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In short, I'm wondering how likely is the following sequence of events. The context is research in pure mathematics.

  1. A researcher submits a paper containing new results for review in a journal in hopes of publication.
  2. The reviewer acknowledges that the new results are both correct and indeed would constitute a novel and a nontrivial addition to existing results in the area. However, they reject the paper since the proof is lengthy, computational and difficult to follow.
  3. Immediately or after some time, the reviewer comes up with their own proofs for the same results, shorter and more presentable than the one from the original paper. The reviewer then submits their own work to some other journal and it gets published.

(The presentability of results is of course subjective to the reviewer's affinities and background, but for the sake of this question assume that the reviewers assessments regarding presentability in 2. and 3. are reasonable and difficult to be argued against.)

I see no reason why this would not be possible as the reviewer is not technically plagiarising anything. Firstly because there is no published work to plagiarise (because the original paper was rejected), and secondly because their paper would just contain the same theorems but with entirely unrecognizable proofs (and superior ones, at that). Their paper could even acknowledge that the original researcher made them aware of the result.

If all of this is possible, how should the original researcher go about defending against it? An obvious safeguard is publishing a manuscript of the original paper to arXiv or a freely accessible personal web page, and to try and publish the paper in some other journal before the reviewer manages to publish theirs. Would this suffice?

My concern is that the main contribution of the original paper is the novelty of the results themselves. Once the reviewer (or any other experienced researcher in the field, for that matter) was made aware of them and studied them carefully, it is indeed likely that they could come up with a superior proof, or even with an improvement on the theorems themselves. I would assume that this would render the original work unpublishable and superfluous.

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    "the reviewer is not technically plagiarising anything. Firstly because there is no published work to plagiarise (because the original paper was rejected)" There is no requirement that plagiarism only counts as plagiarism if the original work is published. You can plagiarize from preprints, research notes, talks, conversations, etc. Plagiarism (excluding self-plagiarism for simplicity) just means you are taking someone else's work (note that "work" does not mean "published paper") and presenting it as yours. Apr 18 at 10:41
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    Question. In paper 3, does the reviewer refer to 1 ?
    – GEdgar
    Apr 18 at 16:36
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    I believe this happened once. There was a trail of emails and documents proving that the reviewer has pillaged the work from someone else and the paper was withdrawn.
    – Tom
    Apr 19 at 13:04
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    @AgnishomChattopadhyay I disagree in the following way: "double-blind" means "identities are not disclosed as part of the reviewing process", but it never means "it's impossible to determine the author's identity if we try to". A referee who wants to find out who the author is will almost surely be able to even without an arXiv preprint. (They shouldn't try to either way, of course.) Apr 19 at 18:02
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    @AgnishomChattopadhyay That is a problem with the concept of double blind reviews, not with pre-publishing on arXiv.
    – TimRias
    Apr 20 at 17:52

7 Answers 7

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Pure mathematician here. The sequence of events described is very unlikely to happen, because of cultural forces in pure math designed to prevent it. If the situation the OP described did happen, it would be bad for everyone involved:

  1. The authors would rightly feel like they were scooped, since they proved these results first, and then the referee (who had non-public access to their work) proved the same results. If they had not been the referee, they would not even have been aware that the results were true.

  2. The editor would rightly feel betrayed. This kind of behavior is a major breach of ethics on the part of the referee. The editor would talk, and the referee would get a reputation as someone who cannot be trusted.

  3. The referee would suffer terrible reputational harm, when the story came out.

Now on to some more specific points:

I see no reason why this would not be possible as the reviewer is not technically plagiarising anything. Firstly because there is no published work to plagiarise (because the original paper was rejected), and secondly because their paper would just contain the same theorems but with entirely unrecognizable proofs (and superior ones, at that).

