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Cover of the Featured Reviews, 1995–1996.

Mathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses (and occasionally evaluations) of many articles in mathematics, statistics and theoretical computer science. Selected reviews (called "featured reviews") are also published as a book by the AMS.

The journal was founded by Otto E. Neugebauer in 1940. The goal was to give reviews of every mathematical research publication. As of November 2007, the Mathematical Reviews database contained information on over 2.2 million articles. The authors of reviews are volunteers, usually chosen by the editors because of some expertise in the area of the article. It and the German journal Zentralblatt für Mathematik are the only comprehensive resources of this type (the Mathematics section of Referativny Zhurnal is available only in Russian, is smaller in scale and difficult to access). Often reviews give detailed summaries of the contents of the paper, sometimes with critical comments by the reviewer and references to related work. However, reviewers are not encouraged to criticize the paper, because the author does not have an opportunity to respond. The author's summary may be quoted when it is not possible to give an independent review, or when the summary is deemed adequate by the reviewer or the editors. Only bibliographic information may be given when a work is in an unusual language, or when it is a brief paper in a conference volume. Originally the reviews were written in several languages, but later an "English only" policy was introduced.

In 1980, all the contents of Mathematical Reviews since 1940 were integrated into an electronic searchable database. Eventually the contents became part of MathSciNet which, along with reviews also has citation information (limited to other articles in MathSciNet, however). Mathematical Reviews and MathSciNet have become an essential tool for researchers in the mathematical sciences.

Unlike most other abstracting databases, MathSciNet takes care to identify authors properly. Author search allows the user to correctly find publications associated with a given author record even if other authors have exactly the same name. MathSciNet will sometimes even contact authors to ensure that they have correctly attributed their papers. On the other hand, the general search menu uses string matching in all fields, including the author. This is needed to access some old reviews (before 1940), which have not been completely integrated yet and cannot be found by searching for the author first.

MathSciNet provides BibTeX entries with all reviews and its abbreviations of journal titles have become a de-facto standard in mathematical publishing. Both Mathematical Reviews and Zentralblatt für Mathematik use the Mathematics Subject Classification codes for organising their reviews.

MathSciNet contains information on about 2 million articles from 18,000 mathematical journals, many of them abstracted "cover-to-cover" [1][2]. In addition, reviews or bibliographical information on selected articles is included from many engineering, computer science and other applied journals abstracted by MathSciNet. The selection is done by the editors of the Mathematical Reviews. The editors accept suggestions to cover additional journals, but do not reconsider missing articles for inclusion [3].

• Referativnyi Zhurnal, published in former Soviet Union and now in Russia.
• Zentralblatt MATH, published in Germany
• INSPEC
• Web of Science
• IEEE Explore
• Current Index to Statistics

• MathSciNet Review – by the Science and Technology Librarianship.
• Allyn Jackson, "The life of Mathematical Reviews", Notices of the American Mathematical Society 44 (1997), no. 3, 330–337.

• Mathematical Reviews database with access to the online search function for the database (for subscribers), and link to information about the service, such as the following:
  1. Mathematical Reviews editorial statement outlines the mission of Mathematical Reviews;
  2. Mathematical Reviews guide for reviewers is a useful resource both for reviewers and users of Mathematical Reviews.
  3. MathSciNet FAQ
• Some interesting reading about Mathematical Reviews. Two articles published for the 50th anniversary of MR in 1990.
• Exceptional MathReviews collected by Kimball Martin and sorted by amusement factor.
• A half century of reviewing, an article by D.H. Lehmer