# Should questions asking to prove false claims be downvoted or closed?

There is this question where the poster asked for helping proving a claim that in general is not true. Many people gave counterexamples to the claim. The question received downvotes as well. Later additional information was given that made the question well-posed.

I don't think such a question should be downvoted or voted to be closed. Given any mathematical statement, the implicit question is whether or not it is true regardless of whether the problem statement says it is true. Even if an easy counterexample exists the implicit question becomes, "what information is missing to make this a true claim?".

I think such questions should be preserved because they allow for genuine learning and would hopefully correct other's mistakes in the future.

Are there other examples of such situations as the question above? What do people think?

• – Milo Brandt Mar 13 '15 at 23:30
• Thanks @Meelo. It's related, but I think this question is different. I couldn't find one like it. – abnry Mar 13 '15 at 23:32
• Such a question could be put "on hold" until re-worded. The forum software has that scenario built in. – GEdgar Mar 14 '15 at 12:12
• The deeper issue is that, once several answers are posted pointing out the error, it is not so helpful to "fix" the question. It would be better to ask a new question, and delete the original. Otherwise, we end up with a mashup of answers to the new version and answers to the old version. This can be seen in the question linked in the post above. – Carl Mummert Mar 14 '15 at 13:15
• I agree: it should simply be answered. Note that it is by no means always true that the question was mangled. – Brian M. Scott Mar 15 '15 at 6:28
• I have recently followed Kolmogorov-Fomin's Elements of the theory of functions and functional analysis (the original 1980 edition) and often found statements that, unless one assumes additional hypothesis that the text does not explicitate, are not true in general, therefore I have found myself in the position of asking about statements and receving answers by kind fellow MSE users explaining that what I was asking is not true, or true only under some unstated assumption. Nevertheless, sadly, mankind is not only made up of that kind of people – Self-teaching worker Mar 17 '15 at 16:28

It should be neither closed nor downvoted, if anything because both are quite contrary to the whole spirit of the mathematical endeavor!

• Closing a visibly incorrectly copied exercise is not counter to the whole spirit of the mathematical endeavor. – quid Mar 14 '15 at 0:23
• It was visibly incorrect for many, but visibly not to the person who posted the question. As an instructor, I've been asked the most implausible and patently false things by students, and "downvoting or closing" those questions would have been a terribly bad idea. – Mariano Suárez-Álvarez Mar 14 '15 at 2:16
• The course of action I mainly propose is to request clarification as opposed to guessing the intent. This makes sense here and with students. Once asked OP in the specific case had no problem to clarify the question and also fully understood that a key piece of information was missing. – quid Mar 14 '15 at 9:15
• Asking for clarifications is something that I'd like to see happen before downvoting or voting to close. – Mariano Suárez-Álvarez Mar 14 '15 at 16:10
• +1 Exactly my viewpoint (is Jupiter aligned with Mars?) – Bill Dubuque Mar 16 '15 at 3:06

It may be relevant to downvote such a question, but that wouldn't merely be because it is asking for proof of something that is false. Something more is needed -- for example, sometimes a user will post a string of questions that boil down to "here's a random conjecture I made for no particular reason without verifying even the single-digit instances; please prove it for me". I would downvote that -- and the fact that the conjecture is easily false would contribute to my feeling that the OP ought to research his questions better before asking. But that kind of cases is an exception.

In any case, closing questions just because the ask for something false to be proved would be wildly inappropriate. Except for trivial typos, such a question always indicates that the asker has some misconception -- either about what is true or about which assumption can reasonably be left unsaid, or sometimes about notation where the asker copies a formula wrong because he's not aware that some detail carries meaning. In each of those cases it should be our mission to disabuse the asker of that misconception. Sometimes a nudge in comments will be enough, but the primary tool for this should be explaining in an answer why the statement is false, and perhaps take a guess at what the asker really wanted to prove.

Closing the question would prevent explaining to the asker what is wrong with his claim. It doesn't help anyone just to see "this question is closed because what it asks for a proof of is false". Just asserting that it is false falls short of what I think should be our standard -- if we're confident enough that it is false to close the question, we should be able to produce an actual disproof.

If anything, a question that clearly points towards a concrete misunderstanding of the asker's is miles beyond the standard "here's my homework and I don't know how to start", which doesn't point towards anything but laziness.

Of course, once an answer explaining why the desired conclusion is wrong has been posted, the OP should not edit the question to "correct" the statement, but rather post a new question. But that is a different problem, and not one that would be solved by closing the original question without even telling the OP why his claim is false.

• Frequently it is a trivial typo or omission. Just look at the example linked. – quid Mar 15 '15 at 13:56

In theory, I would not downvote it. In my opinion, the proper response is to write up an answer explaining why the claim to be proven is in fact false.

In practice, I would also consider the intent of the asker. Does he genuinely believe the claim is true, or is he deliberately asking us to prove a false claim because he craves the attention? Although in the latter case I'm not sure what the proper close reason would be, hopefully not the dreaded "off-topic" for something that is actually on-topic.