The referee's behavior is a clear breach of ethics. It does not matter at all whether the paper where the referee got the ideas was published, or even whether it was a public preprint or not. The Oxford dictionary defines plagiarism as "the practice of taking someone else's work or ideas and passing them off as one's own." Clearly, the referee learned of the statements of the theorems from the preprint, took those ideas, and passed them off as their own, even if they wrote different proofs for the theorems.

In math, sometimes the main contribution of a paper is to prove a known conjecture using new techniques or cleverness. Other times, the main contribution is to ask an interesting question, even if the techniques to answer it are standard. Sometimes, an unethical person could scoop a work in progress just by getting the statement of the theorem the authors were proving.

Their paper could even acknowledge that the original researcher made them aware of the result.

This is a step in the right direction but is not sufficient. The ethical thing is for the referee to write to the authors and suggest a joint paper where the contribution of the original authors was figuring out the theorem that is true, and the contribution of the referee is a streamlined proof. If the referee had figured out the streamlined proof while refereeing the paper, they could have also given the proof to the authors as part of their referee report. Things like that do happen in math, and it's a nice, encouraging thing to do for junior authors when you find yourself refereeing their work.

If all of this is possible, how should the original researcher go about defending against it? An obvious safeguard is publishing a manuscript of the original paper to arXiv or a freely accessible personal web page, and to try and publish the paper in some other journal before the reviewer manages to publish theirs. Would this suffice?

Yes, a good first step is to put the paper on arXiv. In math, we have strong cultural barriers that prevent other researchers from scooping results that are on arXiv (though, of course, sometimes two teams will legitimately prove the same result at the same time). It is better to put the paper on arXiv than on a personal web page, because the arXiv timestamp is widely respected in the field. The authors should also reach out to the referee to make sure they know about their previous work (because we're a single-blind field, the authors would not know that the referee had been the referee for their paper), and to coordinate how the papers cite each other. It would be fair if the referee's paper explicitly says the results were first proven by the authors (and cites their preprint on arXiv) and if the authors point out that subsequently to their work, shorter proofs were found. The authors' paper should still be published, but indeed it's good not to delay submitting it to another journal.

My concern is that the main contribution of the original paper is the novelty of the results themselves. Once the reviewer (or any other experienced researcher in the field, for that matter) was made aware of them and studied them carefully, it is indeed likely that they could come up with a superior proof, or even with an improvement on the theorems themselves. I would assume that this would render the original work unpublishable and superfluous.

When I was just starting out in math research, I often felt that way about my preprints. Here are some things to keep in mind:

A. It often seems clear to you after you've figured it out but might still not be that obvious to others. We often underestimate the novelty of our own papers because we understand them well, whereas we often struggle to understand the papers of others.

B. Experienced researchers are incredibly busy with their own research and unlikely to go around writing down shorter proofs of other peoples' results. And, the cultural factors I wrote about above tend to prevent unethical behavior, so even if someone did quickly write a shorter proof of your result, they would acknowledge you and would not prevent your work from being published.

C. When you do a bit of math, you should want others to come along and build on it, finding a shorter proof, generalizing the result, working to strengthen the conclusion, etc. That is the nature of research, at least if the research you did was interesting.

D. Even if someone did build on your paper, that would not make your paper unpublishable. It has happened to me many times that I proved something basically at the same time someone else did, with similar proofs. In all cases, my work cited the other work and theirs cited mine, and both works were published. Editors and referees understand that publications are important for your career, and that research consists of incremental contributions. Furthermore, the fact that someone else was interested enough in your work to quickly build on it looks good for your work, and suggests to the editor that it's important and likely to be highly cited.

In conclusion, try not to get anxious about potential worst-case scenarios. Try to do interesting work, and try to come up with good, clear proofs that are not "lengthy, computational and difficult to follow." When you finish a paper, submit it to arXiv and send it to a journal a week or two later (giving time for comments you might receive as people read the arXiv version). Then, while the paper is under review, go write a different paper. Soon enough, you will be well-established and won't have to worry about others scooping you.

