Guide for Reviewers--Mathematical Reviews

Mathematical Reviews Database:
Guide for Reviewers

Mathematical Reviews Telephone: (734) 996-5250
Reviewer Services Department FAX: (734) 996-2916
P.O. Box 8604 Email:
Ann Arbor, MI 48107-8604

Updated June 2008

The Mathematical Reviews Database

The Mathematical Reviews (MR) Database contains bibliographic data and reviews of published mathematical research from 1940 to the present.  Bibliographic data for new publications (including journal articles, books, collections and other published material) are added to the Database on an ongoing basis.  Most of these items are sent out for peer review (or are reviewed by summary).

Information in the MR Database is published in several electronic formats—MathSciNet on the Web, MathSci on SilverPlatter™ (CD-ROM) and MathSci on Dialog© —as well as in the paper Mathematical Reviews and Current Mathematical Publications.  For more information see the Editorial Statement.

The content of a review

What is a review? A review should primarily help the reader decide whether or not to read the original item. The review may range in length from a few lines to about 600 words. In most cases the review should state the main results, together with enough notation to make the statements comprehensible to someone already familiar with the field. The main ideas of the proof should be sketched when this is feasible. If the results are technical, requiring extensive notation or elaborate formulas, it is preferable to describe them with a few well-chosen and relatively nontechnical sentences. Helpful comments that evaluate the item or connect it with related items or approaches are welcome.

Reviews as described above, which benefit from independent reviewer expertise, are of the greatest value to the community. Instead of a review of this kind, one of the following options may be appropriate in a few cases:

  1. You may recommend using the author's summary, with or without your signature, or a few sentences from the summary or text of the item as the review, when you believe the selected text provides as good guidance to the reader (along the lines described above) as a review you might write yourself. Please do not keyboard or translate the selected text. If you recommend that the summary be used, you may use the Web review submission form, writing “Use the summary” in the Review text box, or send the recommendation by e-mail, clearly listing the author, title and 7-digit MR Number; you do not need to send a paper copy of the summary. If you recommend a portion of the text other than the summary, we ask that you mark clearly the relevant passages on the item and return either the item or a photocopy along with your recommendation.
  2. You may recommend that the item be listed without a published review. (See the Editorial Statement for guidance on when this is appropriate.) In this case, no review will appear in the MR Database, but the item will be accessible through a search of the MathSci products or printed MR indices.
If you choose option (2) and the item is a book or collection, please return the item so that our editors can reconsider it. In all cases above, if at all possible, please proofread your review and, if appropriate, preview the result of TeXing (see more about review format below).

References. Reviewers are encouraged to include references to closely related work. Because we try to verify each reference, you should give as much information as possible, including full author name, title of the cited item, year of publication, journal name (or book or video publisher), volume number and paging. Please include the MR Number if possible. References in the right format, including the MR Number, can often be found by using MRef. References to items in the MR Database will become active links in your review, in MathSciNet. However, no special formatting is required when you submit your review.

Evaluative reviews. Your review may include a positive or negative evaluation of the item. Negative critical remarks should be objective, precise, documented and expressed in good taste. Vague criticism offends authors and fails to enlighten the reader. If you conclude that the item duplicates earlier work, you must cite specific references. If you think that the item is in error, the errors should be described precisely. You should take into account that the MR Database does not include author responses to critical reviews.

Book reviews. Important new books deserve careful reviews. However, a good review does not need to be very long; less than 300 words are often sufficient. You should always try to limit your review to a maximum of 600 words. We understand that such a review takes time to prepare. A detailed review is sometimes appropriate even if the book contains few new results; for example, if it is an expository survey of a field in which there is considerable interest, many readers will use your review to determine whether to consult the book. The same is true of expository articles.

Reviewing schedules

Time for reviewing. Your promptness in returning reviews can noticeably improve the timeliness of the MR Database. It is expected that you will spend no more than six weeks completing the review of an item. We understand that this may not be enough time, depending on the length and complexity of the item and your other commitments. You may request, at any time,  that this limit be changed. It is understood that reviewers holding multiple items will require additional time to complete the reviews. You may sometimes receive items in excess of the number that you have said that you are willing to receive. If we are sending you too many items, or too many at one time, please let us know.

Reminder notices. If you have held an item for about two months, a first reminder will be sent to you. If you receive a reminder notice and you decide that you cannot finish the reviews of some of the items you have at the rate of one a month or faster, please let us know immediately about these items. MR will transfer them to another reviewer. Books or collections must be returned to MR to allow this transfer to another reviewer.

