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(Note: This question might be off-topic for MO but the only other plausible alternative that comes to mind is Academia Stack Exchange, and there are some features of this question that are, to some extent, peculiar to research mathematics.)

I recently learned that it is more difficult than I expected to document, in a permanent manner, a correction to an error in a published paper (let me call this an "erratum" although some people call it a "corrigendum").

The most obvious approach is to publish an erratum in the same journal that published the original paper. However, many journals have a policy that the erratum has to go through the full refereeing process all over again. While I don't personally know of any case where the erratum was rejected, the nuisance of having to go through the refereeing process is enough to discourage some authors from bothering to submit a formal erratum.

Another approach is to try to post the erratum on the arXiv. However, it seems that the arXiv has certain policies on errata that may also pose obstacles. For example, suppose that the original article is an old one that is not already on the arXiv. Apparently the arXiv will not accept the erratum unless the old paper is first posted to the arXiv. But in some cases there may be no way of doing this without violating copyright.

A third approach is to post the erratum on your own website. But most people's websites eventually disappear after they die, so this is not a solution to the problem of permanently archiving the erratum.

Is there any other good way of permanently archiving an erratum to a published paper?

It seems that many mathematicians take pride in, and rely on, the high accuracy and reliability of the published mathematical literature. However, if there are barriers in place that disincentivize the publication of errata, the reliability of the literature suffers.

ADDENDUM (July 2019): I thought I'd give an example to illustrate some of the difficulties. I recently submitted a corrigendum to a 2006 Notices of the AMS article of mine, "You Could Have Invented Spectral Sequences."

The good news:

  1. The Notices accepted the corrigendum without making me go through a full refereeing process, and published it on their website.
  2. If you go to the main Notices website, you can find the link to corrigenda/errata without too much difficulty (although it appears that currently, my corrigendum is the only item there).
  3. When I Google the article title along with "site:ams.org/notices" then both the article itself and the corrigendum show up.

The not-so-good news:

  1. If you didn't know about the corrigendum and just navigated to the relevant back issue of the Notices on their website, you would find no indication that there is a corrigendum.
  2. It's not clear that the aforementioned Google search works for everyone (e.g., it doesn't currently work if I instead try Google Scholar or DuckDuckGo).
  3. The Notices told me that the corrigendum will not appear in the print version of the Notices.
  4. I wrote to Mathematical Reviews and Zentralblatt MATH a few weeks ago to ask them if they would make a note of this corrigendum, and have not heard back from either one.

ADDENDUM (November 2019):

The MathSciNet review of my article now contains a pointer to the corrigendum on the Notices website.

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  • $\begingroup$ If the error is significant, it may deserve its own paper. Perhaps you might suggest what deserves to be called an erratum. Gerhard "For Ideas, Check Out 31337" Paseman, 2018.12.23. $\endgroup$
    – Gerhard Paseman
    Commented Dec 23, 2018 at 22:44
  • $\begingroup$ Not directly related but I find it extremely useful when MathReviews links to erratum in its reviews of papers, because otherwise there is often no easy way to know their is erratum. $\endgroup$
    – Sam Hopkins
    Commented Dec 24, 2018 at 1:19
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    $\begingroup$ @SamHopkins : Your comment is actually related because I once tried to add a reviewer comment to an old review of mine, after an error was discovered in the paper and I wanted to mention this. MR told me that they hesitate to do that kind of thing and they prefer that an official erratum be published. $\endgroup$
    – Timothy Chow
    Commented Dec 25, 2018 at 1:59

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There are two issues here, one is ensuring that the erratum is still online somewhere many decades from now, the other is ensuring that it can still be found. The first issue is actually simpler to resolve than the second.

1) Concerning the first issue, the persistence of a link, the InternetArchive (a.k.a. the "Wayback Machine") will make a snapshot of your file and store it indefinitely. They crawl the internet and may eventually find your file, but you can submit the URL to make sure it happens right away. Wikipedia makes extensive use of the InternetArchive to restore access to broken links.

2) The second issue of findability is more tricky. The study Linking of Errata: Current Practices in Online Physical Sciences Journals showed that many publishers do not do a good job of ensuring that the reader of the original article is directed to an erratum. They recommend the development of standards for the linking of original articles to errata, but these have not yet been widely implemented.

These two issues apply to any field of science, but mathematics is somewhat special because of the "eternal" value of a proven theorem. The presentation "Towards a world digital library" makes the case that "The mathematical accumulated knowledge is a scientific commons that should be preserved and made easily accessible for eternity". It discusses several initiatives, such as EUDML with that mission.

As far as I can tell, none of these repositories allows an author to submit errata on their own. For that purpose the route through arXiv seems the way to go for now. That repository is extensively mirrored and is committed to ensure its content will be retrievable a century from now. Since revised versions of a submission are linked to a common identifier, the second issue is resolved as well. Even if the paper is not yet on arXiv you can most likely post an author-prepared version without violating copyright. If it's a really old paper, this may mean retyping the text, but that may well be worth the effort.

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It seems pretty obvious to me that errata should be published in precisely the same way as the original contribution. If the author knowingly went through the nuisance of having to go through the refereeing process to have published the original, the same should apply to any additions or errata.

By the way, my impression is that nowadays one sees various errata, letters to the editors, etc. much less frequently than before, and the reason for that is not that people make fewer mistakes now. I know of quite a number of cases when the authors are perfectly aware of serious mistakes in their papers and still make no effort whatsoever to acknowledge them. Apparently this is becoming a part of the current culture.

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    $\begingroup$ I can understand that an editor might want to exert some editorial control over an erratum, but one of the purposes of refereeing is to decide whether the result is worthy of publication. That bar has already been met if the paper was published, and I don't see why it should have to be surmounted again. If the concern is that the erratum itself might be wrong, well, this is a case where I think the principle that the author assumes primary responsibility for correctness applies. I think it will be extremely rare for an erratum to be substantially wrong. $\endgroup$
    – Timothy Chow
    Commented Dec 24, 2018 at 0:57
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    $\begingroup$ So, I would argue that the threshold for accepting an erratum for publication should be lower than for accepting the original paper for publication. The fact that it isn't seems to be contributing to the unfortunate "current culture" that you point out. $\endgroup$
    – Timothy Chow
    Commented Dec 24, 2018 at 0:58
  • $\begingroup$ I know of some paper in my research area that had an erratum to an erratum (I won't name names to avoid hurt feelings). And, I think something like this also happened with Dan Biss. But I agree it's rare. $\endgroup$
    – David White
    Commented Mar 25 at 15:59

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