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In the indexing section of a Mathematics journal, out of several indexing (e.g., Scopus, MathSciNet etc), it is mentioned that the journal is reviewed by AMS Mathematical Reviews.

What does mean it ?

Google says Mathematical Reviews itself a journal published by AMS, but I am not sure it is a journal.

But in any case what does mean a particular is reviewed by AMS Mathematical Reviews ?

Is it a good criteria for a journal?

Any information please...

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Mathematical Reviews is now better known as MathSciNet. It's a subcription-based online database of mathematics research papers and books, produced by the American Mathematical Society. Before the online era, it existed as a paper periodical called Mathematical Reviews that was sent out to libraries and subscribers, but it was never really a "journal"; it only included metadata and not original articles.

An entry in the MathSciNet database contains the bibliographic information for the book or article. For selected items, there may also be a review: a summary of the article written by an independent expert who was recruited by the MathSciNet editors. Despite the name, the "review" doesn't usually evaluate the paper as "good" or "bad" but instead summarizes the contents in the reviewer's own words, sometimes including more background information, context, sources, etc. If there is no review (e.g. the paper wasn't selected for a review, or a reviewer couldn't be found, or the reviewer decided that they had nothing to say) then the database entry includes the article's original abstract instead.

When a journal is indexed by MathSciNet, it means that articles published in that journal are entered into the database. Usually this is cover-to-cover, i.e. including all articles in the journal, but in some cases it could be more selective. MathSciNet has pretty broad coverage and will generally index any journal that seems to be of interest to the community, so being indexed by MathSciNet is a pretty low bar. If a journal is not indexed, it's likely either very new, very obscure, or of such low quality that the MathSciNet editors don't think it is of any significant interest at all.

I don't think it's accurate to speak of a journal being reviewed, since as I understand it, the decision to seek a review is per-article. Even in top journals, not all articles receive reviews (though it's not necessarily clear whether the editors tried to solicit one). Still, presumably papers in strong journals are more likely to be reviewed, as this is some indication that the paper is interesting. In obscure or lower-quality journals, it could happen that none of the articles are reviewed.

So in short, if the publishers say their journal is "reviewed" by Mathematical Reviews, they probably just mean that it is indexed, and that at least some of the papers receive reviews. I would take this as a signal that the journal is probably not complete garbage, but I wouldn't read into it much more than that. As I said, it is a very low bar.

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  • Thank you very much for all the valuable informations. I am more convinced now with you.
    – learner
    Commented Jun 28, 2023 at 3:11
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Math Reviews was a paper journal back in the day, but at some point it transitioned to being online-only. Mathscinet is the web interface to search Math Reviews, and the brief reviews of papers it gives you are exactly the content of Math Reviews.

The goal of Math Reviews is to index the entire mathematical literature, so being indexed there is not really a meaningful signal as to how good a given journal is.

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  • Thank you for the answer
    – learner
    Commented Jun 27, 2023 at 12:57
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    Actually, it is a meaningful signal in the sense that, if a journal is NOT reviewed, then (assuming it is a math journal) it is not a reputable one at all and you should not publish math papers there.
    – Alexander Woo
    Commented Jun 27, 2023 at 13:02
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    @AndyPutman, Are all mathematics journals reviewed by AMS Mathematical Review, by default?
    – learner
    Commented Jun 27, 2023 at 14:17
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    @learner: I’m not sure exactly what you mean when you say “by default”. They have an editorial board that manages things and decides when to start/stop indexing journals, so some judgement is performed (eg here is a recent statement about what they are looking for: ams.org/publications/math-reviews/mrpolidxjl), but they aim for broad coverage and don’t try to distinguish between “good” and “bad” journals.
    – Andy Putman
    Commented Jun 27, 2023 at 14:37
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    To give you an idea of how little filtering MR does, during its brief existence they did index papers from the Antarctica Journal of Mathematics, which was most famous for being the butt of various internet jokes back in the day (google can find plenty about it). Similarly, it now indexes plenty of pretty sketchy/predatory journals, but I don’t want to get into fights so I won’t mention any current ones by name.
    – Andy Putman
    Commented Jun 27, 2023 at 14:51

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