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The guidelines do not clearly specify how much work one is assumed to do in writing a MathSciNet review. What is the consensus? Is one expected to read the whole paper and check the the proofs in detail?

Valentas
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2 Answers2

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You are not expected to check the proofs. You are expected to write an informative text which will reflect the contents of the paper. So that the reader can get an idea what did the author prove (or claims to prove), and decide whether s/he wants to read the paper. Of course, if you find a mistake you mention this. Or if you know that the result is not new. But you are not supposed to check the proof: it is the job of the referee.

Alexandre Eremenko
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    Regarding the last sentence that it's the job of the referee(s), here are varying opinions found on MO: http://mathoverflow.net/questions/40729/does-a-referee-have-to-check-carefully-the-proof?rq=1 – Yuichiro Fujiwara Jan 05 '15 at 17:11
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    @YuichiroFujiwara, indeed, in my experience, some reputable journals explicitly say that ensuring "correctness" is not the responsibility of the referee, but of the author. Correctness of proofs is not the same as correctness of conclusions, which potentially adds to the confusion. – paul garrett Jan 05 '15 at 17:19
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    So let us say unambiguously that checking the proof is the job of the author, with an optional assist from the referee. :-) – LSpice Jan 05 '15 at 18:01
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    Whose responsibility is it to engage with post-publication identification of systemic errors? – Adam Epstein Jan 05 '15 at 18:19
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    @AdamEpstein I see very rough analogy with software (with license agreement "No warranty of any kind") and users of said software. – joro Jan 05 '15 at 18:55
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    @Adam Epstein: It is nobody's responsibility:-) When you use some published result, it is only YOUR responsibility to check that it is correct. – Alexandre Eremenko Jan 05 '15 at 18:56
  • I think we all agree that, as a reviewer for MR, you're not supposed to check the proofs. Trouble may arise if you find a mathematical mistake in the paper, because you are supposed to explain why it is false, or provide a counter-example, and this can result in painfully long and not so informative reviews. – Alain Valette Jan 05 '15 at 22:21
  • @AlexandreEremenko Who said anything about using? – Adam Epstein Jan 05 '15 at 22:29
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    As an example of how to deal with the situation of finding a mistake in a published article, I once wrote "The reviewer was unable to follow some of the author's arguments, and suspects that necessary conditions might be missing in some of the statements claimed". I was later contacted by the author, and I explained why I had written that. Unfortunately, it was not possible to write something more informative in the review, for the reason explained by Alain Valette. – André Henriques Jan 05 '15 at 22:46
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I echo the answer that you are not expected to check the proofs as a MathSciNet reviewer. That said, I personally choose to do so, because I believe that this leads to better reviews. When I read a review I want it to tell me what to expect from the paper, and if there is a gaping hole I want to know that fact before I spend hours stuck on it. Of course, this is assuming that the paper is of somewhat moderate to small length, which has often been the case in the papers I've reviewed. I also feel like putting my name on a review gives it my stamp of approval, and for me that stamp means something more than just looking over a paper quickly.

It might surprise you that I've found many errors in papers I've been asked to review. Some unfixable and central to the paper, some small and unfixable, lots of minor typos (which I don't mention in my reviews unless there are just gobs of them), and in one case an error that was quite subtle and it took a good week for me to find a fix. (I added the fix to my review, but only at the recommendation of the author of the paper.) Of course, you better be sure there is an error (perhaps by communicating with the author if appropriate) before mentioning it in a review. In all these cases, I hope that the people who read my reviews find them helpful.

Pace Nielsen
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