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    This is the correct answer, and good advice. In pure math, I believe in general people are pretty careful about attributing results, at least recent ones. You can find many papers with notes such as "Theorem 1.1 was also obtained independently by X and Y in ..." when two groups prove similar results around the same time. Apr 18 at 12:40
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    I think most of this answer talks about a scenario that is quite different from what OP asks about. OP wrote: "Their paper could even acknowledge that the original researcher made them aware of the result", indicating that they are not thinking of a situation in which the reviewer makes active efforts to pass off the theorems in the paper as their own; rather, the reviewer cites the earlier work and publishes a paper claiming only the novel element of "shorter, more presentable proofs". That situation is the one I address in my answer.
    – Dan Romik
    Apr 18 at 17:17
  • ... As for the situation of a reviewer committing plagiarism, that would indeed be very unethical. However, to the extent that this is something OP needs to worry about, I don't see why they need to be more worried about the reviewer committing this plagiarism than about anyone else committing it. As I said in my answer, once the paper is on arXiv literally anyone can try to improve on it (and literally anyone can plagiarize it if they wish to behave unethically). The reviewer has no special advantage, and no more incentive than anyone else does to behave unethically.
    – Dan Romik
    Apr 18 at 17:19
  • @DanRomik I addressed that part of the question ("Their paper could even acknowledge...") in the middle of my answer. But, because the OP was asking whether uploading to arXiv could protect against the scenario, in the beginning of my answer I was assuming the paper had not been uploaded to arXiv and was not publicly available. From the mid-point of the answer on, I address how putting the paper on arXiv changes things. I think most of what's in your answer is already in mine, but, hey, it doesn't hurt for the OP to hear it twice. Apr 18 at 17:20
  • @DanRomik "...why they need to be more worried about the reviewer committing this plagiarism than about anyone else committing it." The paper is indeed already on arXiv but I have several quite specific reasons to be worried about the reviewer in particular, rather than anyone else: 1. The result is quite obscure and unlikely to attract the attention of the right people who would be even interested in shortening the proof. 2. The paper is indeed quite long, technical and contains lengthy computations which are themselves very elementary but extremely tedious and difficult to follow. Apr 18 at 22:43
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When you upload your paper to arXiv you make it so not just the reviewer of your paper, but anyone in the world, is completely free to try to improve on your work (whether by strengthening or generalizing the results, finding different/better proofs, or in any other way). This is not at all a Bad Thing or something that should particularly concern you; it is for the most part a Good Thing. Your paper is public and timestamped and therefore you have established priority over your ideas. If someone else comes up with an improvement, they will get credit for the improvement, but they are required to credit your earlier work by citing it (the preprint version if your paper is not yet accepted anywhere) and giving a clear explanation of which ideas in their paper are novel. If they do not give such credit, they are committing plagiarism. All of this is true regardless of whether the author of the paper with the improvements is/was the reviewer of your paper or anyone else.

You raise the practical concern that once a paper with improvements of your proofs is published, "this would render the original work unpublishable and superfluous." This is simply not true. You are still free to submit your paper to journals, and any fair-minded person assessing your contribution will still be able to see that your paper with the supposedly inferior proofs pre-dated the other person's paper with the slicker proofs. They will understand that your paper brings forward original ideas that were then built on and improved by others. Thus the work is entirely publishable. Moreover, the fact that other people are finding your work relevant enough to keep building on it can well be seen as making the work more appealing and more publishable, not less. (And conversely, the other person's follow-up paper may end up being perceived as less publishable than yours, not more, because it only proposes new proofs of already known theorems.) Moreover, it is rarely the case that a "shorter or more presentable" proof of a theorem makes the original proof appear completely uninteresting; usually even a longer proof can still have an interesting idea or insight that is not made superfluous by a shorter, slicker proof.

