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I have seen a few responses on MO that I think are either incorrect or possibly incorrect.

What is the best way to draw attention to possible incorrectness?

(I provide two examples below; if this is poor form, then please edit them out.)

  1. A user posts that it is impossible to prove the Fundamental Theorem of Algebra using the Brouwer Fixed Point Theorem. But another user (disclaimer: me) provides a source purporting to provide such a proof. Due to timing, the former received many up-votes early on; as of this writing, it has twice as many votes at 22 to 11. For both claims, see here. [Added (quid): the answer claiming impossibility was deleted by its owner.]

  2. There is a post claiming that: Most (actually almost all) of ancient Chinese mathematics literatures [sic] are written in the forms of poems. But this claim is unsubstantiated insofar as I can tell, and one might suspect that, e.g., the last example provided is not an instance of an actual poem. Again, this post has garnered many up-votes (15 as of this writing) but I'm not sure how anyone could properly evaluate it without more information or the ability to read Classical Chinese. [Added: An MO user (Marty) posts in the comments there: I asked a colleague -- an expert in Chinese poetry -- about this, and his response is below... "Well the post is fascinating, but completely wrong." etc.]

I can think of a few ways to address such possible incorrectness. One is to leave a comment on the original question or the disputed answer; however, I worry that this method has very low visibility unless it is carried out shortly after the response is posted.

Alternatively, one might edit the post, thereby bumping it up and drawing attention to it, or put up another post disputing the earlier one. But I view such approaches as somewhat aggressive and possibly overkill. (I hope that my examples above are not viewed similarly!)

Yet another route would be to draw attention to the post here in meta.MO. I suppose that is the approach I have taken for the two examples above, but I am curious as to what should be done more generally (if anything at all).

Edit: For a related feature suggestion, Stefan Kohl comments he's left a post here.

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    $\begingroup$ By all means leave comments, or answers where appropriate, correcting mistakes. But in most cases, is it really important to "draw attention" to incorrectness, as opposed to simply correcting it? $\endgroup$ – Mark Meckes Jan 1 '14 at 9:43
  • $\begingroup$ If you're sure and can correct an error, can't you just edit the answer (or post a new, correct answer)? If you aren't confident enough to make an edit or post, I guess a comment would be more appropriate in most cases. As for the number of upvotes a (potentially) erroneous answer received, I'm not sure if it's that important. (cont.) $\endgroup$ – Yuichiro Fujiwara Jan 1 '14 at 11:09
  • $\begingroup$ ... A highly upvoted answer only shows up on top if you choose to let MO do so. I don't know what the default setting is, but if a user lists answers in order of activity (by clicking the "active" tab on the top right of the answer section if it's not ordered that way now) for example, your newly posted answer that corrects the error you found will be on top. Actually in the first case in your question, the wrong(?) answer is at the bottom of the list if viewed on the active tab. $\endgroup$ – Yuichiro Fujiwara Jan 1 '14 at 11:10
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    $\begingroup$ I certainly hope that future readers of a MO post (if indeed there are any) would be able recognize the difference between upvotes on MO and publication in a peer-reviewed journal. $\endgroup$ – Mark Meckes Jan 1 '14 at 18:00
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    $\begingroup$ There is a reason for 'drawing attention' to corrections @MarkMeckes: users that read the incorrect answer before the correction could be mislead by it and never notice the correction. I would consider this as a rather common scenario in case of somewhat late corrections via only a comment. $\endgroup$ – user9072 Jan 1 '14 at 19:39
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    $\begingroup$ @quid: That's true enough, but it's not reasonable to assume that such users will necessarily see a new answer either. We don't all check MO every day. $\endgroup$ – Mark Meckes Jan 1 '14 at 19:48
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    $\begingroup$ If at all possible, an incorrect answer should be corrected. In any case, some kind of edit must be made so that past votes are unlocked. $\endgroup$ – François G. Dorais Jan 1 '14 at 22:32
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    $\begingroup$ I have made a related feature suggestion -- introducing error flags -- here. $\endgroup$ – Stefan Kohl Jan 2 '14 at 22:15
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    $\begingroup$ Benjamin Dickman: I was the owner of the first post that you have mentioned in your post. You have written that I claimed that <it>it is impossible to prove the Fundamental Theorem of Algebra using the Brouwer Fixed Point Theorem</it>. I have never made such a claim. I just cited a paper (preprint) indexed by Mathematical Reviews, which claims that this assertion is true. I also emphasized that that paper was not accessible to me. $\endgroup$ – Name Jan 5 '14 at 15:54
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    $\begingroup$ @YazdegerdIII I too was unable to find the full text. But a comment (by François?) notes the preprint you cited asserts only that a particular technique of a couple of mathematicians would not work, not that the BFPT in general is unsuitable for proving the FTA. So, IIRC, your claim went beyond what was stated in the preprint. I left a comment and made an additional edit to the OP, but after seven months had not seen any clarification from you. Unsure of what to do, I posted here and took the advice of a moderator. I apologize if you feel singled out or that my actions were unwarranted. BD $\endgroup$ – Benjamin Dickman Jan 5 '14 at 16:01
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    $\begingroup$ An added note: This metapost is about a more general question, of which the above were intended only as two clarifying examples. I was not sure whether to include them at all, and put in a parenthetical comment asking that others delete them if they seemed to be "in poor form." (Though no one did remove them, perhaps they have distracted too much from the main question.) Nevertheless, in the specific case of the FTA question, I assume that the first answer's owner agrees it was incorrect, since they ultimately deleted it. $\endgroup$ – Benjamin Dickman Jan 5 '14 at 17:14
  • $\begingroup$ It may be worth pointing out that in your second example the owner has engaged with your objections, but just has a different view. Also the owner seems to have edited his answer a couple of days back to say that "Some of ancient ..." (instead of most" or all"). $\endgroup$ – Lucia Jan 11 '14 at 15:34
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One possibility, in the event of having left a comment but received no response, to edit the answer itself and add a line like:

