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The paper I just got to review consists of Theorem A and its Corollary B, the latter settling a major open problem in the field, it is said.

Unfortunately, the problem is not open, it was done in an obscure paper half a century ago (a not uncommon mistake, I must stress this doesn't imply or suggest foul play). I haven't yet started to read the submitted paper properly, but I know that - if correct - Theorem A on its own merits publication. I worry that if I point out the obscure paper to the author in the review, they may want to withdraw or very substantially change their submission, possibly making swathes of my review irrelevant and thus wasting my time and work. What is the proper etiquette here? Should I:

  1. complete an honest review of the whole paper and only then inform both author and editor that the problem was settled before?

  2. write a very short "why don't you mention that old paper?" review framed as "needs MAJOR revisions"?

  3. contact the editor and ask them to pass the information before I agree to write the review?

  4. write my review with a comprehensive comparison between the submitted paper and the old obscure one?

  5. other?

Point 4. is just a bonus question to see if people here do think that it's referee's duty to do so (I am of "in the perfect world we would have time for that" persuasion). I am wary of point 2., since it may prompt some editors to reject the paper outright, and it doesn't seem fair in this case. Hence I wonder about point 3. For what is worth, in my field I do have access to the paper before I agree to referee, so my impressions are not based just on the abstract, in particular I am sure the author does not cite the obscure paper.


UPDATE: Thanks everyone for your suggestions. Here's what I did, and why.

The paper under review and the older paper were both quite short for the field, so I spend one afternoon skimming through them. I concluded that the methods were significantly different, but there are parts of the older paper that will influence the body of the paper under review, and not only merit a "We note that the Corollary B appears in (...)" line.

I then filed a review recommending a resubmission after revision, pointing to the prior paper and how I see it might influence the present work. I explained that I didn't go too deep in the paper (for the reasons mentioned above) but I will be happy to review it if resubmitted. I also tried to be supportive, stating that the results seem correct (I could write that after that afternoon reading) and interesting, and in particular appropriate for publication.

I also wrote directly to the editor and appraised them of the situation. I politely asked them to a) contact the other reviewers and notify them about the prior work, as I honestly expect they may not know about it, or b) pass my review to the author before all other reviews come in. The editor sent me a generic "thank you for your time", and that was it.

I accepted Allure's answer, as I think that if the papers were not so short, I wouldn't be able (and willing to spend time) to compare them so quickly and thus would pass that responsibility entirely to the author. I also wouldn't be able to quickly write anything resembling a review, and so probably would just ask the editor to contact the author and persuade them to resubmit after they take a look at the old paper. Moreover I convinced myself that I should contact the editor outside of just filing the review, since it may take arbitrarily long for the other reviews to come in and are eventually made available to the author, and all this time is wasted for them (not to mention for the fellow reviewers, as in this particular case it is possible they too can be unaware of that older paper). What motivated me in the end was the possibility that the author could find out that older paper while still waiting for the reviews, and then worry (as before, arbitrarily long) about ramifications - hence I think it was better for me to break the news to them with a generally positive message as soon as possible.

While I don't know if I will be called to referee this paper again, it's nice that we mathematicians have arxiv and so I will be able to see what happens with it either way - published in this journal? elsewhere? better? For all interested, I promise to update this question again in five years or when the paper is finally published (whichever comes later:)

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    Are the authors incorrect when they say that people in their field consider Cor. B to be a major open problem? Or is it genuinely thought to be an important open problem and it's escaped many people's attention that it was solved a long time ago? (The latter situation is possible in mathematics, but I think it matters which situation you're in.) – Noah Snyder Oct 20 at 14:21
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    @NoahSnyder, the latter. I happen to know (and respect) people cited in the paper under review as the source for the problem being open, and I checked with them. They had no idea the problem was solved decades before they stated it in their papers as open. Nor did the reviewers at MathSciNet, both for their papers and for papers based on and connected to them, and so on. – lemon314 Oct 20 at 20:52
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    @NoahSnyder, I should also clarify that this ancient paper with the solution seems valid (I am reading through it now) and in any case comes from top tier journal. It is just from a completely different field, with the then genuinely open problem as a mere afterthought or an illustration of methods developed there. The citations are exclusively from field X while the problem belongs to Y. As the fields are indeed quite far apart, I am not entirely surprised that people in Y apparently completely overlooked it - as you say, this does happen. – lemon314 Oct 20 at 20:58
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    Wow that's rough! I feel bad for the authors. Certainly a tricky spot you're all in now. – Noah Snyder Oct 20 at 21:52
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    Nobody seems to have asked the obvious context: what is the lead time for this journal, what is the accept rate, how long would the author's expected lead-time (in another journal) be on the revised paper if they got a rejection on the current one, and are they a Masters/PhD/postdoc/other and what is their timeline? As a Masters student in a PhD world with an 18-month 'real-world' deadline to get published and get back into the job market, I was constantly amazed at the PhD attitude that needlessly inflicting avoidable 2-4-year delays on the submitters was acceptable. – smci Oct 20 at 23:57
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If I understand your question, you're saying that Corollary B has already been proved half a century ago, but the authors are apparently unaware of it.

