I am currently reviewing a mathematical paper that presents its main and sole result as an extensive formula. This formula relies on the notation defined in another paper, and the formula itself spans nearly an entire page.

I am unsure about the appropriate approach for writing my referee report on this paper, as it seems burdensome to fully restate the entire result. Would it be acceptable to provide a summary such as, "The main result presents a precise formula for something (without explicitly writing it out). This generalizes..."?

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    In cases like this it is worth stepping back and asking, “What is a review for?”. The principal purpose of a review is to tell the reader of the review whether it is worth investing the time in reading and understanding the paper - because you don’t get refunds for time spent! Focus on that entirely and you will find the task easier. Commented Jan 6 at 9:36
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    As an aside: When I'm presented with a complicated formula in a paper I'm reviewing, I type the thing in Maple and test it on a good number of cases. I estimate that half of the time the formula doesn't work as promised. Usually it's a typo, but sometimes it's something like "doesn't work on perfect squares." It's simple and it makes me look like a really smart and conscientious reviewer. But maybe this formula is too long(?)
    – B. Goddard
    Commented Jan 6 at 13:38
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    This "reiview" is a review of an already-published paper? Or it is for a paper submitted to a journal (or conference) and your review is to help the journal decide whether to publish it?
    – GEdgar
    Commented Jan 6 at 18:57
  • @GEdgar I use "review" for things we do on an "already-published paper", while in my understanding, "referee" is for the other thing that you mentioned.
    – HaJine
    Commented Jan 7 at 0:48

1 Answer 1


Sure, the review is not meant to be a test of your ability to restate the main result of the paper, and there is no benefit to doing so when the result is a long formula. It is fine to summarize the result or even refer to it in broad terms as long as you include a few salient points that explain what area of study the result relates to and why it is interesting.

Your suggested language sounds fine. You can include a reference to an equation number or theorem number from the paper if you want to be more precise.

One thing to try to avoid is a review that can arouse suspicion that you haven't actually read the paper or that you only looked at it enough to get a very superficial understanding of what it's about. This can be frustrating both for the editor and for the authors. So saying something like "This paper studies a question about knot invariants" is much too vague of a summary. On the other hand, going to the other extreme and quoting the main theorem verbatim also doesn't necessarily inspire confidence that you understand what the result is about, since quoting doesn't require any thought or understanding. For this reason, when I write reviews I prefer paraphrasing (or a combination of paraphrasing and summarizing) the main result in my own words.

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