n.b. (Benjamin): this answer appears to be incorrect. Please see my separate answer.

I think when the original answerer does not address critical comments, it's perfectly reasonable to edit.

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    $\begingroup$ Scott, and if it turns out, that the answer is indeed correct, should the author edit the other answer and add a line like: "n.b. (Scott): my answer is correct. I do not have any idea what you are talking about. Please, remove your line from my answer and do not destroy it anymore."? $\endgroup$ – Michal R. Przybylek Jan 1 '14 at 23:51
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    $\begingroup$ @MichalR.Przybylek a more reasonable way to proceed seems to be to rollback and add a clarifying comment, or to edit out the comment adding some explanation or something along these lines. Of course the editing suggested here should only be used with care and after waiting for response for a reasonable amount of time. But there are also accounts that are abandoned and so on. $\endgroup$ – user9072 Jan 2 '14 at 1:03
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    $\begingroup$ @MichalR.Przybylek, it seems you're asking a question expecting the answer "no", and that is indeed my answer. I think quid described a good course of action. $\endgroup$ – Scott Morrison Jan 2 '14 at 3:00
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    $\begingroup$ Scott, true, the question was unfair. I am in the process of turning my blood into water, but, as you may see, it has not been completed yet. @quid, do we agree that every answer should be posted with care? We agree. However, wrong answers happen, and they will happen as long we remain humans --- a part of being a human is making mistakes. This also means, that there is a non-zero probability that a correct answer will be edited in the proposed way, and its author will not notice the fact (nor anyone else; btw, Upvoters, have you checked that Benjamin's answer is indeed correct?...). (cont) $\endgroup$ – Michal R. Przybylek Jan 2 '14 at 13:06
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    $\begingroup$ I am simply afraid, that Scott's suggestion will be overused. It is just too dangerous. On the other hand, I do not mind if such changes are done by moderators --- I trust moderators much more than some random users. $\endgroup$ – Michal R. Przybylek Jan 2 '14 at 13:07
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    $\begingroup$ I also do not understand why "past votes must be unlocked". What is the reason to cancel your upvote? $\endgroup$ – Michal R. Przybylek Jan 2 '14 at 13:18
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    $\begingroup$ This seems like a bad idea to me. Editing a post to change the intent of the author seems too much like vandalism for my taste. What would happen in `the real world' if someone has published a wrong proof? You could write to the editors, the editors could retract the article, you could write your own article etc -- the one thing you can't do is to edit the original article and claim it is wrong there. Editors could do that, so if moderators wish to edit a wrong post, I have no problems with that. $\endgroup$ – Lucia Jan 2 '14 at 16:15
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    $\begingroup$ @quid: My point was indeed that I don't want people editing other posts and changing the content substantially. I could only see moderators being allowed to do this, but I agree that even here things can be problematic. $\endgroup$ – Lucia Jan 2 '14 at 17:01
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    $\begingroup$ @quid, I don't follow your logic. What's your point? Should the edit be done if A posted an answer, his answer was highly upvoted, but some user B believes that A's answer might be wrong? Or, should it be done if A posted an answer, his answer was upvoted, but it is obvious (for any reason) that his answer is wrong? Quid, believe me or not, but if you answer a question, then after a year, you may not be willing / have time / energy to think about the same question again and answer every new issue. $\endgroup$ – Michal R. Przybylek Jan 2 '14 at 19:13
