What is a review? A review should primarily help the reader decide whether or not to read the original paper. The review may range in length from a few lines to one or two double-spaced typewritten pages. In most cases it 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 paper or connect it with related papers or approaches are welcome.
Instead of a review of this kind, you also have the following options:
If you choose option (2) or (3), please return the item so that our editors can reconsider it. We often do not have a duplicate copy.
References. In your review it may be desirable to include one or two references to related work. Because we try to verify each reference, you should give as much information as possible, including full author name, year of publication, journal name (or book title), title of the cited article, volume and paging. Please include the MR number if possible. No more than two references to related work should be cited unless they are absolutely necessary for your review.
Evaluative reviews. Your review may include a positive or negative evaluation of the paper. Negative critical remarks should be objective, precise, documented and expressed in good taste. Vague criticism offends the author and fails to enlighten the reader. If you conclude that the paper duplicates earlier work, you must cite specific references. If you think that the paper is in error, the errors should be described precisely. You should be aware that the author cannot reply to criticism in the pages of Mathematical Reviews.
Book reviews. Important new books deserve careful reviews. However, a good review does not need to be very long; less than one typed page is often sufficient. You should always try to limit your review to a maximum of two or three pages. 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. On the other hand, you might decide that a book or article needs only a very brief description.
Time for reviewing. The maximum period allowed for completing a review is normally six weeks per item. We understand that this may not be enough, depending on the length and complexity of the paper and your other commitments. Since many additional weeks are required for editing, composition and printing, your promptness in returning reviews can noticeably improve the timeliness of Mathematical Reviews. You may sometimes receive items in excess of the number stated on your reply card. If we are sending you too many items, please let us know. If you live outside North America you should return your reviews by airmail or e-mail. We hope you are able to obtain support from your institution to cover postage to return your reviews; if not, let us know and we will include return postage with each item we send for review.
Reminder notices. If you have held a paper 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 the papers you have at the rate of one a month or faster, please return those you are unable to review for transfer to another reviewer.
Return for transfer. We may send you a paper in an inappropriate field or language, or in excess of the number that you can conveniently handle because of other demands on your time. In any of these cases, you should return the paper promptly for transfer to another reviewer. No explanation is necessary when you return an article for transfer, but you should return both the article and the review sheet. However, we appreciate your suggestions for alternative reviewers.
Transfer to a colleague. If you think that a particular paper 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. If you do, 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 papers 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.
Languages. We ask for reviews in English. Since 1983, all reviews in MR have been published in English so that they can be easily searched in MathSci. However, if you have difficulty writing in English, you may write your reviews in French, German, Italian, Russian or Spanish and we will translate them into English.
Appearance of manuscripts. For a review sent in hard copy, the review sheet which you send us is the manuscript which we will use. 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 control number stamped 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, in this case, please return the review sheet with the review.) Several people will read this manuscript and add their annotations. Therefore, it is essential that the manuscript be clearly legible with plenty of space between the lines. We prefer typewritten reviews, but a neatly handwritten manuscript is acceptable.
Electronic Reviews. TeX is now the typesetting language used in MR. Instructions for electronic submission of TeXed review manuscripts (as an alternative to typing your reviews) are given on the back of the table of contents page of the recent issues of MR. You can also get the electronic files relating to electronic submission by sending an e-mail request to mathrev@ams.org.
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 at a minimum, but we need your help.
Please submit your reviews in final form ( ready to be marked for typesetting if in hard copy). Always proofread your review before submitting it; this is especially important if someone else has typed the final copy of your review. Explain briefly in the margin any unusual symbol or notation.
Formulas. You can help us to reduce printing costs by avoiding excessive or unnecessary quotation of complicated formulas. We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. Thus, instead of the (coded) display:
$${1\over{2\pi i}}\int_\Gamma {f(t)\over (t-z)}dt$$
we might use
$(1/2\pi i)\int_\Gamma f(t)(t-z)^{-1}dt$.
Typesetting instructions. Formal copyediting of a hard-copy manuscript is the responsibility of our staff. However, it is helpful if the reviewer clarifies ambiguities by means of marginal notes (e.g., "one" (1) vs. "ell" (l), "zero" (0) vs. "oh" (O; in TeX math $O$), "union" ($\cup$) vs. the capital letter "you" (U), "wedge" ($\vee$) vs. "vee" (V), "wedge" ($\wedge$) vs. capital "lambda" ($\Lambda$), etc.).
Our color code for indicating various fonts is explained on the review sheet. Greek letters should be written in by hand (or typewritten if the character is available on your typewriter), and underlined in red pencil. Other important markings are for script (encircle with blue pencil) and Fraktur (underline with green pencil). Boldface is occasionally useful (for instance, to denote vectors as a substitute for arrows over letters); a wavy line in blue pencil below a letter indicates boldface. We automatically italicize mathematical symbols, and we do not use italics for emphasis, so in general the reviewer need not indicate italics.
Subject classification of reviews. The review sheet that we send you asks for your suggestions for the 5-character classifications of the paper being reviewed. We value your suggestions, because in general you have read the paper more carefully and possess more expertise than the editors. The current mathematical subject classification scheme is published in print in the most recent annual index issue of Mathematical Reviews and can also be sent to you on request.
Duplicate reviews. We have an understanding with Zentralblatt für Mathematik that allows us to print the same review that you submitted to them. Please notify us if your review has also been sent to Zentralblatt.
Change of address. Please inform our Reviewer Services Department at once of any change in your address or name. This will prevent the loss of review material and will save time and money.
Reviewing preferences. Our basis for sending articles to you is the reply card on which you indicated your reviewing interests and language skills. If we are sending you inappropriate articles, or if your interests change, please let us know your current reviewing interests.
When to keep it. Papers and books sent to you for review become your property once you have reviewed them. You should return a paper or book if you do not review it or if you recommend that it be listed only in the index. Also you should return an item (or a copy of the summary of an item) if you recommend using the summary as the review.
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- and Chinese-reading reviewers is chronic).
Subscriptions. Any requests for subscriptions or problems with current subscriptions should be addressed to:
American Mathematical Society
or:
cust-serv@ams.org
TEL: 800-321-4267 or 401-455-4000 (worldwide)
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Write to us. We invite all reviewers to write to our Reviewer Services Department if you have questions, complaints, or special requests. We are keenly aware that MR depends on its reviewers for its existence and we welcome your correspondence---all of which will be read, carefully considered and, when appropriate, answered. However, MR normally does not accept unsolicited requests to review specific papers.
Mathematical Reviews is a publication of the American Mathematical Society. The editorial office is at the University of Michigan. The postal address is
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