How to handle repeated poor questions attempting to prove Famous Conjecture

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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