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51

I only hope that computer-aided proof checking saves mathematics before it collapses under the weight of decades of irresponsible publishing. Of all disciplines, peer review in mathematics should serve to guarantee nearly absolute confidence in the validity of published results. Many subjects have grown so complex that one can't reasonably expect new ...


29

In a word: never. But slightly more usefully, here's my 50øre. If you publish a paper that depends on the result, are you going to be embarrassed if the referee says, "Can you clarify your use of Theorem X?". If you feel happy saying, "A,B, and C all published result depending on it, so I figured I was safe." then go ahead. If you're not quite so ...


22

I regard it as part of my job as a referee. But the amount of time I spend checking proofs really depends on whether the point of the paper is to prove something I already believed but didn't know how to prove (in which case I spend a lot of time) or to tell me something new, in which case I might spend very little time on the proofs and rather focus on ...


21

Here is a rule of thumb I learnt the hard way: if the article A you are using seems to be under-quoted, that is to say if articles published later quote other sources while A seems to be perfectly acceptable, then beware of A. Suggesting this rule of thumb pains me greatly because I think there are already too much path and cultural dependancy in citation ...


21

I agree with everyone else -- you should disclose, and I see no problem with this. Let me raise a subtler issue: A few years ago, I had the experience of being repeatedly sent a paper where the result was correct but, in my opinion, not close to significant enough to appear in the journals where the authors were sending it. I sent a report to this effect ...


20

There obviously won't be a single answer that fits all circumstances, but here is my pennyworth. If a result is sufficiently accepted by experts you have good reason to trust, then the result can be trusted. (Obviously the better you understand it the better, but sometimes one has to save time.) If a result does not satisfy the first criterion, then be ...


20

I am answering this anonymously, also for obvious reasons. As a referee, I get quite annoyed when, after having recommended rejection for a paper, and given several detailed reasons for the rejection, the same paper comes back to me from a different journal with no changes at all. In other words, the authors didn't even try to address my objections. In this ...


19

No-one has quite answered: When accepting without checking, how do you phrase it? I think? So, here's a thought. I'm always of the opinion that you should give the maximal amount of detail where referencing something. Give the exact Theorem number in the paper you reference (not just ``by results of [12] it follows that...''). Explain carefully the ...


18

My personal feeling is that not making the author wait for a second referee to write a report is doing them an enormous favor, even if the paper gets rejected. If you aren't going to write the paper a good enough report to get the paper published, most probably whoever else would referee it instead won't either, and they will take a lot longer. I have to ...


17

I agree with David: I think that my job as a referee consists mainly in checking that the proofs are correct. However, checking that the proof is correct can in practice not be done by line-by-line checking. Referees are not computers, nor are the writers of the articles. Rather I have a kind of critical, "falsificationist" approach. I try to see what are ...


15

I wouldn't touch this with a barge pole. It reads like a Nigerian scam.


14

I did exactly as others have suggested: created a fake email account (this was pre-Gmail; I think I used "sithmail") called [author name]reviewer, and corresponded that way. Actually, I did this not to ask about the paper, but to strongly recommend to the author that he put his article on the arXiv before signing anything (and pointed out that the editor ...


13

I have done this as a reviewer, and have had it done to me as an author. I have no problem with it. I do think you should disclose to the editor that you've reviewed the paper before. (This can create the awkward situation of having to say "I reviewed this for journal A, and didn't think the theorem was interesting enough, but it fits just fine in your ...


13

This question was discussed on E. Kowalski's blog. Here is a comment I made: Dear Emmanuel, You have raised an interesting issue, with (I believe) no simple answer. I think that Terry’s suggestion on how to deal with the situation is a sensible one. I might add another piece of advice. (Note that, as with Terry’s advice, this is not advice on how ...


13

I more or less agree with Sheikraisinrollbank, but for the sake of argument... I've always found it slightly hard to fully separate "Is this paper interesting" from "Is this paper correct". It seems like mathematics (especially towards the pure end) is full of interesting, plausible "facts" we don't have proofs of. Isn't part of the point of maths to find ...


