Question is as in the title:

What care do reviewers take when writing a review for a published paper in mathematics?

I have seen some reviews from MathSciNet. These reviews slightly overlap with the abstract of an article but say much more than an abstract of a paper, in a clearer way.

I am not asking for a referee report of a submitted paper. I am asking for a review of an already published paper.

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    This is not a well posed question. Please feel free to edit if you think some edit can make it more clearer or wellposed.. – Praphulla Koushik 2 days ago
  • What sort of review are you interested in? Some "after publication" reviews are just summaries and condensations for a more general audience. Are you thinking of something else? – Buffy 2 days ago
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    @Buffy I am interested in all sorts of reviews one come across in MathSciNet, which also includes just summaries... – Praphulla Koushik 2 days ago
  • Why don’t you just go to MathSciNet and have a look at some random reviews there? What can anyone here tell you that you won’t easily learn that way? – Dan Romik 2 days ago
  • I don't think I understand what you mean by "care". I'm a MathSciNet reviewer but I don't know how to answer your question. Are you asking for a general summary of how the reviewing process works? Things that the reviewer has to pay specific attention to? A description of the level of precision or correctness that's expected? Please clarify. – Nate Eldredge yesterday

MathSciNet reviews are not the kind of reviews an editor would get for a submitted paper. Rather, what is posted on MathSciNet is more of a summary of the article and someone putting it into the context of the broader field -- something that would help a reader understand not only what the paper provides, but why it is relevant. As such, the authors of these reviewers don't have to go through all proofs with care -- they don't even have to understand the proofs as long as they understand the theorems.

On the other hand, reviewers of math papers often go to great lengths to ascertain that the proofs in the paper in question are in fact correct. That typically requires a great deal of care, detailed insight, and work.

  • I'll guess this is the same for other, similar, reviews as well. – Buffy 2 days ago
  • +1 Please feel free to share if you have any favourite review that helped you to get a broader picture of the situation :) – Praphulla Koushik 2 days ago
  • @PraphullaKoushik -- sorry, I don't usually consult MathSciNet and wouldn't know... – Wolfgang Bangerth yesterday

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