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I am reviewing a paper for a top-ranked journal in robotics. The main results of the paper are about control and not specifically robotics. I am aware that robotics is a multidisciplinary subject which has also a ton of control in it but the problem here is the following. The paper is, mathematically, really hard to follow. The mathematical details would require maybe more than 2 weeks for me to review and to go through the equations.

What would you do in this case? I was thinking to suggest to submit to another journal, more control-oriented.

What do you think?

Thanks for your opinions.

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    Is it you who has a hard time to understand, or is it generally people in robotics who would have a hard time to understand the paper? In case of the former, you might want to inform the editor that you might not be the right expert to review the paper (and ask whether you should continue anyway), in case of the latter your suggestion to submit at another journal might be good, but you should still try to review the paper as good as possible. – Mark Nov 16 '17 at 10:57
  • I can't answer your question because the paper has been sent to me and I think in robotics for sure there has to be someone who is able to understand the paper better than me. Though, I think that this is a small portion of roboticists. I am asking this question because I wouldn't like to reject a journal paper just because I don't fully understand it. – desmond13 Nov 16 '17 at 10:59
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    The editor can make those decisions if you just present the situation to her/him. If one or more of the other reviewers are able to understand the mathematical details, your opinion on the other aspects of the paper may be enough for the editor. Otherwise, he may decide to find an extra reviewer that specializes in these areas. – nengel Nov 16 '17 at 11:10
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    i definitely wouldn’t reject the paper for this reason. (if you think the paper’s central argument/results — not just the math — are obscure, then rejection might make sense.) it sounds to me like you have some understanding of the math, but it would take you a while to fully verify it. if i were you, i’d take a few days to check for gross errors in the math, and then review the paper— even knowing i hadn’t fully verified it. then i might send, along with my review, a short letter to the editor of the journal saying i did the best i could and that a reviewer with diff expertise might be ideal. – dbliss Nov 16 '17 at 14:32
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    I am amazed of how many good suggestions I am getting here. Thanks a lot for your time in writing a comment/answer. – desmond13 Nov 16 '17 at 14:42
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Decision based on maths. If an overhaul of the mathematics would significantly reduce the time required for an expert to understand them, then you should state that in your review and that might well be a reason to require major revisions. On the other hand, if such an overhaul would only help non-experts, then that might well merit a mention in your review, but I don't think such an overhaul is necessary for acceptance.

Reviewing. Two weeks is ~4% of the year. Committing that amount of time to a single review (as would be required for you to study the details of the mathematics) seems unreasonable to me. Perhaps you can raise this with the editor. They might well suggest that you disregard the details and focus on other aspects of the manuscript, they can always ask another reviewer to check the details.

Scope. To determine whether the manuscript is in scope, you could compare the volume of material on control with articles published by the journal. If you think it is out of scope, then perhaps raise this with the editor.

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    it’s hard for me to believe that removing mathematical detail would ever help a reader of the paper trying to replicate the results. i doubt an overhaul of the math is justified. i think the thing that needs to be said is this: at least in my field, reviewers are not expected to fully verify every single variable in every equation in a manuscript. this would take too much time. that said, reviewers are expected to scan for gross errors. can the OP handle scanning in this way? – dbliss Nov 16 '17 at 14:36
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    I should say that, in mathematics, committing 2 weeks to reviewing a paper is unusually long but not unreasonable. At the most extreme, it is said that the papers of Wiles and Taylor-Wiles finishing the proof of Fermat's Last Theorem took more than a person-year's worth of time (distributed over a number of experts in different parts of the paper) to review. – Alexander Woo Nov 16 '17 at 15:43
  • @dbliss I'm not recommending removing mathematical detail; is there an ambiguity in my post? I can't comment on whether an overhaul is justified, but I do believe it is plausible, given that a well-structured proof is far more accessible than a poorly structured proof. – user2768 Nov 16 '17 at 15:46
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If you feel qualified to comment on some aspects of the paper, but not all, you can do just that. You should simply be very clear on what you comment on, what you did not checked, and so on. The editor will decide whether to ask another complementary opinion (which means, in case you do not plan to deliver your review soon, that you should inform her or him early that e.g. you will not assert the mathematical correctness).

Mentioning that the paper is mathematically heavy is certainly something you should include in your review, of course, to help the editor judge if the paper is suitable in this journal.

In my book, referees do not accept or refuse papers. Editors do, and referees inform editors decision as much and, more importantly, as precisely as reasonably possible. This includes a wide variety of opinions and comments.

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