13

Anonymity is the referee's right (or privilege), not an obligation. I think the referee should be free to disclose his/her identity to the author.


13

On a somewhat practical -- and frighteningly co-incident -- note, just this morning a reviewer revealed his identity to me on the grounds that his own as-yet unpublished work overlaps my paper that he is currently reviewing. As a reviewer, encountering a draft which overlaps your current project would be a bit of a nightmare scenario for a variety of ...


13

I actually think these "communicated by" lines are very useful: they let young authors know which editors publish which topics. It's not always clear to me which editor is the right one to submit to, but I can look up similar papers and find editors that way.


12

Presumably, whichever field this is, you are an expert in it, and the editors respect you as such. So, if you hate the paper, and think it should not be published, I don't see the downside to telling this to all editors who ask. If you don't hate the paper, but think it is not quite Annals-worthy, you can just say in your review "I don't think this paper is ...


12

I think PaPiro's answer is entirely correct, based on my own experiences as author, referee and editor. One principle is that the referee is carrying out a task at the request of, and for, the editor. I would say that the the referee's task is to supply information to the editor, who will use this to decide what should be done with the paper. The standard ...


10

Journals of scientific societies (such as PNAS, CRAS) were, once upon a time, records of meetings and a member of the society would actually present the papers he accepted to the other members, so in this case I believe it's just a tradition. In the case of Nonlinearity it's probably just an affectation. Pay no attention to this stuff.


10

For many years now, I have refereed only non-anonymously. It has not been uncommon that the authors of a paper I recommended with reservation—or, especially those I rejected—to write me directly, and we subsequently engage in an online (but off-journal) dialog to improve their paper, often for another venue. Almost uniformly these dialogs have ...


9

I have had similar experiences to the OP and I think the OP is handling it correctly. If I'm rejecting a paper which is (apparently) correct and new on the basis of an opinion that the result is not good enough for journal X and I get it again from journal Y of a similar quality as X, then clearly I have a different opinion from the author about the paper's ...


9

Note throughout that there are two only-partly related issues: literal correctness, and "importance", and that the latter is tangled up with "status" and "relative prestige" of journals. And, don't forget, all journals get far more excellent papers than they can fit into their "pages", so they will reject many excellent ones, for essentially random ...


9

The questions raised are real but can't be answered by giving rules of thumb, I'm afraid. Mathematics is hierarchical by nature and has a long history, with results often building on earlier ones. Peer review of published work varies a lot in thoroughness, but even done conscientiously can't root out all subtle errors. Most of us bring a bit of ...


8

I can't say anything about this particular email you received, but I have received invitations to join the editorial board of two journals, which I declined. One was a very reputable journal, but one I did not publish in and to whose community of authors/readers I did not feel I belonged. (One would be right in asking why I was ever approached and I don't ...


7

I am some combination of being too junior and not eminent enough in my field so as to have never received a request to be an editor for a mathematical journal. But here are the criteria that I would use if I were ever in such a situation: 1) If the journal already exists, then it would have to be one that I respect and probably one that I have already ...


7

If you are sent a paper to referee that is not publicly available, I believe it is your duty to provide your report and then pretend you have never seen the paper, at least until it appears somewhere public. You shouldn't be thinking about proving any conjectures made in the paper or generalizing its results. You shouldn't be contemplating collaborations to ...


7

I agree with the side saying that you should do the refereeing for the second, third, etc time if you are asked. In particular I very much agree with no name and Ben in the reasons they cite. I would add the following. Very often there are only a few people who can truly evaluate a paper's worth. If you are one of those and you decline refereeing the ...


7

I think there are ethical issues here that other people have not brought up, even after the refereeing job is done. By letting the author know about your (very positive?) referee report, they may feel more likely to "repay the favor" in the future. This seems potentially problematic to me (although in many cases it won't be). Obviously, if you ...



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