Another hypothetical concern from this scenario is that because the reviewer is free to improve on your work as I described above, they might be tempted to reject your paper so that they can reap a benefit for themselves by scooping you with their own paper. This is also not a realistic concern: while it would indeed be unethical for the reviewer to reject your paper out of an ulterior motive, they have no incentive to do so, since as I explained above, your arXiv preprint gives you priority for coming up with the theorems in your paper and being the first to prove them. The reviewer's follow-up paper gains no advantage or extra credit from your own paper having been rejected. If anything, the incentives are pointing in the reverse direction: if your paper is accepted, particularly to a prestigious journal, then the reviewer's follow-up work will get an extra boost in credibility and prestige as it can now claim to be improving on work from a top journal.

To summarize: upload all your preprints to arXiv and you will be protected. If you think your proofs are ugly and may be superseded by slicker proofs other people might come up with later, that may be a valid concern, and it makes sense to spend some time trying to make your proofs as presentable as possible prior to going public. But this is a pretty microscopic concern and is not usually worth worrying much about, since experienced researchers know that it is in the nature of things (and usually a Good Thing) that their work will be built and improved upon by others. Finally, it does not make sense to worry specifically about the reviewer of your paper coming up with improvements to your results and trying to sabotage you in some way.

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  • Thank you for taking the time to explain incentives behind the reviewer's possible actions. I address one of your points in the comments to David White's question. Apr 18 at 22:47
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    @mechanodroid it sounds like the reviewer rejected your paper because your proof is too complicated, and said they found a much simpler proof. While that may be disappointing to you, I don't see this as evidence that the reviewer is doing anything wrong or unethical, or that their decision to recommend rejection was not made in good faith. And since your paper is uploaded to arXiv, you don't need to worry about getting scooped. The thing to do in this situation would be to resubmit to another journal, possibly after first using the feedback you got to improve your paper. Good luck!
    – Dan Romik
    Apr 19 at 4:33
  • Indeed, in this particular case the reviewer has not done anything wrong. My original question asked about the probability of them doing something wrong afterwards. You have adequately answered my question, thank you. Apr 19 at 7:56
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There is a similar case, well-known in mathematics.

G. D. Birkhoff, a distinguished mathematician, was a mathematics editor for the PNAS (Proceedings of the National Academy of Sciences (U.S.)). A young unknown mathematician (John von Neumann, later he became very well known) submitted a paper to the PNAS. The result there is nowadays called the "mean ergodic theorem". The paper was assigned to Birkhoff to review. In fact, Birkhoff accepted the paper for the journal. But Birkhoff was inspired by it, worked very hard for a few months, and came up with a stronger theorem, nowadays called the "pointwise ergodic theorem". He wrote that as a paper of his own. The two papers were published in the same issue of the PNAS. But Birkhoff's paper did not mention von Neumann's paper. Only many years later did Birkhoff admit in print that he had been inspired by the von Neumann paper.

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    Very interesting. Do you have a reference where this story is told, or where Birkhoff made the admission you mention?
    – Dan Romik
    Apr 19 at 20:32
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    For context, in some circles, G.D. Birkhoff has reputation for being ... "ingenerous". Oh, ok, yeah, also vocally anti-semitic (von Neumann was ethnically jewish...) I do think that this taints some of these situations... Apr 20 at 1:33
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    Birkhoff's theorem is several orders more complicated than vin Neumann's mean ergodic theorem . Birkhoff's proof was so complicated that over the years several illustrious mathematicians provided gradually simpler proofs. Apr 20 at 10:37
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    It’s a great answer and story, upvoted. And thanks for the cool reference @usr1234567, I agree with you that the relevance to OP’s actual question is limited, both because it appears Birkhoff was not the reviewer for von Neumann’s paper, and (perhaps more importantly) because von Neumann did not upload his paper to arXiv.
    – Dan Romik
    Apr 20 at 14:02
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    @usr1234567 George Birkhoff acknoledges the work of von Neumann on the first page of of his paper on ergodic theory. pnas.org/doi/full/10.1073/pnas.17.2.656 Apr 20 at 17:05
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In the '80s and '90s, some high-temperature superconductivity researchers would modify initial their submissions to journals and make significant last-minute corrections to avoid such problems.

