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I've noticed a couple of users, some more active than others, that repeatedly post questions that either claim a proof or a viable approach to a proof of some famous conjecture, such as the twin prime conjecture, Goldbach's conjecture, Collatz conjecture, Riemann's hypothesis and so on, or sometimes Fermat's last theorem (for which they usually claim a one-page proof outline).

Technically, their questions are not directly against any rules of Math SE. Often they have junk in them, enough to justify closure (unclear or lacking context), but they still take up people's time in reading, which is clearly a pure waste of contributors' effort since they are not actually interested in learning real mathematics.

What is the best way of getting them to stop this behaviour? I have heard that users with too many downvoted questions will be banned (temporarily?) from asking new questions, but it hardly seems to have any apparent effect.

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    $\begingroup$ Another possible close reason is "too broad." Also see meta.math.stackexchange.com/questions/19652/… $\endgroup$ – quid Jan 28 '17 at 16:01
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    $\begingroup$ @quid: I see... Though I was referring to posts by users that clearly didn't want to bother to learn mathematics. I welcome posts by those who post a serious question asking where they had gone wrong and learning from it (even if it is about an open problem). Unfortunately, I don't wish to name specific examples given the poor reception of me doing so on Meta... =) $\endgroup$ – user21820 Jan 28 '17 at 16:06
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    $\begingroup$ As often as I scan for questions and also during my nearly daily reaching of my limit of 20 first posts, I do not see these issues that often at all. I think they are annoying when they occur, but often they require a moment of thought to refute, and that is good exercise. Plus, it helps people appreciate how tough these problems really are. If we are truly a site for everybody, that means even people who naively think they've solved the Collatz conjecture, I fear. $\endgroup$ – The Count Jan 29 '17 at 1:04
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    $\begingroup$ @TheCount: As I said already in my post and comments, I welcome true inquiry, even about attempts to solve the Collatz conjecture. What I do not welcome are repeated refusals to learn the mathematics before asking yet more nonsensical questions. I hope you don't need explicit examples to see what I mean. $\endgroup$ – user21820 Jan 29 '17 at 5:11
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    $\begingroup$ @user21820 Not to start a problem, but if you reread your response I think you will find it to be brusk and dismissive. True inquiry is any inquiry at first, and I don't know how many repeated questions from the same user actually occur on these issues. And I don't know why you don't just ignore them and move on. $\endgroup$ – The Count Jan 29 '17 at 15:16
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    $\begingroup$ @TheCount: I can just ignore them, but I don't like the fact that they are wasting everyone's time, not just mine. I am dismissive of bad questions. We are not a site for everybody, even as the how-to-ask FAQ and the consensus on Meta makes clear. What is less clear is where we should draw the line. In this question I'm only talking about egregious cases. I believe that simply closing both eyes to such issues is precisely what is making Math SE a less and less conducive place for mathematical inquiry and exchange. $\endgroup$ – user21820 Jan 29 '17 at 15:33
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    $\begingroup$ @user21820 Well you certainly have more experience here than me, but I would swear I see complaints about new users way more often than I see new users actually causing problems, and I guess I just don't understand why such questions can't be flagged and forgotten on our end. $\endgroup$ – The Count Jan 29 '17 at 16:52
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    $\begingroup$ I love the kinds of questions this post is referring to. I happen to think they aren't a good fit for M.SE, but if anyone could email or chat ping me a link to any that get posted it would make me very happy. $\endgroup$ – Antonio Vargas Jan 30 '17 at 1:01
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    $\begingroup$ @TheCount: Indeed new users rarely cause lasting trouble. I'm mainly referring to long-time users who answer a significant number of basic calculus questions and then think they are so clever and refuse to listen to experts who encourage them to learn the fundamentals of whatever topic they are interested in first. A significant proportion of them will even refuse to admit explicit mathematical mistakes despite multiple people pointing them out (see my previous Meta post). That makes the issue difficult to solve. I flag for closure then deletion, but they repeatedly ask similar questions... $\endgroup$ – user21820 Jan 30 '17 at 5:58
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    $\begingroup$ @user21820 I identify myself as the object of this question. When I first used this site I couldn't even write in Latex. In 2 years research into the Collatz conjecture I've learnt vast amounts about logic, set theory, ordering theory, modular arithmetic, a vast array of theorems and lemmas, equivalence classes, supernatural numbers, p-adics, metric spaces. So your question depends fundamentally on the false premise that such people have no interest in learning mathematics. For that reason I have downvoted it. $\endgroup$ – samerivertwice Jan 30 '17 at 13:28
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    $\begingroup$ @user21820 The next thing I would humbly point out is that for some, the Internet is the only place to learn maths and the very generous help of users of this site is a precious commodity which they would not knowingly abuse. $\endgroup$ – samerivertwice Jan 30 '17 at 13:29
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    $\begingroup$ @RobertFrost: You're incriminating yourself by identifying yourself with this Meta question, since it is about users who do not want to listen to people who advise them what they should learn. If you want to learn, then the question does not apply to you, so why on earth do you think it does? $\endgroup$ – user21820 Jan 30 '17 at 13:32
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    $\begingroup$ @user21820 in that case I think the question should take more care to discriminate between people who don't want to learn on one had, and on the other hand people who are in your eyes a little over-optimistic in the problems they attempt to solve. $\endgroup$ – samerivertwice Jan 30 '17 at 13:36
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    $\begingroup$ No I have re-read my question and found nothing that is problematic. Over-optimistic or not has nothing to do with it. It is about people who claim to have a proof or sketch of proof of a famous conjecture in some poor question (namely full of claimed falsehoods or that the community easily classifies as "unclear"). Nothing less, nothing more. $\endgroup$ – user21820 Jan 30 '17 at 13:39
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    $\begingroup$ @RobertFrost: I'm fully aware that some of your questions are concerning interesting things that are rarely asked. That's precisely why I answered them. However it's not clear to me how helpful you found them, since I don't recall you accepting most of them. $\endgroup$ – user21820 Jan 30 '17 at 13:40
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It is difficult to find a really satisfiable course.

