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Basically a few weeks ago I submitted my paper to a journal. It turns out that the paper is publishable, however a referee found a much better proof of my Theorem, and now I'm at odds on how to proceed. Do I:

  1. Amend my paper by substituting my proof with the referee's proof? Doing so makes me uncomfortable as I would not have contributed the most important part of the paper, someone else did.
  2. Continue publishing the paper with my (inferior) proof, but mention the referee's much better proof.
  3. Continue publishing the paper with my proof, but do not mention the referee's suggested proof.

What should I do?

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  • Just say that you had an original proof but have not included it as the anonymous referee suggested a better proof which you have used.
    – Tom
    Commented Feb 3, 2022 at 18:45
  • I would choose number 2. At the end of the day, the purpose of a paper is to convey info. Given the better proof, why not present it? You do not know which version of the proof will inspire other works. In addition, the referee will be happy that he/she has been helpful.
    – Prof. Santa Claus
    Commented Feb 3, 2022 at 19:02

3 Answers 3

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Ask the editor, but I would suggest to use the reviewer's proof.

You say that will make you feel uncomfortable because you didn't make the most important contribution to the paper. This isn't necessarily true. First of all, you wrote the paper. Without you, there wouldn't have been any proofs to improve upon. Secondly, you do not know how the reviewer came up with their proof. Perhaps something they read in your paper gave them this idea. Perhaps not. We don't know, so try not to make any assumptions in that regard. They shared the proof with you, put something in the acknowledgements to recognize their contribution.

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  • It is not unheard of that referees became co-authors that way. I even heard an anecdotal story that in one of those cases, the reviewer got sent the resubmitted manuscript again ...
    – user151413
    Commented Feb 3, 2022 at 20:02
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I agree with the others. Publish the better proof. Acknowledge it. But also mention that you originally had your own proof--otherwise readers may think you did not have a proof before you received the referee's proof. Example:

Theorem. statement
Proof. [I wish to thank an anonymous referee for this proof, which is better than my original proof.] proof

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    A quibble - I would be careful saying something is "better" than your published/submitted work. Perhaps "more concise", or something that does not downplay the quality of your own work.
    – RegressForward
    Commented Feb 3, 2022 at 20:16
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Ask the editor.

But since the referee suggests a better proof, it is probably safe to use it, and acknowledge the unknown referee for pointing it out to you. I would certainly go for improving the paper (=giving the better proof).

But as I said: Ask the editor. They might reach out and check with the referee whether he/she is fine with that.

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