Transfer of items. We may send you an item in an inappropriate field or language.  We may send you more than you can conveniently handle at one time, because of other demands on your time. You may feel that you cannot be objective reviewing the work of someone in close "proximity" to yourself, such as a close colleague or a spouse. (Asking an author or co-author of an item to write a review of that item is always an error on our part.) In cases like these, please inform MR as soon as possible for transfer to another reviewer. No explanation is necessary; however, the editors always find it useful if you can provide a short explanation and we appreciate your suggestions for alternative reviewers.&nsp; If the item is a book or collection, please return both the original item and the review sheet.

Transfer to a colleague. If you think that a particular item could be better handled by one of your colleagues, you may transfer it to that person even if he or she is not a regular reviewer for Mathematical Reviews. If you do so, please let us know at once, giving the complete name and address of your colleague so that we may record the transfer in our files.

Becoming inactive. At your request, we can make you "inactive" as a reviewer and stop sending you items for review until a fixed date, or until you tell us that you are ready to review again. Such a request should be sent to our Reviewer Services Department (

Review format

Reviews should generally be submitted electronically, using the interactive Web review submission form. This can greatly speed the MR production process.

Format for electronically submitted reviews. TeX is the typesetting language used in the MR Database. However, if your review does not contain mathematical symbols, knowledge of TeX is not required to submit your review electronically. Many reviewers find that knowing simple TeX such as $x$ and $x^2$ is sufficient. Click here for complete instructions for electronic submission of review manuscripts.

Paper manuscripts. A review should be sent in paper copy only if you are unable to submit your review using the Web form or by e-mail. Please use only one side of the review sheet; continue on a separate sheet if necessary. If you lose the review sheet, send your review on plain paper.  In this case, the author, title, 7-digit MR Number (the barcode on the item) and your name should be stated clearly at the beginning of the review. You may also use plain paper if your printer will not accept the review sheet, but please return the review sheet with the review.  It is essential that the manuscript be clearly legible. Thus, reviews should be keyboarded rather than handwritten if at all possible. It is helpful on paper manuscripts if you clarify ambiguities by means of marginal notes (e.g., change of fonts, "one" (1) vs. "ell" (l), "zero" (0) vs. "oh" (O; in TeX math $O$), "union" ($\cup$) vs. the capital letter "you" (U), "join" ($\vee$) vs. "vee" (V), "meet" ($\wedge$) vs. capital "lambda" ($\Lambda$), etc.).

Accuracy. Ambiguities in the manuscript or notational complexities can lead to the introduction of errors during the editorial process. We strive to keep such errors to a minimum, but we need your help.  Please submit your reviews in final form. Always proofread your review before submitting it.  This is especially important if someone else has keyboarded the final copy of your review. The interactive Web review submission form at offers you a PDF preview that you can proofread for accuracy, including the accuracy of your TeX encoding.

Languages. We ask that reviews be written in English. If you propose using an unedited summary, there is no need to translate it.

Subject classification of reviews. The review sheet that we send you asks for your suggestions for the 5-character classifications of the item being reviewed, according to the 2000 Mathematics Subject Classification (MSC2000). We value your suggestions, especially in completing partial classifications and correcting errors, because you will have read the item more carefully and possess more expertise than the editors.

Odds and ends

Change of address or name. Please inform our Reviewer Services Department ( at once of any change in your address (paper or email) or name. This will prevent the loss of review material and will save time and money.

Reviewing preferences. When you first became a reviewer, you indicated to us your reviewing interests and language skills.  You may have requested an update to our files on these matters since then.  If we are sending you inappropriate items, or if your interests change, please let us know your current reviewing interests.

When to keep the original item. Items sent to you for review become your property once you have reviewed them.

Recommending new reviewers. New reviewers are frequently enlisted on the recommendation of a current reviewer. Your suggestions are very welcome. A potential reviewer should ordinarily have already published reviewable work. Exceptions are made in the case of strongly recommended recent Ph.D.'s, especially if they can offer combinations that we need of expertise in certain fields and languages (our shortage of Russian-reading and Chinese-reading reviewers is chronic).

Write to us. We invite all reviewers to write to our Reviewer Services Department ( with their questions, complaints, or special requests. We are keenly aware that MR depends on its reviewers for its existence and we welcome their correspondence—all of which will be read, carefully considered and, when appropriate, answered. (Note that MR normally does not accept unsolicited requests to review specific items.)

Subscriptions. Any requests for subscriptions to MR Database products or problems with current subscriptions should be addressed to:
American Mathematical Society Telephone: (800) 321-4267
Customer Services Telephone (worldwide): (401) 455-4000
P.O. Box 6248 FAX: (401) 455-4046
Providence, RI 02940-6248 Email:
USA Web site:

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