The trouble already starts with the question : When is a downvote or a close vote the right reaction, when not?

I understand that homework-questions where the OP shows absolutely no effort and additionally more or less demands an answer, are not welcome here.

The problem is that many users seem to post an answer nevertheless more or less automatically because they want to increase their reputation. And it often works!

High reputations lead to strong privileges. It is debatable whether all this privileges are useful for the site.

Now, the next problem. The site expects to show some effort or to give a source. The askers who present a try of a proof of a famous conjecture might be convinced that they solved it!

If I understand the rules of this site correctly, the behaviour is not against those rules.

Another thing is, that it might appear annoying that people actually think they have solved a very difficult problem , although the probability that they actually did is very small.

You can argue that such questions are not in the scope of this site, that it is too difficult to find a refutation, for example. But this is not always easy to justify. Maybe, the OP had an interesting idea, which at last fails.

What is much more annoying for me is that questions like "Is 1 a prime number?", which could be answered by a simple remark and nothing more, receive many answers. Moreover, the question and the many answers usually receive tons of upvotes.

Additionally, very short answers , sometimes containing only a very small hint, are often upvoted massively which is unfair, in my opinion, against answers which caused the answerer much effort and a long time to solve.

Reputation and the resulting privileges are not bad in principle, but since the upvotes, downvotes, closevotes are necessarily more or less subjective, this can sometimes lead to effects that are in contrast to the invention of the site. I do not see a way to solve this dilemma.

