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I was part of a paper where the section I wrote for my contribution (as an undergrad) was edited by the person mentoring me. The prose for this section explains things correctly, but the mathematical notation doesn't quite make sense or add up to me. I initially wrote the mathematical notation differently (to back up the prose), but they changed it. I raised this once verbally, but that didn't end up going anywhere -- I wasn't sure if I just didn't interpret the notation correctly (as I am an undergrad after all) or if it wasn't quite correct. The section also contains work which was built upon and improved by the person mentoring me (they made modifications to the original contribution I had made) so in some sense, I thought that they had intentionally changed it with that in mind. It's been nagging at the back of my head though, and as of now it is heading into publication (it passed peer review). I assumed because it passed peer review, that I was incorrect about the mathematical notation (and it was indeed acceptable).

What are the consequences if this is a mistake? It feels like one, but I am not sure. The results of the paper are not changed in any way -- the prose and psuedocode explaining the algorithm are fine, but there's 2 lines of mathematical notation which do not seem correct to me.

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    I agree with the accepted answer, but all coauthors are jointly responsible for a paper, so usually your mentor should try to answer your question; ideally you should get to consensus, or he should explain why that's not possible, sth like — "yes, I can see why that's confusing, but this notation will make sense once you've learned <fancy theory X> in a few semesters, and it's too hard to summarize for you"; and even then, will the readers know. (I know category-theoretical notation that'd qualify).
    – Blaisorblade
    Commented Aug 21, 2023 at 13:00

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Probably nothing happens unless there is really an error and someone notices and contacts the corresponding author who, I assume, is someone else. Then it might get corrected.

But a lot of sophisticated readers might just ignore the error, if it indeed exists, and be guided by other things, such as the prose.

People make errors, others recognize them. Not every error needs formal correction.

You seem to have done what you could and the overall responsibility lies elsewhere. Let it go unless someone points it out to you and then you can provide guidance as needed.

Some journals will publish an errata page for published papers. This implies that someone has pointed out errors to them and asked for correction. This would most often be the corresponding author, though it might be others. But someone has to at least think the error needs correction and the editor needs to agree.

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    Ah, thank you so much! Very relieving to hear something like this.
    – quark88
    Commented Aug 20, 2023 at 17:54
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    I'd echo the point that more sophisticated readers will look at the (information-theory-wise) more robust prose, where a spelling or grammar error is usually easily correctible, as opposed to the relatively fragile formulaic stuff, which is more fragile due to its being more information-dense. So, don't worry.
    – paul garrett
    Commented Aug 20, 2023 at 20:50
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    Not sure about mathematics but in physics a mathematical notation error will usually get an erratum -- a set of short statements that "equation (14) should have had X instead of Y", for example. These corrections are common and expected.
    – Shern Ren Tee
    Commented Aug 20, 2023 at 21:55
  • @ShernRenTee you should post this as an answer.
    – qwr
    Commented Aug 21, 2023 at 17:57
  • @qwr (1) It was (implicitly) covered by Buffy under "Then it might get corrected" (2) It therefore didn't add that much content on its own (3) It was physics-specific; I don't know how errata / corrigenda / et cetera work in other disciplines.
    – Shern Ren Tee
    Commented Aug 22, 2023 at 2:40

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