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I am wondering on how to interpret these types of "reviews". As per the guidelines of Math reviews

Two other treatments of items are possible, but should be used sparingly. You may recommend that the item be listed without a published review, or you may recommend that the author's summary be used as the review. In the second case the quoted summary would be given above your signature, to indicate that the summary is being used on the recommendation of the reviewer. If you decide to recommend one of these options, simply put your request in the Review text box (e.g., "Publish without a review", or "Use the summary as my review"). However, in most cases, the mathematics community would prefer an insightful review to either of these two treatments.

From another post here, I understand the first option to mean "do not bother to read this article". I wonder about the second one; a first interpretation could be "everything is correct with this paper and the abstract is good enough to guide the reader". Alternative, it could mean "I didn't bothered to review it".

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    Note for readers outside of maths: this question refers to AMS's Mathscinet, a database of mathematical papers that includes reviews curated by researchers. It is not about the usual peer review process. – Federico Poloni Jun 23 at 18:53
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My sense is that the interpretation of a "summary only" review depends significantly on the culture of the research field of the paper and its historical relation to MR. I just looked at each article published in one of the main journals in my (applied) sub-field last year and exactly one of them had a non-summary review. On the other hand, a similar trip through recent issues of Journal of Number Theory shows that summary reviews are quite rare.

Personally, I have used this type of review once (out of approximately 30 reviews) with an intended meaning that matches your first interpretation. After reading the paper and writing my review I looked at the abstract again and realized that it was remarkably similar to what I had put together. Given that, it seemed reasonable to allow the author's words to speak for themselves.

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When I review for MR I often use a paraphrase of the author's summary when it is a good description of what is in the paper. I don't mean that to say "not worth reading" or "I didn't read it". I would probably not use the MR option that merely reproduces the abstract, precisely because it might suggest a negative opinion of the work.

That said, I tend to review short papers that are OK but not earthshaking. A review of an important paper should do more than repeat or rephrase the author's summary.

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  • This sounds right to me, but I may be biased. When one of my papers gets a summary review, I think I must have written a good abstract. Does not mean I wrote a good paper, but at least I summarized it well. – Terry Loring Jun 24 at 6:10
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There are two reasons that a Mathematical Review will be a summary rather than an actual review:

  1. The assigned reviewer recommends using the abstract or a part of the introduction as a review. This could be for several reasons: the reviewer thinks author's description of the paper is good and they don't have anything to add, the reviewer doesn't understand the paper well enough to review it, the reviewer doesn't have/want to put in the time to read and review the paper, ... Ideally in the latter 2 cases, the reviewer would decline the review request, but I doubt this always happens.

  2. Mathematical Reviews can't find a reviewer for the paper. This could be because no one agrees to review the paper, but primarily it is just that in certain fields there are many more papers published than reviewers available so in order to keep up with the constant flow of new papers, the editors have to decide that some papers will be sent for review, some just get summaries from the text of the paper, and some don't get any reviews. This is why, as @drdrd discusses in their answer, at least some areas of applied math may have more summary-only papers than number theory. (And I believe the proportion of modern papers with only summaries is even higher in zbmath.org than in MathSciNet, primarily due to a smaller pool of reviewers, at least from what I've observed in number theory papers.)

Anyway, it is not the case that a paper with only a summary is "lower quality" (whatever that means) than a paper with a proper review. Though it is true that the "best" papers in an area tend to get proper reviews, many very good papers just have summaries. However, if a paper does not get a summary or a review (and is beyond the preliminary stage), that tends to correlate with being published in lower-tier journal, but again is not a definite measure of quality.

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