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I have come across a couple of math articles published between 2005-2010 that have clear errors in them (the articles have a common author). Most of the errors are typos but a couple of errors, let's say, reinterpret basic theory. No erratum has been issued for the articles. The journals are peer reviewed (which is another story) but they are not from what one would call top-tier journals. However, I note that these articles have been, and continue to be, cited despite the errors - sometimes by articles in journals that are considered top-tier. In one case this has kept perpetuating a typo error in an equation. (It seems those citing the articles just accept what was written - again another story).

I have written to the author but no reply. The journal response was basically that unless the author wants to correct it, nothing much can be done. It was also said that as the articles were now 'old', correcting them was - in their words - not efficient.

My question is should I persist in having the errors corrected? Or do I just leave such errors to be repeated? I have considered writing a letter to the editor for publishing to highlight the errors - in the hope it will 'force' a correction the original articles (assuming the letter would be published). Ideas welcome.

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    I'm having difficulties to understand which kind of errors you are referring to. Do the typos change the mathematical meaning of the results? And what does it mean to "reinterpret basic theory" in mathematics? Correctness of mathematical results is not a matter of interpretation.
    – Jochen Glueck
    Oct 15, 2022 at 19:18
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    @JochenGlueck - I'm not getting into specifics as this question is about how to report errors found in an old article. Hopefully the answer can also apply to articles on other topics and not just limited to math. If I want to explore the math errors specifically, I can raise that with the appropriate math community on StackExchange. PS: oh, yes, the typos do effect the results (otherwise why would I raise them as errors).
    – Mari153
    Oct 16, 2022 at 1:33
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    The nature of the typo is important. The typo may be small enough to be considered trivial to experts in the field, such that they are unlikely to even notice it. If the citing papers don't make the same mistake, that's a hint that this may be like pointing out someone's typo within Stokes' Theorem. Politely let the journal know about it once, then there is unfortunately little else you can do. Personally, I think going a bit nuclear on the editor like you've suggested is a touch much for an "um, actually..." technicality/error.
    – Jerome
    Oct 16, 2022 at 4:04
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    Welcome to science in 2022. See also Ted Hill, How to publish counterexamples in 1 2 3 easy steps. But don't worry, you might succeed in just 15 years.
    – darij grinberg
    Oct 16, 2022 at 15:12
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    (An easy thing you can do right now is to point out the error in a paper or preprint you write. This way, at least if a reader follows citations backwards using Google Scholar, he will eventually find the correction. Many errors have been corrected this way. This isn't that much different from journals publishing errata in the next volume.)
    – darij grinberg
    Oct 16, 2022 at 15:16

4 Answers 4

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Neither the journal-level impact nor the age of the papers should matter. The articles still form part of the current stock of scientific discourse, especially if they remain to be cited.

You already reported it to the editors and the authors first. They did not bother to publicize the error.

A next step could be to publicize it either in a letter to the editor, as you thought about already, or to do it via 'post-publication review' platforms like PubPeer. You can do it anonymously or with your name attached to your comment.

(Note that PubPeer comments do sometimes lead to corrections or even retractions.)

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Have you considered publishing an erratum / corrigendum yourself? An introduction to the topic with a correction (and possibly some other minor additions) would be welcome in a lower-tier journal, I believe; this especially if the error continues to get cited and propagated.

You can cite several examples of other papers that build on the incorrect result, so that their authors also have the occasion to get notified (I believe many authors have a 'vanity search' active so that they get notified for citations to their own papers).

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    (+1) And the title of the paper could be “A cautionary note on …”. One of my late colleagues told me about an academic who ran up their publication list with lots of these cautionary notes. ;-)
    – Ed V
    Oct 15, 2022 at 12:12
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Note that not every error in a math paper necessarily invalidates the entire paper. You don't say that what gets referenced in those citations implies that what is false (or unproven) is actually true. The citations could, in principle, be of other, correct, parts of the paper.

Moreover, if the errors are widely known but not considered important or relevant to the purpose of the citation then those errors matter little, except to novices who might be misled.

Another issue in mathematics is that some papers have flawed proofs, but no one doubts the validity of the theorem. I once worked in an area with the reputation that all papers had such errors. Many of those "flawed" papers were by very eminent mathematicians.

And, if the errors are both serious and you have evidence questioning the results themselves, not just the correctness of the proof, then you have an opportunity to write a correcting paper. If you get that published, people will wake up to your concerns, especially if those results are important to what is cited from the flawed paper.

Note that in Real Analysis, epsilon-delta proofs that are three or so levels deep are devilishly difficult to get right - even for experienced experts in the field.

And note The Magical Number Seven ....

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If a paper in a top journal cites and uses a flawed result in an important way, I'm sure the author of the paper would like to know about it. You could write to these authors and say you believe there is a mistake in the cited work, which led to a mistake in this author's paper. This would both serve the purpose of correcting that particular top-journal article, and raising awareness of the issue.

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