I am now writing up a math paper, and there is an Arxiv paper posted back in 2009 which proved a weaker version of my result. But I don’t think their paper will be published in any journal – their proof is clearly wrong. Since that is eight years ago, I suppose the author spotted the error already.

My question: Should I cite their result in my paper? Note that we are both using the same technique (introduced elsewhere), just that they overlooked a key technical issue.

  • Several answers to this question also discuss this topic. – malexmave Jul 31 '17 at 14:38
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    @Justus: As in Noah Schweber's answer, "wrong" is not the same as "junk", and a paper with an incorrect result may still contain valuable work that is worthy of citation. – Nate Eldredge Jul 31 '17 at 16:26
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    Why is it important that the paper is on arXiv? Journal papers also have errors. – JeffE Aug 1 '17 at 4:09
  • I agree with academia.stackexchange.com/a/93945/22768. I'll add: if you don't cite the work, then you could be accused of presenting results that are already known. – user2768 Aug 1 '17 at 10:43
  • I think there's a difference: If a paper is published in a journal, at least some expert read it and somehow approves it. Thus it worths pointing out an error. But if it's only in arxiv, it doesn't worth pointing out the errors, since no one thinks that's correct in the first place. @JeffE – Arctic Char Aug 2 '17 at 6:01

Disclaimer: I have very limited experience, so what follows may not accurately reflect professional conventions. That said, from my limited experience I think it does.

EDIT: Disclaimer the second: the answer below assumes that you are correct, and also says nothing about what you should do besides what to write in the paper. Noah Snyder's comment below is absolutely correct.

I think this is something that you need to do, to provide an accurate history. This doesn't have to be done "loudly" - I think a footnote would be fine (e.g. "A weaker version of this result was claimed in [people], but the proof given there is incorrect - they [thing that they do]") - but I think it's important that an accurate history of the result be presented.

In my opinion, this is true whether or not you knew of their work before starting/finishing your own; we all benefit from a clear discussion of the literature (and in particular this may do a service to others who read the 2009 article and don't notice the error at first).

This is assuming that the article in question is "serious" - as we all know, there are of course "articles" which are too wrong for the above to apply. I think my criterion would be: "Is this article something which a 'reasonable' mathematician, competent but not necessarily expert in the specific subfield, might take as generally correct?" Obviously this is subjective, but I think in most cases it's actually pretty clear which side of the divide a given article lies.

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    You should also check with another expert that they agree with you about the error, and its polite to give the authors a heads-up in case they have a response (e.g. maybe they ended up publishing the result and correcting the proof in a different paper you missed). – Noah Snyder Jul 30 '17 at 23:30
  • @NoahSnyder Amen to that! I've added a bit to my answer to clarify. – Noah Schweber Jul 30 '17 at 23:31
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    I was going to mention your addendum, I'm glad you added it. We don't go out of our way to cite irrelevant literature and saying that the Earth is not flat when measuring its circumference. – user63725 Jul 30 '17 at 23:34
  • I think you should incorporate the comment made by @NoahSnyder (assuming he is ok with that and the CC-BY-SA license) into the answer. A comment is volatile and may be removed at any time. – Mindwin Jul 31 '17 at 14:56
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    Agree with @andorian: the last paragraph is a critical distinction which has been overlooked by other answers / comments. One should not cite "junk", but just because the paper is wrong does not mean it is junk. – Nate Eldredge Jul 31 '17 at 16:25

I will differ somewhat from the other answer: if the other work is obviously wrong and has not been published, there is no need to mention it.

It's likely that mentioning it will only bring the author negative attention. In papers, you do not normally say things like persons X, Y and Z attempted this before but failed, but I--at last--was successful. When you talk about the history of a problem, you should generally stick to the published history, or note where people made unpublished positive contributions.

I would also try sending a preprint to the author of the previous work to see if they have comments, and mentioning that their work has an apparent error. It's possible they aren't aware of it (or maybe they have left academia, or maybe it's right for reasons you don't realize). If they were aware of the error, then they should have retracted the paper (in which case it would definitely not need to be cited).

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    A note: If a paper is considered "published" when it was uploaded to ArXiv may differ between disciplines (e.g. from what I've heard, in physics, ArXiv is often the important version, and traditional journals, while still regarded very well, have lost some of their importance). Something to keep in mind for similar cases in other disciplines. – malexmave Jul 31 '17 at 8:28
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    It's likely that mentioning it will only bring the author negative attention. – Not necessarily. Honest mistakes are made all the time and if this author took some steps in the right direction, this makes their work not completely worthless. What may cast a negative light on them, however, is if they were of the mistake and did not updated the Arxiv paper to mention this. – Wrzlprmft Jul 31 '17 at 14:27
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    If it's publicly available, it's published. That's the definition of "published". – JeffE Aug 1 '17 at 1:09

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