Why isn't it common for papers in pure and applied math (and other related fields) to be modified/corrected after it has been published?

Question

As research grows even more intricate in fields such as pure and applied math (and other technical areas), very few reviewers now have a complete picture of any single field. Thus it should be common for more mistakes to be published (in a journal or in a conference).

This said, it is very uncommon for anyone to (at least successfully) edit an article after it has been published. Some reasons for editing may include:

1. a (reasonably minor) error has been spotted, e.g., a negative sign is missing, typos that are not simply grammatical mistakes.
2. an important reference that was missed.
3. a result which has been proven wrong because of a very technical edge case that everyone has missed, but was not essential to the proof.
4. simulation was off by a tiny factor
5. some other minor, and not detrimental issue to the paper, such as a misplaced figure, mis-referenced equation (cannot tell you how many published papers have [?] in them)

Nor are there really any mechanism in place to promote authors to fix errors after publication. Yet plenty options for authors to repeat upload till "final version".

I am very curious as to why this is the case.

Answer 1

The primary reason is that journals are "publications of record". They just record a specific version of a paper, namely the one that actually gets printed, along with important data such as who wrote it and when it was submitted.

You are of course free to put corrected versions onto your website, or maybe onto preprint servers. But in the end, that's not the "version of record" as you can change whatever you want on it -- you can add and remove authors, etc., and it's hard for anyone to track down when exactly a particular change was made if a dispute should arise who came up with an idea first. It's of course true that journals today could just do that on their websites: allow newer versions of papers to supersede older versions, but then that would require some kind of editorial process that journals are not equipped to handle.

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Completely separately, though, I take issue with your opening statement: "very few reviewers now have a complete picture of any single field. Thus it should be common for more mistakes to be published". I don't think that there is proof that that is true -- science was difficult 50 years ago, and it is difficult today. I don't believe that authors or reviewers or editors are any worse equipped today to assess the contents of papers than they were 50 years ago, and so I see no reason why we should expect more mistakes.

Answer 2

To add to @WolfgangBangerth's answer:

• We to have the tool of errata in place. If the mistake is non-negligible, but not so substantial that a new paper is warranted, write an erratum.

• For books, we have editions. This could be done for papers as well, an indeed e.g. arXiv does that (calling it version rather than edition).

• Papers are supposed to record the cutting edge of research. Thus, we expect or at least need to consider that their content may become outdated.

  • They give a record of what was known at the time of their writing. "Known" includes what the authors realized back then, not what the authors could have realized from their data had they already had the enlightening insightful thought that in fact happened only years later.
    It is important to keep record of this, we do not want to muddle historical tracks.
  • It is maybe not worth while fixing typos & Co. a few years after publication in a situation where the reader anyways has to do their due diligence on updates of the topic/content.
    The effort could better be spent towards gaining new insights.