher) are "general mathematics", i.e., crackpot articles, and that in a fairly restricted, moderated, research-oriented medium that seeks to exclude meaningless non-mathematics. I think that seeking stricter exclusion than that of odd questions from a general Q&A site would be self-defeating.The OP is one reader out of hundreds. The question can be viewed long after the OP has lost interest or quit the site. The site is more than a personal answer oracle for OP's, though it can play that role in many cases. $\endgroup$
    – T..
    Dec 23, 2010 at 14:45
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    $\begingroup$ @T.. The difference between arxiv.org and SE is that the former is hardly moderated at all, while the latter is explicitly moderated by the community. The endorsement requirement on arxiv is a very mild form of moderation. It is not the case that GM was created for crackpots. Some articles in that category contain perfectly valid mathematics. It just so happens that that's the only category crackpots ever publish in. SE explicitly relies on giving users the power to close qns and the qn we are talking about has now been closed without any moderator intervention. Site design encourages this. $\endgroup$
    – Alex B.
    Dec 23, 2010 at 15:01
  • $\begingroup$ @Alex, it would be of some cultural interest to identify valid mathematical articles that belong (only) to the math.GM category on arxiv, as this category carries a de facto stigma of classification as junk, and most capable authors would avoid submitting their material to that category except as a gesture of humility. The endorsement system is relatively recent, by the way. Arxiv and its LANL version go back almost 20 years and the General Mathematics category was formed primarily to avoid detailed accept/reject decisions on crackpot material. In SE terms it is "tagging" not "closing". $\endgroup$
    – T..
    Dec 23, 2010 at 15:42
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There are two things to consider here, assuming the question is in the gray area of "mildly" off topic.

  1. Is the presence of this question a "broken window"? In other words, does it send the wrong message to readers about the site and the type of content we want on it? Also relevant is, how often do you get questions like this -- if you're drowning in them, or if they are rare.

  2. Is the question itself of high quality? Is it written clearly, is it interesting, does it make sense? Is the user who asked the question the type of user who will potentially be an interesting contributor to the site? Sure, maybe their first question was mildly off topic but if they look like a potential asset to the community, perhaps next time they'll be on topic and quality.

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While I agree with you, I think you have chosen a very bad example.

Normally, one would give OP the benefit of doubt, but in this case I agree with the quick closure.

The OP has a history (check sci.math, comp.theory) of claiming proofs for popular open problems like these and seems unwilling to listen to reasonable arguments as to why his so called proofs are "not mathematics".

Based on the kind of fallacious reasoning that appeared, I am guessing it is the same OP.

Besides, in this case, I really don't see how an explanation of the flaws is really useful to the rest of the mathematical population.

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  • $\begingroup$ He presented it as a flawed proof: "where is the flaw". There was no overt grandiose claim of a new proof. I have seen postings of his where he does not contest corrections. Tagging it with [false-proofs] or whatever would solve any problem you just mentioned, would it not? $\endgroup$
    – T..
    Dec 22, 2010 at 21:52
  • $\begingroup$ @T..: Space is finite. We just can't keep tagging stuff and be done with. We got to do some cleanup sometime and the best time for that is when it is fresh. Having non-mathematical stuff lying around will only cause issues like higher noise in search results etc. IMO, we should try to discourage crank questions like these. These are a big waste of everyone's time, IMO, possible great answers notwithstanding (especially if we know OP has such a history). $\endgroup$
    – Aryabhata
    Dec 22, 2010 at 22:00
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    $\begingroup$ I claim that what he presented in the current form is not a proof, flawed or not. If the crux of the argument is based on some hand-waving, undefined concept, I don't see how it can be wrong. Arguments based on something undefined can neither be true nor false. $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 22:04
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    $\begingroup$ If the site is not, in principle, for any math question but only those above some subjective (and arbitrary) quality standard, that is a change of mission that should be articulated. What is the point of developing the ratings and tags if the bottom line is clearing out the riff-raff by brute force? $\endgroup$
    – T..
    Dec 22, 2010 at 22:09
  • $\begingroup$ @Willie: it is possible to answer his question (as I would have posted) in a way independent of the details of the handwaving. e.g., the same argument contradicts the fact that any k-term progression can be predicted to contain a term divisible by k. $\endgroup$
    – T..
    Dec 22, 2010 at 22:11
  • $\begingroup$ @T..: You yourself said it. Math question. $\endgroup$
    – Aryabhata
    Dec 22, 2010 at 22:12
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    $\begingroup$ It was obviously a math question. If you want to throw out everything ill-defined, well, the list would be pretty large, and it's a massive change of purpose for the site. Questioners by their nature are not experts, and yes, some have unconventional views about what mathematics is or how it "should" work. It comes with the territory of an internet site. $\endgroup$
    – T..
    Dec 22, 2010 at 22:24
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    $\begingroup$ @T..: Just because some of the terms are mathematical, it does not imply it is a math question. For me, it obviously wasn't and other people seemed to agree too. If OP was willing to listen, I suppose the close votes would not have been cast. btw, if the question is reopened and you post your answer, I am guessing OP will claim that you have found a big hole in mathematics. FWIW, If the question gets reopened, I will not vote to close. This site has great features to prevent junk prevalent in internet sites. I suggest we use them. $\endgroup$
    – Aryabhata
    Dec 22, 2010 at 22:27
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    $\begingroup$ He asked why a specific hard theorem can't be proved by a simple argument -- or, if you don't think it rises to the level of an argument, why the truth of the theorem is not supported by a (vague) heuristic. If you think postings here have to meet a higher standard than that, what else was needed to cross the threshold of being a math question? $\endgroup$
    – T..
    Dec 22, 2010 at 22:46
  • $\begingroup$ @T.. Evidently you see an argument around the problematic sentences that I didn't. In this case I agree with the re-opening. $\endgroup$
    – Willie Wong
    Dec 22, 2010 at 22:50
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    $\begingroup$ @T..: It was an argument, but it was not mathematical. It was en.wikipedia.org/wiki/Not_even_wrong. Anyway, the question has been reopened. I will stop this discussion. $\endgroup$
    – Aryabhata
    Dec 22, 2010 at 22:57

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