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Suppose author X writes a paper, and in this paper, they prove a result that is a very small part of their paper. However, the result has a mistake. Based on personal judgement, it appears the mistake is an innocent mistake that does not disrupt the intellectual flow of the paper. i.e. it is very reasonable to believe the author X had the ability themselves to get the proof right. In fact, it may have been simply a typo. Nonetheless, it is unarguably incorrect.

Author Y comes along and builds other results off of the (corrected) ideas by author X. Author Y wants to (for good reason) cite author X, as their results would not have been obtained without author X.

What is the correct way to do this in a paper? The way I see it, there are 2 possible actions for author Y:

  1. Pretend like author X didn't make a mistake at all and give them full authority on their theorem.
  2. Say something like ... "the results are based off the ideas by author X" but don't give as much of a "these are author X's results" flavor. Author Y then after mentioning author X, proves the theorem themselves.

Action 2) seems to be the most reasonable in the sense that it is intellectual honest and doesn't shame author X for no reason. However, is it considered plagiarism to be somewhat vague about what author X did?

Thank you.

EDIT: I realize another option is to allow author X to correct their mistake and then do action 1. But with how slowly paper publishing occurs, this seems unjustly detrimental to author Y so I don't consider it a real option.

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  • Inform author X of the typo/error so they can proceed and publish an errata or whatever they feel is appropriate. Independently of this: I suggest to go as in option 1), maybe including a footnote indicating that there is a small inaccuracy in the printed statement in author X's work, and that the statement you are giving is the correct/intended version. Aug 28, 2017 at 23:00
  • @AndrésE.Caicedo do you disagree with Robert Columbia re 'We provide a corrected proof in Appendix A.' or otherwise?
    – BCLC
    Oct 20, 2021 at 17:06

3 Answers 3

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Given the situation as you describe it, in particular that there is evidence that the author could have corrected the presumably-small mistake themselves, I'd recommend that you quote the true assertion, and/while noting, literally, that there is an easily correctible error or typo in the proof as written.

Catching typos is important, but is not "research", of course. And, yes, once typos or silly mis-statements are pointed out, many authors can repair them without hesitation. So I myself generally consider "paper X" to be "paper X with all trivial typos and obvious blunders corrected". (Still, yes, sometimes the boundary of this is not clear...)

In particular, yes, I give credit to authors for obtaining a result who've slightly messed up the argument, both for observing what is true, and for at least approximating the proof.

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  • My advisor did precisely this in one of his papers. He cited the earlier paper for a particular result and added a footnote, which pointed out the easily correctable error in the older paper.
    – Buzz
    Aug 29, 2017 at 2:32
  • To add to this, mathematical typos are pretty common, and when they're "obvious" they're probably only worth pointing out if they're in a statement of a result, rather than a proof, as a note to people who might look at the paper without reading it carefully.
    – Kimball
    Aug 29, 2017 at 14:52
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    I've seen all sorts of ways of addressing this issue, some more questionable than others. In a recent paper, the authors solve what they call a conjecture of so-and-so. They also describe some issues with a potential attempt to prove the conjecture. If you go to so-and-so's paper, you see that there is no conjecture, instead the result is stated as a theorem, and a proof is given. The "issues with a potential attempt" actually describe the mistake in the published proof. Aug 29, 2017 at 18:02
  • Thank you for the advice. All of the answers seem very reasonable! Aug 30, 2017 at 13:19
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    @BCLC, providing a corrected proof, if the errors are not completely trivial, can be worthwhile, in my opinion, as it really does carry out the execution of the expected corrections, rather than merely claim that "corrections exist". :) Some referees would want such an appendix to be cut, but nevermind. Oct 20, 2021 at 17:12
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I believe that paul garrett is pretty much correct here, but here's a way you can incorporate this into your paper:

Smith and Jones (1995) found that the area under the rhomboid apparatus was upper-bounded by the third order discriminant. While their final result is valid, a minor flaw was found in their proof. We provide a corrected proof in Appendix A. Given the established upper bound, we now show that the lower bound is negatively correlated to the complex derivative under the hyperspace gradient....

This approach gives your reader the "best of both worlds". You acknowledge the source upon which you build your own findings, acknowledge the minor flaw in that source, and provide a proof that your reader can rely on.

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2) Say something like ... "the results are based off the ideas by author X" but don't give as much of a "these are author X's results" flavor. Author Y then after mentioning author X, proves the theorem themselves.

You’re missing the forest for the trees here. The result is author X’s result. A small mistake that anyone can correct cannot reasonably be said to change that fact. It would be rather small minded of you in such a situation to try to give the impression that author X does not deserve 100% of the credit but that someone like you had to come along and “prove the theorem themselves”. Depending on your precise phrasing, it can even come across as intellectually dishonest and/or insecure.

The best thing that you can do to serve both author X and your readers is give author X full credit for the result, while at the same time pointing out that their proof contained a small error (and as I said there is no inconsistency between saying those two things), and then explaining, in as much details as you feel is needed, how the error can be corrected.

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