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:
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.
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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:)
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.
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.
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.
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.
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.
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.
We are trying to construct a workload model for the Faculty of Science and Engineering at my institution. Part of this involves assigning a fixed number of "points" for each published paper. It seems that our colleagues in some of the sciences publish many more papers than we do in Mathematics, which leaves us asking for the number of points per paper to be far higher in Mathematics than elsewhere. But we need to be able to back up our impressions with facts.
What I would like to do is to get some idea of how many papers one might expect a research mathematician to publish over, say, a five-year period. I recognize that there are a lot of problems here with the words "expect" and "research mathematician", not to mention problems with counting a 100-page paper on the same footing as a 5-page paper, or a paper in a "top" journal on the same footing as a paper in a not-so-top journal; I want to stay away from all those subjective and opinion-based issues.
I would like to know whether there are any publically-available figures along the following lines: pick a university where faculty are expected to be engaged in research; find out how many publications each member of the Math Department has had over (say) a five-year period; publish the median, or some other measure of the distribution of the publication numbers (not the mean, which could be skewed by a small number of members publishing a large number of papers).
I'm aware of the paper by Jerrold Grossman, Patterns of collaboration in mathematical research, SIAM News 35 (2002), but that's a study of all papers listed in Math Reviews, which includes people who published a paper or two and then left research mathematics for other fields. I'm really interested only in people who are employed by departments where publication in refereed journals is expected.
This question is, in a sense, flawed. You are asking about studies of a certain number $X$. Taken on its own this may be a reasonable question; the problem is that your stated motivation for why you are interested in $X$ is that you would like to (or your university would like to, and you seem willing to go along with it) use $X$ in a way that many reasonable mathematicians would agree is not just useless, but is in fact extremely harmful. How can anyone answer this with a straight face? Personally I would not answer even if I knew of such a study! There may be valid reasons to study $X$ and to be interested in it, but the motivation given for the question completely undermines the discussion.
By agreeing to have your Faculty of Science and Engineering use $X$ as the measure of anything without making any attempt to take into account $Y$ and $Z$, let alone the much more intangible and ultimately most important parameter $W$, you would be allowing your university to create a hugely distorted image of your and your colleagues' research output. The fact that there will be some normalization factor that would ostensibly bring mathematics on par with other disciplines is completely irrelevant. So, as I said, although I'm sure it was well-intentioned, the motivation for the question is fatally flawed in my opinion. It may be worth having a discussion about average publication rates in the context of how to measure the productivity of mathematicians and whether it's a good idea to try to do so, but that would be a separate question that would need to be phrased in those terms. 152ee80cbc
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