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    $\begingroup$ @MichalR.Przybylek such an edit should be allowed if a user B asks for clarification/challenges A's answer and A is unresponsive for some time (as said in the answer). Of course B should be reasonably sure about their claim; but then I doubt there are that many users above 2k+ that will make bogus edits of this form to worry about this. It could happen. But let us deal on a case by case basis with these cornercases. For your final sentence: if an OP is unable/unwilling to maintain their content IMO they should be grateful if others do so for them (in a diligent way). $\endgroup$ – user9072 Jan 2 '14 at 19:41
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    $\begingroup$ At this point we seem to have a concrete problem of incorrect answers remaining uncorrected, or with easily missed connections, and a hypothetical problem of inappropriate editing of others' answers. Let's deal with the first one, according to my suggestion (users don't gain editing privileges for nothing), and then deal with the second one if or when it arises. $\endgroup$ – Scott Morrison Jan 2 '14 at 22:50
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    $\begingroup$ @BenjaminDickman, my concern is that an answer starting with "I believe..." does not show enough confidence. Quid and Scott, I am not old enough to be interested in politics (i.e. I think I will not continue the discussion), but it seems that you miss the point --- the issue is not about dealing with incorrect answers, but with judging which answers are incorrect (Scott, have you checked that the answer was indeed incorrect?). Quid, I do not buy your logic, that if someone does not want to engage in a discussion, it means that he is wrong. (cont) $\endgroup$ – Michal R. Przybylek Jan 3 '14 at 1:52
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    $\begingroup$ Scott, you answered a general case, not the specific one --- if my impression is wrong, then please say it in your post. $\endgroup$ – Michal R. Przybylek Jan 3 '14 at 1:53
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    $\begingroup$ @MichalR.Przybylek: Community editing is one of the pillars of MathOverflow functionality: everyone shares the responsibility for the correctness of every post. In particular, you should trust that if someone misedits a post then someone will rectify the situation. mathoverflow.net/help/editing $\endgroup$ – François G. Dorais Jan 3 '14 at 8:51
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    $\begingroup$ @MichalR.Przybylek of course nobody is under obligation to engage in lengthy discussion. Yet if somebody does not find the time to respond at all to a (reasonable) comment questioning the correctness of a math claim they made then IMO they need a very good reason (which could be as trivial as having overlooked the comment). If they have no time/interest/energy to back up their claim they could at least respond this. $\endgroup$ – user9072 Jan 3 '14 at 22:19
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Mathematicians tend to care a great deal about correctness. If you bump the question by adding your own answer (or even a minor edit), this will tend to draw attention to your comments that the other answer is incorrect. In several cases, highly-upvoted answers have been voted down after it was pointed out that they were incorrect, while other much later answers were voted up. It is unfortunate that other sites like stat.stackexchange.com do not similarly value correctness. Perhaps they will in time if they reach a critical proportion of people with either a professional level of competence or the maturity not to vote up incorrect answers with pretty pictures or high reputation authors over unadorned but correct answers.

