Someday, as strange as it feels to me right now, I might be asked to review an article for publication. A while ago my advisor and I were talking about this, and it hit me that I don't really know how to be a good reviewer, beyond the basics:

  • Respond timely to things,

  • Make your report clear and detailed,

  • Have actually read the paper,

  • Etc.

Beyond this, though, I'm completely in the dark. So I'd like to ask:

What's some good advice for a first-time reviewer?

My field is math, but I'm really interested in general advice (although advice specific to math, or another field, would also be interesting and useful).

I'd like to make this question "community wiki" or analogous, but I can't seem to figure out how - if someone can do so, please do, and then I will delete this paragraph.

  • 1
    Make constructive suggestions? Be polite but frank/honest? Mar 22, 2015 at 21:43
  • I don't recall seeing CW getting used on Academia SE like it is on MathOverflow. Different SEs have different cultures, and you don't need to use CW here for "soft" questions. (Most questions on this site are "soft.")
    – Kimball
    Mar 23, 2015 at 6:19
  • @Kimball I think we have basically stopped doing CW altogether here. There may be a meta discussion about this somewhere. That being said, I think SE in general is moving away from CW.
    – xLeitix
    Mar 23, 2015 at 7:45
  • There's a MSE, or possibly MSO, thread somewhere about how CW answers are allowed but usually discouraged, an CW questions are no more.
    – Flyto
    Mar 24, 2015 at 6:27

4 Answers 4


This is mostly just a whole bunch of comments strung together.

First, I think you should look for advice specific to refereeing math papers, as refereeing in math is quite different than most other fields. (Though it's perfectly valid to ask for general advice now, at some point you should want to know about refereeing specifically in math.)

Second, here are some places with advice:

  1. Attributes of an ideal referee, Notices of the AMS
  2. Refereeing a paper, from MathOverflow
  3. How do I referee a paper, from TCS SE

One thing I would disagree with in the first article is the statement that "The referee is expected primarily to check the correctness of the paper." I would say the primary job is to assess the importance of the paper, which includes correctness, though it is not always expected that the referee check every detail.

Anyway, since your question is rather broad, I suggest you read this and other Q&A's here and on MO, and then if you have more specific questions you can ask them separately.

  • 1
    Great suggestions, and I'll add the Leek group guide to reviewing academic papers Mar 23, 2015 at 21:21
  • @DavidRobinson Note not everything in that link applies to math. E.g., "You should never take more than a month to review." (I did include a the TCS link, but the TCS culture is rather similar, though not identical, to math.)
    – Kimball
    Mar 24, 2015 at 1:34
  • The OP did ask for general advice. Besides which, I think it's actually good advice not to take more than a month to review a paper even in mathematics, or in other cases when the journal or culture of the field allows it, or the cycle will never speed up. (The writer of that link is a statistician, and an associate editor for Biometrics). Mar 24, 2015 at 2:45

I think reviewing is a good "golden rule" situation: treat others as you yourself would like to be treated. For me, that means:

  • Be prompt
  • Be respectful and professional in tone
  • State clearly what you find of value in the paper, as well as your critiques
  • Clearly separate critiques into three categories:

    1. Serious problems that can affect the soundness or relevance of the work presented
    2. Issues that need to be addressed, but don't call the work into question
    3. Minor points for the improvement and polishing of the manuscript.
  • Base all of your statements on supportable fact, not opinion.


in addition to the above; Be frank if you: a) are unable to be timely b) feel you are not qualified to review the article (lacking knowledge in the used methodology, statics or field).

This will save all parties time and resources


It's hard to give good advice in a concise way about what makes for a good review. The thing is, one knows a good review if one sees one (and the opposite is true as well). So, with my students and postdocs, I occasionally given them reviews I write or receive as examples, and we discuss what makes it good or bad.

If you are a graduate student without having much of a track record publishing yourself, then chances are that you will get papers to review from one of your professors, and that you will know him/her personally. When that happens, ask them for examples of good and bad reviews they have received in the past, then base your review on those.

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