How to deal with questions about crank-heavy topics?

Question

It was bound to happen and thankfully, it did now rather than later: we received the first question about a claim regarding P?=NP.

Some topics, in particular this, attract lots of public attention and laymen research. I do not want to belittle such efforts, but according to experts (i.e. complexity theory researchers) most of them are no good at all and in total, the signal to noise ratio is small.

How do we deal with such questions? As we generally allow questions of the form "Please help me understand X!" (or so I believe) this can not be the angle. Should we discourage people to ask questions about stuff that is likely to be cranky, or do we rather take the opportunity to educate people about how to tell "good" from "bad" work?

Answer 1

Here's the policy I would favor. I'm open to being contradicted if you've had experiences on other sites (Theoretical Computer Science, Math, Physics, …) that show that this policy is not viable.

Questions like “Is this proof correct?” or “I'm sure this proof is wrong but what's the fallacy?” or similar variants should be closed as “not a real question”, because they are overly broad (or worse, rhetorical like “I challenge you to find a fallacy”). You can't expect a review of a proof of anything more than a few clearly written lines in a Stack Exchange answer. Favorite crank topics can be held to a particularly high standard.

Unclear problems should be closed as “not a real question” too (ambiguous, vague, incomplete). If someone who's reasonably versed in the domain of the question cannot determine the precise statement of the problem from the question, close. Again, favorite crank topics can be held to a particularly high standard.

On the other hands, questions like “Is [clearly stated problem] in P” are valid questions. I don't see any grounds to refuse them. Again, the more the topic attracts cranks, the more precision and clarity should be required. If that problem is a variation on some well-known NP-complete problem, the answer “here is why this problem is NP-complete, and it is a well-known open problem whether it is in P” is a perfectly acceptable answer. If the question calls for more than that, close as “not a real question” (overly broad).

Furthermore, we need to be careful not to encourage copycats. This means quickly closing “dodgy” questions, and subsequently deleting them unless salvaged. Also, borderline questions should be edited to deemphasize the crank relationship.

With regards to https://cs.stackexchange.com/questions/305/whats-wrong-in-this-article-claming-p-np, I have voted to close as “not a real question”. I left the following comment:

You are claiming that some variation of a well-known NP-complete problem is in P. This is an extraordinary claim requiring extraordinary evidence. Some random article found on the web does not constitute extraordinary evidence. Therefore I am voting to close this question as overly broad; it is not our goal here to make broad advances to science in a single post.

Thanks to Artem Kaznatcheev for setting me straight in chat about what the question was really asking.

Answer 2

I don’t think that in-depth reviews of whole articles (10 pages in this case) are in the scope of CS.SE. If the author submits his work the usual publishing routine will perhaps produce some reviews.

Now, if a third person has a question about such an article it should be specific and narrow. For example something along the lines: “The author has defined X, but in his first lemma where he uses X, I think he is not following his own definition?” The question should show that the inquirer has at least made some effort himself towards answering the question. Asking for the typical gaps (“it is easily verified that Y holds.”) in a proof are valid questions, however the inquirer should include what he himself got so far. On TeX.SE people are usually asked to provide a “minimum failing example” so the community has a quick starting point for examining the problem at hand.

Just pointing to a result an asking whether it is true or not is simply to broad. Something like “Maybe here is a problem?” is incomplete as the inquirer should at least state where his suspicion comes from.

For example in question it is not clear what has been tried so far by the inquirer. For my taste just stating “I was unable to find a proof of the fact.” could at least include where he has looked at so far (Hopcroft & Ullman?, Harrison?, Salomaa?). (Then I don’t have to go through this again. It’s a courtsey towards the person taking their time to provide an answer.)