If that's the case, you should point it out now, before you start reviewing. As you point out, the authors will probably have a lot to rewrite, which could make swathes of your review irrelevant.

I would tell the editor the issue and suggest pointing it out to the authors (i.e. option 3), but also say that you can review the paper anyway if they prefer. You can potentially save a lot of time this way. If they say you should review regardless, you probably don't lose much time, either.

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    Some wording would change, definitely. But isn't the paper now just a (new) Theorem A plus a new proof of Corollary B, whereas the initial claim was a (new) Theorem A and a previously unseen Corollary B, an important problem in the field? Because, alternative proofs of important results are still valid paper material. It might not go with that much bang as the authors initially hoped, but it does not make the paper unpublishable. – Oleg Lobachev Oct 21 at 20:55
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    @OlegLobachev right, but if as the question says it will likely result in withdrawal and resubmission, one might as well point it out now. It's possible one will again be asked to review the paper when it's resubmitted, and that would be the time to critique the alternative proofs of important results. – Allure Oct 21 at 23:24
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Let me suggest that you do a proper review and somewhere, it doesn't really matter where, note that part of this is already settled and needs at least a citation of prior work. Since the work is old it may just be an oversight on the part of the authors as you suggest yourself.

However, in mathematics, the reasoning behind a statement, the proof, is almost always more important than the final statement itself, especially if the proof is novel in any way. This is because proofs offer insight in to how to approach problems that simple statements do not.

The fact that an old result emerges simply as a corollary to a new result isn't especially surprising, actually. It is an interesting fact that might, in itself give some insight into problems related to the old result.

If all questions in mathematics could be answered by the same set of techniques, then it would be a pretty boring field.

And, as you say, Theorem A seems on the face of it to be independently valuable. Do your best job and don't neglect to point out problems and omissions along the way, as you normally would.

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    While I do agree with the sentiment, the harsh reality is that some journals bar entry for any papers that don't settle outstanding or fashionable problems. Not specifying if that is the case here, the author might have chosen the journal based on having what he thought was a novel solution to a known conjecture. Without that I fear the editor may reject him even if I recommend acceptance/another round after major revisions. – lemon314 Oct 19 at 13:13
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    Not to mention that I know that after reading the old paper the author will need to change their paper substantially, and it would honestly seem pointless to me to write a detailed (I err on the side of meticulous) review now, when the text will be then remodeled or cut entirely. I asked the question since it's quite extraordinary to me to know that there will be major changes to the paper not because of what I write in the review, but because of what I can recommend to the author even before I start reading their work. – lemon314 Oct 19 at 13:21
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    Your job, as the reviewer, is to assess the paper and make a recommendation to the editor. It is the editor's job to either accept (possibly with revisions) or reject the paper. If the paper solves an already solved problem, the editor should know this. If the method is novel, the editor should know that, as well. Remember: your job is to arm the editor with the information they need in order to make a good decision. You, yourself, are not making any decisions. – Xander Henderson Oct 19 at 19:26
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    The thing is if it's a top journal they're likely to reject just based on this one piece of information, so why put in a ton of effort into the rest of the paper when it's all going to be duplicated by someone else at the next journal? I think Allure's answer is better. – Noah Snyder Oct 20 at 21:55
  • Wouldn't it be better to get the ball rolling on letting people know about that possibly significant fact early? This would make sense if you were sending letters by mail that took weeks to deliver, but communication latency is just however long it takes them to check their email (maybe with an extra round trip from editor to author and back to reviewer). Start thinking (and maybe write some notes) about what you'd say in a full review in case they do still want that for the original paper, especially if it has your attention/interest now. (I'm not in academia so IDK if this is good advice) – Peter Cordes Oct 21 at 9:47
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I think you take too much responsibility for other persons' (presumed) actions. I'd say write in your review what you know (that the problem was settled before) and what you think (namely that Theorem A merits publication in its own right). Be as comprehensive as you like; certainly you help the author and maybe editor by providing some more detail, this mainly depends on the time you can spend on this.

