Math reviews, how to interpret "the summary as review" cases?

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.


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.


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.