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I recently agreed to review a journal paper (in theoretical computer science). After I started to read it in depth, I found out it is much harder than I expected - over 60 pages with over 20 theorems with detailed proofs. Also, the topic is not exactly my expertise - I do not know a lot of the related works that the authors base their results on. So far, I managed to verify about 10 of the shorter theorems. They seem correct, though I have some minor comments. The other theorems seem so long and complex that it will take me weeks to review, especially if I would need to read and understand the theorems in the cited papers that these theorems are based on. What should I do?

I thought of writing to the editor and explaining the situation in detail. Maybe the editor will be able to find another reviewer that will verify the other theorems. But I do not know how such letter will be perceived. In particular:

  • Is it common for a reviewer to review only a part of the paper, and leave the rest of the paper to other reviewers?
  • On the other hand: is it my duty, as a reviewer, to complete my review, regardless of how much time it takes?
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    Typical reviewing times vary a lot between pure math, different parts of applied math, CS, etc. What (sub)field does the journal live in? – user37208 Oct 18 '18 at 19:53
  • is it expected that you review and 99% confirm theorems? I thought in math fields it is acceptable to publish work that might be later proven to be wrong – aaaaaa Oct 19 '18 at 1:10
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    @aaaaaa - Most people believe that reviewers should believe beyond a reasonable doubt that all theorems are correct AND all proofs have sufficient detail for an expert audience. This doesn't necessarily mean checking every proof in detail. It's definitely embarrassing for all involved (more so for the authors and less so for the editors and reviewers) to publish work that is later shown wrong, though it is understood that honest mistakes occur. – Alexander Woo Oct 19 '18 at 3:35
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    "it will take me weeks to review" Um. It's sixty pages. How could you possibly review something of that length in mere days or hours? – David Richerby Oct 19 '18 at 14:13
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    If I submit a 60 page paper, I don't expect to hear from the editor in less than a year. – Alexander Woo Oct 19 '18 at 21:16
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Is it common for a reviewer to review only a part of the paper, and leave the rest of the paper to other reviewers?

I have done that on at least two occasions. Sometimes it is the only honest option.

On the other hand: is it my duty, as a reviewer, to complete my review, regardless of how much time it takes?

Not really. It is commonly considered a duty of a career mathematician to contribute to peer review of mathematical works (at least) proportionally to their own publishing. Whether you achieve this by refereeing some really tough papers or a lot of simple ones is up to you.

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Consult the editor

Adding to @darijgrinberg's answer: Consult with the journal's editor(s) before making any decisions.

They might:

  • Tell you more about what's common in a situation such as the one you're in.
  • Possibly decide they want to switch reviewers or divvy up the review work
  • Tell you what they expect from you (including telling you or hinting at you what they would regard as unethical).
  • Pressure you into continuing (not such a great outcome - but I have to add this in fairness)

Don't feel awkward or inappropriate about taking this up with the editors, it's the responsible thing to do.

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