Please be extremely cautious about changing someone else's answer to say that it is incorrect. Think about how you would feel if someone who misread the question or misunderstood the relevant mathematics changed your correct answer. The reward is often not worth the risk. Even if you are used to being right 99.9% of the time, you should not assume this is the case when you disagree with someone else who is also right 99.9% of the time.

There are several answers of mine which people have insisted at length are incorrect. In one case I'm confident that the multiple people disagreeing with me are confused and I think I understand their confusion. I think it would be terrible if they defaced my accepted and highly upvoted answer just because of their confusion. In another case, the person vehemently disagreeing eventually admitted misreading the question. In a third case, my answer covers one interpretation of the question, and was accepted, but there are other interpretations other people prefer. I think their comments and alternative answers (and down votes) are fine, and more appropriate than changing my answer.

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    $\begingroup$ I agree entirely with this answer. Commenting on a (possibly) incorrect answer, and supplying one's own answer are adequate ways of drawing attention to errors. Changing someone else's answer to say it is incorrect is a step too far in my opinion. $\endgroup$ – Lucia Jan 3 '14 at 16:46
  • $\begingroup$ Thanks for your response, too. $\endgroup$ – Benjamin Dickman Jan 3 '14 at 18:05
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    $\begingroup$ I kind of disagree with this. There shouldn't be half-measures with respect to community editing. You should trust the community (which includes you) to correct any erroneous edits from other community members. Ideally, this always happens without a hitch but site moderators will intervene in case of edit wars or other system failures. $\endgroup$ – François G. Dorais Jan 3 '14 at 20:07
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    $\begingroup$ But surely there are guidelines on what are good edits. For example the help page mentions edits that clarify the meaning without changing that meaning. When we evaluate suggested edits we check for radical changes or vandalism. I think one should promote good practices in editing at all times, rather than just hope that the community will fix problems if people go too far. $\endgroup$ – Lucia Jan 3 '14 at 20:31
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    $\begingroup$ I think the negativity against stats.SE adds nothing useful here and seems somewhat rude (I have nothing to do with that site, this is a general point). $\endgroup$ – user9072 Jan 3 '14 at 22:26
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    $\begingroup$ "Think about how you would feel if someone who misread the question or misunderstood the relevant mathematics changed your correct answer." Not different from the way I would feel if they left a comment (that is I see no problem as long as they proceed in a reasonable way) as long as the edit is done in such a way that it is visible (without entering the edit history), as in Scott Morrison's suggestion that this is an addition/edit/commentary to the post and not due to me; then it would IMO also not really change the meaning of my OP. Comment vs edit (marked as such) IMO is technicallity. $\endgroup$ – user9072 Jan 3 '14 at 22:46
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Slightly tangential answer:

I don't think there is anything wrong with having incorrect answers on MO. People make mistakes, and other people are free to point out the mistakes in the comments. And as long as some form of the correct exists in the record, I don't think having incorrect answers in anyway reflect poorly on the community as a whole.

A perhaps bigger problem is the situation when people upvote incorrect answers which they either have not checked themselves or that they do not understand.

Now, this problem manifests a lot less for mathematical questions and mathematical answers, since the training of mathematicians often allow us to make educated guesses about the usefulness of answers even without following it through fully. And I certainly do not advocate voting only for answers one can personally vouch for.

But for a soft (and borderline off-topic) question like the second one linked to above, which is about mathematics and poetry, the vast majority of the MO users would be mere amateurs. Therefore the voting patterns there will reflect more of the common pitfalls about the voting on other SE sites. (There's a reason that the fastest gun in the west syndrome refuses to die on most SE sites: speed is often rewarded over elegance and correctness.)