But of course if the question is a duplicate, then it should be flagged as such, e.g., "Prove $-1$ is a prime number."

• Fully agree, especally with the first paragraph. – goblin Mar 18 '15 at 11:38

My take on this: if a question asks to prove something the falsehood of which is relatively easy for a reasonably experienced mathematician (by which I mean person who regularly engages in the practice of mathematics, for whatever reason, not necessarily a professional or research mathematician), then generally a legitimate answer would be to provide an explanation of the falsehood. I wouldn't downvote such a question per se, in fact, I might even upvote it if the topic was of sufficient interest. After all, part of the mathematical quest involves trying to prove things which are false; it's one way we discover what is true and what is false.

But much more difficult are questions whose truth or falsehood is difficult to ascertain. These are often deep and difficult. I have thus become careful to check whether I think the assertions in these questions are true of false before putting in too much effort.

A question that asks: "Prove that: [some false claim]" is unclear and should be treated as such.

What this means in practice can differ depending on the situation and the preferences of the acting user. It can be reasonable to vote to close if it seems too unclear what is meant, it can also be reasonable to give a tentative answer if one has a good enough guess what is actually meant. Yet in any case there is a problem with the question that needs to be fixed.

The situation in the linked to question-thread illustrates the problems such questions cause. For one thing, there are several answers that do not answer the current version of the question at all.

• Well, if a question is downvoted or closed too quickly, the poster may not correct the question in time as was done in this case. That's something to consider. – abnry Mar 13 '15 at 23:39
• I do not understand (in a literal sense) what you mean to say by: "the poster may not correct the question in time." Could you please explain what you mean, especially the "in time"? – quid Mar 13 '15 at 23:52
• The corrected question may be a worth posting and being answered. If it gets closed or downvoted it may not get the attention such a question would normally get without an initial error. – abnry Mar 13 '15 at 23:53
• If it gets closed, and is then edited to clarify, the question is put in the reopen-queue, where it gets attention. If it is actually reopened, it is put at the top of the active-list again, giving it again attention. It is true that a situation as described is not optimal for the question. However, I disagree that it is necessarily worse than what you seem to propose, as there is a lot of room for misunderstanding, false interpretations, and frustration on all sides. – quid Mar 14 '15 at 0:00
• It is not unclear at all. If someone asks "How can I prove X?" and the answer is "You can't," then that seems like a decisive answer directly addressing the question. The only problem I see with the given question was that its meaning was edited after receiving answers - all the answers effectively address some version of the question, so it seems that there's quite a few answerers who found nothing unclear about the question. – Milo Brandt Mar 14 '15 at 3:06
• @Meelo Ah, but the question isn't usually "How can I prove X?", it's often "Prove X." (which isn't even a question). Maybe if users stopped asking questions as if they were assigning us homework, the situation would be different. (Note: I'm not advocating downvoting such questions. I'm more or less venting.) – Najib Idrissi Mar 14 '15 at 7:15
• @Meelo For X false, "How can I prove X?" is somewhat different already, but still a bit problematic. My problem with "Prove that: X" is that it is unclear if: a) OP means "Prove or disprove" or b) made an error in stating the problem, or c) something else. The situation here very clearly hinted at a problem with the question. Personally, I consider it as potentially inconsiderate to simply provide an answer to a question as asked (though it really is not as asked even, in this case) when it seems very likely that the asker made an error in stating the question. – quid Mar 14 '15 at 10:26
• Such questions are not in the least unclear. They may or may not be what the asker intended — I’ve encountered quite a few that in fact were — but they are certainly clear and deserve answers. If there is a reasonably obvious possibility way in which the asker might have misstated a correct result, then of course this possibility should be raised; ideally this occurs quickly in the comments, and a good answer will at least mention the possibility, but an answer that simply points out the falsity of the assertion is still worthwhile. – Brian M. Scott Mar 15 '15 at 6:34
• @BrianM.Scott as I tried to convey there is a spectrum of possibilities. However some answers one encounters answering obviously misstated questions as written in all seriousness without further comment feel rather like practical jokes to me. And, not rarely lead to considerable confusion. Yesterday somebody asked if something was an inner product. The expression was something like a1b1 + a2b1 + a2b1 + 2a2b2, they had set up a symmetric matrix associated to it and were mainly wondering about definiteness. To write an answer detailing why it's not symmetric seems besides the point to me. – quid Mar 15 '15 at 11:11
• It is overwhelmingly likely that there was a flip of indexes (so I commented this with some further remarks on other aspects). My point here is not that the questions should be closed and downvoted, I normally do not do this, except eventually for unresponsive OPs, but rather that answerers should consider the intent and needs of the OP, as opposed to acting in a way that can look like exploiting a typo to cash-in some easy points at the expense of some OP. (Though some answerers might simply lack knowledge and judgment themselves so I do not blame them). (@BrianM.Scott ) – quid Mar 15 '15 at 11:11