It is the job of the editor, not yours, to decide about rejection of the paper. Don't base your behaviour on the assumption that the editor might do something, in their own responsibility, that you wouldn't agree with. Neither base your behaviour on assumptions of what the author will do with their own work if you write this-or-that and whether this may or may not be good in your opinion. It is up to them to decide that. So give them open and proper information on the standard way (i.e., in your review) and leave their job to them. Note by the way that if the editor decides to reject, there are many other journals, and maybe the author will in their next attempt to submit just cite the original paper and state clearly what is original about their own approach. As an expert in the field, you may even be asked to review that update.

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    It's not about taking responsibility for others: this means extra work for yourself, compared to alerting the editor and/or author. I'm unconvinced that there's any reason to do a detailed review of a paper in this circumstance if you can check how the journal or author wishes to proceed. – Stuart F Oct 20 at 12:20
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    Fair enough; given that the reviewer thinks that there is still worthwhile content in the paper, however, as an editor I wouldn't want to act based on such an alert only. Surely I'd need to verify it to take any action, and also there are probably one or two reviewers sitting over the same paper at the same time. So as an editor it can cause me quite a bit of work unless I just say, "please write a full review anyway, I'd like to see all reviews before making a decision". Which as editor I'd quite certainly do, so alerting me may well waste more time than writing a proper review. – Lewian Oct 20 at 16:14
  • Of the six answers so far, all with some merit, this one stands out as being complete and right in every respect. – John Bentin Oct 21 at 15:45
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You say that Theorem A is publishable on its own, but is it publishable in the current journal?

If not, I think the best outcome for the authors is to get a quick review explaining that Corollary B is already known, and consequently the results are not as strong as they think and you would recommend submitting a revised version to [some other journal]. They can then get on with this without much delay.

If it would still be strong enough for the current journal, then presumably the authors will still want to publish there. So in order to recommend any course of action you will need to actually check whether the proof of Theorem A is valid; I see no reason to say anything before doing this.

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    This is a great answer that really gets to the critical point. I have a pretty strong presumption that it's in the former case (because if they thought it was a major open problem they probably went for a very top journal), but you're right about what the cases are and what the best thing is to do in each case! – Noah Snyder Oct 20 at 22:00
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When reviewing it doesn't hurt to be practical as well: What would serve the author best in this case? Does this create extra work (resp. fewer rewards) or mean less work for you?

In this case, it sounds like conveying the valuable information of a prior proof to the author would let them decide whether to rewrite the paper (the most likely outcome, you say) or let it stand. So it does no harm to the author, and might save you some work. Sounds win-win to me. But it might also mean that you never get to review the paper (if it is withdrawn and submitted elsewhere), so you need to decide if this is so undesirable an outcome that you want to avoid it.

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    It might, however, create a six month or so delay in publishing if there is an "extra" cycle of review. Ouch. – Buffy Oct 20 at 14:24
  • If the author decides to proceed without rewriting, there will be no extra cycle and the delay should be minimal. If they decide to rewrite and resubmit, they are choosing and accepting the delay. – alexis Oct 20 at 21:12
  • However, sending it back without a review can lead to two cycles of revision, not just one. Give the authors complete information rather than partial. – Buffy Oct 20 at 21:58
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The editor should be happy to receive this:


I believe the author should change their paper substantially, in light of Corollary B having been solved in XXX, and I think this should be communicated to the author forthwith. XXX is a publication of a far away field so it’s not surprising it was overlooked. So it seems inappropriate to write a fully detailed (I err on the side of meticulous) review now, when much of the text ought to be remodeled or cut, and a detailed review would be a poor use everyone’s time and delay the author’s progress. Hence this short initial review.

This work is valuable but less groundbreaking than thought. I think it shows excellent work and will surely warrant publication after the necessary revisions, but perhaps journal YYY would be a better forum.

After sending this I will continue work on a more detailed review, as some additional feedback is warranted beyond the above. Please interrupt me if it’s not needed.”

Is this inherently going to be much slower than option 3? To the contrary, I think.

If the editor will reject him outright even if you recommend another round after major revisions, your submitting a detailed review won’t help, so there’s still no good reason for one. Only if Buffy’s right is there a good reason for one - namely that a reworked Corollary B is still worth publishing as a novel solution to a solved problem, so some effort into critiquing it is worth making, but focus on getting it in fast, not perfecting it.

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