It is perhaps a happy accident that on MO that the vote counts on answers are a better proxy for their correctness than on many other SE sites. And for those of us used to this it may seem strange that sometimes incorrect answers gather lots of upvotes.

For frequent users of this forum, a work around is to mentally readjust one's interpretation of the votes when the question is a soft/off-topic one. For uses who do not frequent MO, hopefully they will have been trained by the rest of the internet to take things like "likes" "+1s" and "upvotes" with always a healthy grain of salt.

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    $\begingroup$ I think the observation about soft questions is well made. Thanks for responding. $\endgroup$ – Benjamin Dickman Jan 8 '14 at 17:06
  • $\begingroup$ I'm slightly less optimistic about the built in quality control of MO. I've seen answers with elementary blunders that were pointed out in the comments accumulate upvotes several times (and that's after just a few months on MO). For answers with elementary blunders not pointed out in the comments, all bets are off obviously (I should know, I wrote some such myself). $\endgroup$ – Christian Remling Jul 6 '14 at 4:05
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I think the best practice is to leave a comment, and if necessary provide more information by writing an additional answer.

A reasonable person who reads an answer, reads comments under it. You should not care too much about unreasonable people. Also, you should not care too much about votes --- if you wrote a good answer, and a bad answer receives more upvotes, it is "the community" who has a problem, not you. And, again, reasonable people who read answers do not assess their quality by the number of up/down-votes.

Once, I thought that mathematicians on MO are just so pervert that they enjoy voting up trivial questions and silly answers. Then I recalled words of a well-known professor that I heard when I was a student:

"Michal, you are mature, so I tell you the truth: teaching is like casting fake pearls before swine"

In short, to get many upvotes you do not have to write a brilliant answer, nor be reasonable --- you have to sound like you were reasonable :-)

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  • $\begingroup$ I mostly agree with your first two sentences. The rest of this answers seems, to me, like it is discussing perceived problems with the MO community at large - perhaps not entirely related to my query. Really what I'm asking about is precisely what I've put in a comment above: I know that journals will have guidelines for how to manage articles that are later realized to have mistakes; I only ask what the MO response should be to an answer that is up-voted as if it were correct, but which is subsequently seen to be incorrect. $\endgroup$ – Benjamin Dickman Jan 1 '14 at 19:02
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    $\begingroup$ @BenjaminDickman, then I do not understand the issue --- what do you want to achieve? There is a wrong answer; there is a comment under the wrong answer which says that the answer is wrong; and there is the right answer. Are you afraid, that in such a situation, someone may come to the conclusion that the answer having more upvotes is right, and obtain some striking results in his research based on this belief without carefully checking it? I, for example, am not afraid :-) $\endgroup$ – Michal R. Przybylek Jan 1 '14 at 19:30
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    $\begingroup$ @BenjaminDickman, one "issue" may be related to the fact that people upvote answers for various reasons. The issue has been risen on meta in a bit different context --- on meta, people downvote questions when a) they don't agree with the "yes"-answer to the question, or b) they don't like the question. Similarly, on the main site --- people upvote answers when a) they checked the answer is correct, or b) they like the poster, or c) they like the answer, or d) (that's me) they found the answer to be useful for them. (cont) $\endgroup$ – Michal R. Przybylek Jan 1 '14 at 20:34
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    $\begingroup$ A temporary solution could be: don't vote up when the answer is correct, but say in a comment that you verified the answer (or vote up on such comment). A long term solution could be: modify the software to separate votes for correctness from "likes". But, like I said, I don't think this is a real issue --- if someone wants to use some results from the site, it's his duty to verify the results. $\endgroup$ – Michal R. Przybylek Jan 1 '14 at 20:36
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    $\begingroup$ The full quote is "casting artificial pearls before genuine swine." $\endgroup$ – Gerry Myerson Jan 1 '14 at 22:30
  • $\begingroup$ @GerryMyerson, thank you for the correction! $\endgroup$ – Michal R. Przybylek Jan 1 '14 at 23:55
  • $\begingroup$ Thanks for the response. $\endgroup$ – Benjamin Dickman Jan 2 '14 at 4:01

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