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  • $\begingroup$ I agree very much with the sentiment of your answer. I feel though that more can be done to cull patently useless questions that are not even driven by curiosity in learning. $\endgroup$ – user21820 Jan 29 '17 at 12:54
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    $\begingroup$ For instance it takes just 5 people to close it, and 3 to delete it. But it's a chore that few people want to put a hand in. $\endgroup$ – user21820 Jan 29 '17 at 12:56
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    $\begingroup$ To my experience, most of the so-called troll-answers are closed/deleted quite fast. A major problem : You have a very interesting question, but it is so complicated that you cannot offer efforts, on the other hand, it is clear that it is not a homework question. Sometimes, such questions receive positive reactions, but often they are closed/deleted/downvoted whatsoever very fast. I am convinced that many interesting ideas where lost because the idea of the "demand of an effort" is not handled more flexible. $\endgroup$ – Peter Jan 29 '17 at 13:02
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    $\begingroup$ I have personally not seen any example of a genuinely good question being closed and deleted. However I have seen many good questions with nearly zero attention (no upvotes or comments or answers). In any case, my question is because I want to know if there is some way that I am unaware of to deal with the issue, to save all the time that I estimate is wasted by contributors who have to wade through the long posts and back-and-forth comments, just to finally conclude that the asker is not interested in real mathematics. $\endgroup$ – user21820 Jan 29 '17 at 13:56
  • $\begingroup$ @user21820 If you study long posts carefully, you always risk to waste your time (Unless it is obvious that the question leads to nowhere, but these cases are rare). So, either you avoid very long questions completely (which is more or less my approach), or you consider the effort you made leading at last to nothing not as a waste of time, but an experience and exercise in mathematics. Consider that many important results in mathematics were achieved AFTER many failures. Usually, difficult problems are not solved at the first try. $\endgroup$ – Peter Jan 29 '17 at 14:07
  • $\begingroup$ My suggestion : Don't put too much efforts in studying claims about the solution of a famous open problem. I once found the claim that an author was able to prove that the Euler-Mascheroni-constant is irrational. He looked at the partial sums converging to this constant and noticed (correctly) that they are all irrational. Of course, this does not prove that the limit itself is irrational. And someone in the math-stack-exchange-forum claimed that a proof of Goodstein's theorem using only the Peano-axioms, would be possible. $\endgroup$ – Peter Jan 29 '17 at 14:17
  • $\begingroup$ Unfortunately, I have not studied the proof of the impossibility yet, and I am not able to prove/disprove it. I think that it can be difficult to recognize whether a prove requires ZFC- or only PA-axioms, I think there is an argument not available with PA alone in the mentioned proof. $\endgroup$ – Peter Jan 29 '17 at 14:20
  • $\begingroup$ Yes it is a well-known fact that Goodstein's theorem is equivalent over PA to Con(PA), and so any proof within PA would immediately show that PA is inconsistent by Godel's second incompleteness theorem. Indeed if there is no easy way to handle such posts I will simply ignore them. I was just hoping there is a way. $\endgroup$ – user21820 Jan 29 '17 at 14:38
  • $\begingroup$ Not quite, a proof within PA implies that it can be proven within PA, that PA is consistent. But this is impossible, since no system can prove its own consistency. $\endgroup$ – Peter Jan 29 '17 at 14:42
  • $\begingroup$ Um your comment is the inaccurate one; no consistent recursive first-order theory extending PA can prove its own consistency, hence if PA proves Goodstein's theorem then PA is inconsistent (unless you doubt the meta-system needed to prove Godel's incompleteness theorem). $\endgroup$ – user21820 Jan 29 '17 at 14:47
  • $\begingroup$ So the end result is that there is no end to these "upvote - Downvotes - Close votes " dramas ? $\endgroup$ – A---B Jan 29 '17 at 16:28
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    $\begingroup$ Agreed for the most part, but regarding the amount of work that an answer requires, keep in mind that it is the helpfulness to the reader that matters, not how much work went into it. Effort is not an index of value; a cake that took eighteen hours to prepare and bake, that tastes funny, is still a lousy cake. And a cake isn't a bad cake just because it only took a few minutes of the chef's time to put it together. $\endgroup$ – Wildcard Jan 30 '17 at 22:27
  • $\begingroup$ @Wildcard You are right. My formulation is unlucky. $\endgroup$ – Peter Jan 31 '17 at 9:10
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    $\begingroup$ "Is 1 a prime number?" -> I like those questions, or at least I like them when they get good answers which explain the reasoning behind the answer (i.e. "No, because the fundamental theorem of arithmetic is a lot simpler if 1 is not prime" rather than "No, because [the definition] says so"). That's actually one of the main selling points of this site for me. $\endgroup$ – Kevin Feb 8 '17 at 6:01
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I believe there are two main causes of these kinds of posts and they are delusional disorder (Grandiose Type) and sometimes disorganized schizophrenia but that often descends into gibberish and there isn't much that can be done other than to delete them so I'll focus on delusional disorder.