These physicists would grow new materials and test their properties to search for signs of superconductivity; there was (and still is, see Ranga Dias) enormous competition to grow materials that show superconductivity at high temperatures. Some authors noticed that immediately after they submitted papers for review, other groups (likely reviewers) would suddenly report having grown the same material and try to scoop the results, so they altered element names in their reported material's chemical formula while submitting for review, and fixing this issue only once the paper was ready to be published.

Funnily enough, it turned out that the fake material whose name they made up also turned out to be a high-temperature superconductor when other groups tried to scoop the paper that was in review by growing it, but the original result was still significantly more impressive because it superconducted at higher temperatures than the "fake" material.

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    It sounds like bad things along the lines of what OP is worried about were indeed occasionally happening in the era before arXiv. Can you comment about whether this is likely to happen today with a paper that has been uploaded to arXiv? (My own answer dismisses OP's concern as unrealistic because of arXiv, but I'm curious if in a context outside of pure math such as experimental physics there are still incentives in play that can cause a reviewer to behave unethically.)
    – Dan Romik
    Apr 19 at 20:35
  • @DanRomik My impression is that when the paper is on the arXiv, it is "out," in some sense. It isn't given the same authority as a peer-reviewed article, but the authors are still expected to defend claims made therein if other researchers fail to reproduce the results. On the other hand, the reviewers' job isn't to reproduce a paper (so if they can't reproduce the results, it isn't inherently a problem), and a paper that is in review but not on arXiv is not a "public" assertion by the authors. Apr 19 at 22:41
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    Thus, reproducing a paper from the arXiv and submitting it to a journal would not, in my opinion, be "scooping" today. And submitting a deliberately incorrect result to arXiv to protect an in-review work today would be significantly more unethical than the scenario described in my post (though it's debatable whether misleading reviewers in that manner is ethical). Apr 19 at 22:41
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As it is written above, stealing somebody's ideas is plagiarism, too, and there is no excuse.

I would do the following.

  1. Write to the editorial board, show them your case and ask them to withdraw the paper by the plagiariser.
  2. If this fails, write to the publisher stating that the editorial board of their journal ignored you about the plagiarism case.
  3. If this does not work, go to court against the publisher. Try to highlight your case in press and social networks as widely as possible.

I strongly believe that this should be well enough, no serious publisher would like to have reputation spots like this.

I should add that people behave like this in science mainly in societies where such behaviour - to steal something from somebody who is weaker than you - is generally common (like in Russia).

Particularly, I had my own case like you described, but was lucky - the paper written after reading my manuscript by a reviewer came, vice versa, to me for revision. So I wrote to the editor about the situation providing proofs. The plagiariser is now likely in the black list of several large international publishers, as they published 0 papers in international journals after this. But I also saw examples when older academics ruined the careers of younger colleagues by stealing their results. You should never go to peace agreements with such people; they must meet the resistance and must be punished for what they do. Their normal business is either to steal as much as the victim allows by its own silence or to persuade the victim to pass his results by own will.

Make your voice loud and do not feel ashamed about making problems for the careers of plagiarisers / do not be afraid to conflict with them! People behaving like this do not understand good will, but they respect only strength.

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I frequently read in the acknowledge section that anonymous referees helped to improve papers. Immediate ideas to improve a paper are usually shared with the author and not kept to the referees to exploit as easy papers.

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I would believe that the original author, at this point, has enough documentation to "prove" that the published material was lifted from the rejected (original) submission. In such an instance, the publication can be retracted in consultation with the journal editor(s). This is obviously an awful situation for anyone to have to go through.

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