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I am a PhD scholar in mathematics, in particular number theory. Recently one of my research papers was published in a journal. This was the 4th revised version. All the 4 versions can be found in arxiv. The previous 3 versions had some major mistakes. However I have made it accurate in the 4th revision making it vastly different than the previous 3 versions, and which finally passed through peer review process and is now published.

The one thing I am worried about: Suppose someone tracks that paper in arxiv and found that it had 4 versions before publication.

Would it make a negative impact on my research or it is normal in research ?

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    Isn't revision to a better version the whole point of doing math and science? The newer the idea you propose, the more mistakes you will make along the way. Don't ever feel shame or regret for "mistakes" of that nature.
    – Mad Physicist
    Commented Apr 19, 2022 at 18:52
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    For most of us, the risk of nobody ever reading the paper on arxiv is far higher than the risk of someone comparing the different versions on arxiv to spot the mistakes. That would be petty, and also a waste of time. I wouldn't worry about the revisions on the arxiv.
    – Clumsy cat
    Commented Apr 19, 2022 at 21:15
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    @Clumsycat. What are they going to do? Accuse you of learning and making progress?
    – Mad Physicist
    Commented Apr 19, 2022 at 22:25
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    Some very rough statistics using the number of results for a google search limited to "site:arxiv.org" with query "this version, v2" (with v2 replaced for other versions) v2: 234000, v3: 79400, v4: 24900, v5: 8040, v6: 2800 This doesn't work for "v1", but there seems to be around 4.5M submissions indexed by google. So, to the extent this approach is valid, from 2nd revision onwards there seems about a 1 in 3 chance for each next revision.
    – towr
    Commented Apr 20, 2022 at 6:11
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    @MadPhysicist Your not wrong, but to be honest, some of my arxiv revisions do include quite embarrassing mistakes. Everything from writing Poison when I meant Poisson to mistakes in formula. However, if anyone is interested enough in my paper that they are checking previous revisions of it, then I'm more flattered than embarrassed.
    – Clumsy cat
    Commented Apr 20, 2022 at 7:06

5 Answers 5

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It is not uncommon for manuscripts to change significantly during the review process --- this is what peer review is for! In my experience, having 4 rounds of review is a bit excessive --- typically most major errors should've been spotted pre-submission by the authors, or, when the main author is an early career researcher, by their supervisor. If major errors make it into the submitted version, it often leads to rejection of the manuscript, to encourage the authors to check their work rather than to lean on reviewers. If this is ensured, minor inaccuracies can be caught during the 1st and 2nd review.

Having said that, ultimately what matters is that you have successfully published a paper. You have surely learnt a lot about research through this process, which is the goal of your PhD project. Hopefully, your subsequent papers will be accepted easier and with fewer revision cycles. Good luck!

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It would not make a negative impact on your research (how could be?) and it would not make a negative impact on your reputation.

From how you describe the work, however, it seems like you would need to find better collaborators, or to look for more internal reviews from peers, since 3 major mistakes in the same paper hints at the fact that the paper was not ready to go public in first place (in my opinion).

But then, arxiv may be used exactly for that, to have a blind peer review, so I do not see the issue with the history of your paper.

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    It's particularly difficult in a PhD because in "real life" it's easier to have collaborators with out impacting on the personal originality of the research.
    – Dan
    Commented Apr 21, 2022 at 8:15
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I am also a PhD student in a number-theory adjacent field. I don't think most people look at old arxiv versions except by mistake. There are many other reasons for there to be multiple versions. For example, one might revise the paper before submitting it to a journal, and then post an updated version to the arxiv with those changes, and then do the same to the refereed text (most journals allow this). There is also no particular shame in a young person posting mistakes to the arxiv, especially if they turn out to be salvageable as yours seem to have been. If these mistakes were caught by people reading the arxiv preprint, then the arxiv is doing one of its jobs. If you caught them yourself, it's probably a hint that in future, you should wait a bit longer to post things.

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    Thank you. Yes your first guess also happened. I myself found mistake and thereby reorganized the paper before submitting to journal. The journal published asked only one major revision. The other revisions are done before submitting to the journal
    – learner
    Commented Apr 19, 2022 at 20:45
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Would it make a negative impact on my research...(?)

Most/all answers say no. However in a competitive situation (be it healthy competition or nasty) it could still be brought up at some point - and when you might least expect it or be prepared to respond.

You might be giving a colloquium or a talk as part of an application for a position or funding, there will be questions, and someone may ask in a very polite way

Your results are fascinating! We can see from arXiv that your route getting there was equally fascinating, can you share some of that with us?

Have an answer in mind! Have a prepared response, so if the question ever arises, be it over tea or coffee or in a very exposed setting, you can respond without skipping a beat.

Make it an interesting story. Bring your listeners along for the ride. If it's necessary to mention a mistake, make the mistake sound interesting and delightful!

Everybody makes mistakes, but we often forget ours when thinking about others'. When you bring them along in your recounting it's more likely to remind them of their own (somewhat) similar experiences.

Do not volunteer this on your own. But have this ready if it ever does come up, no matter how likely.

...or it is normal in research?

It's not typical but what is/isn't "normal" isn't really a concern. I don't think it's a six-sigma event.

As other answers indicate, that part doesn't matter. There's no "normal" in research.

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It's completely normal. Almost all manuscripts go through multiple rounds of revision (even rejection) before getting published; it's pretty much unheard of for a paper to get published as-is with no revision whatsoever. No reasonable academic would judge you poorly for having gone through revisions.

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