People with delusional disorder are often called "cranks" because they tend to be insistent they have found a result and if someone points out a flaw they act as though it doesn't exist. After a while they begin to say the community is denying the validity of their results and can become increasingly belligerent as time goes on, even paranoid. People with delusional disorder can be very functional in other aspects of their life but unfortunately they aren't able to see reality around this one belief that doesn't make sense to the outside world.

I can recall one particularly articulate person back when google first took over usenet who insisted they had an interesting algebraic result but when others pointed out it was trivial they would tirelessly repost their ideas and decry the community for refusing to acknowledge the value of his work. I would say that rather than not being interested in learning they are incapable of seeing reality clearly. That's an important distinction to me because they can't help it and trying to tackle the problem by pointing out the logical failings in their argument is inevitably fruitless.

Unfortunately their behavior can be frustrating and it can be difficult to respond to a relentless assault of false proofs or trivial results being posted as though they were interesting. There is both the need to clear their content so it doesn't clog up the works and at the same time try not to overtly persecute them which can worsen the condition.

In the past I've sent people who seem to fit this pattern private messages discussing why I think they might have this disorder. In particular it they seem well spoken, repeatedly post the same result, but constantly get stuck on some point that becomes this blackhole of circular logic they seem a likely candidate.

Most people will be dismissive or belligerent if you suggest they have a mental illness so I typically start by discussing why it seems strange to me that despite being relatively well spoken and reasonable that they seem stuck on this one idea. I then say I don't intend to offend but that it's such a common condition that shows up in math and science communities relatively often and because mental illness is stigmatized they may not have heard of it and it was worth mentioning. I remind them I'm not a doctor though and they'll have to decide for themselves if that's what's happening to them or not since they know their own history best but I had to speak up because I've known people who've had it in the past and it can be frustrating, alienating and even debilitating for the person suffering from it.

To deal with the behavior I'll point out that math is a social discipline and an idea is only as valuable as your ability to communicate it to others. While they may have a great idea until they can convey it in a way that we can understand it then we're unfortunately at an impasse and their content doesn't have any value to the wider community. That often helps soften the blow when their posts are continuously deleted because they can at least rationalize that they have a great idea but the communication barrier is the main issue. If I can build a rapport with them in chat I'll often ask them questions like "Has anyone understood this well enough to explain it back to you?" and "Does this happen in other areas of your life or is it just this one idea you find others are confused?" and if they answer "No" to both then I will mention delusional disorder and point out that it's common in math and science communities and if they find themselves continuously ostracised when presenting their thoughts they might want to talk to a doctor about it.

This is the best approach I've found so far but honestly I believe any sort of compassionate response is a good move in the right direction. It's hard to for us but it's even harder for the person experiencing delusions and I try to keep that in perspective.

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  • $\begingroup$ Your answer is a very interesting one. It would be good if you can provide evidence that your approach actually has a positive effect. Ever since this meta post (a year ago), I have seen even worse cranks, and some also instigate others against all who criticize them. In any case, I have seen hundreds of cranks and based on my observations I disagree with your claim that they are incapable of seeing reality clearly. Rather, they willfully choose to ignore reality. Some of them are also cunningly manipulative. I can only hope that Math SE will not gather junk like the rest of the internet. $\endgroup$ – user21820 Jun 21 '18 at 15:18
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The whole purpose of the site is to answer questions. Some questions are poor, they will be downvoted, and the person asking will learn to ask better questions.

If someone has genuinely erred, and the reason for which there proof is incorrect is genuinely not obvious to the layman, the purpose of MSE is to demonstrate this.

Then there is of course the potential that they might not be entirely wrong, and might as a byproduct of their efforts come up with something which is not falsifiable, but also not easy to prove true (a sub-conjecture).

In the interest of raising the bar for the mathematical ability of the entire species, I would suggest that perhaps no action is needed. Truly poor questions will always be asked, and there is already a procedure for dealing with them. If the process is too slow for your liking, you can participate in the review process, to stop bad questions at their inception, before they've been around so long, that you just have to wait for the world to downvote them.

https://math.stackexchange.com/review

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