# What does "Check the proof of theorem x" mean as a comment from a referee on a mathematical paper?

In the reviewers comment. A comment from one of the referees was as follows

"Check the proof of theorem x"

Does this mean the theorem is wrong, it should be just rechecked for typos or is it just to make sure it is correct?

Additional info: The theorem is one that I have proved myself.

• Is "theorem x" a theorem you wrote yourself or one proven elsewhere ? They may feel the theorem is incorrect or not applicable in the way you want to use it. Commented Jul 27, 2022 at 2:02
• The theorem is one that I have proved myself. Commented Jul 27, 2022 at 2:18
• Were there any other related comments? Did you include a complete proof? Commented Jul 27, 2022 at 13:26
• This comment could mean anything from "I don't believe this proof" to "this proof contains a typo." Commented Jul 27, 2022 at 16:15
• In that case it's not a very helpful comment. I wouldn't write something like that in a referee report. I also think if you add these details to the question it may get reopened---it's just currently formulated without enough info to understand the context. Commented Jul 28, 2022 at 3:24

Since the theorem is one you have proved yourself, it should be included in the paper (either in the body or an appendix, depending on its importance to the main stream of argument) or it should be referenced if you already published it in another paper. If it is already in the paper, I would recommend you take the instruction of the referee at face value --- check the proof to satisfy yourself that it is correct and clear, and make any revisions you need to make to correct/clarify. Here is an example of what your response to the referee might look like:

Referee: Check the proof of Theorem 4

Agree - Minor edit: We have re-checked the proof of Theorem 4 as requested. We are satisfied that this proof is correct (though if the referee has any specific concerns we are happy to consider them further). In the course of reviewing the proof we decided to add some further clarification to aid understanding of our use of the Lehmann–Scheffé theorem (pp. 27-28).

and here is another example of what it might look like if you make no revision:

Referee: Check the proof of Theorem 4

Agree - No revision: We have re-checked the proof of Theorem 4 as requested. We are satisfied that this proof is correct (though if the referee has any specific concerns we are happy to consider them further). At present we do not propose to make any revision to this theorem, but we welcome any specific deficiencies in the proof being drawn to our attention.

• Almost as if you have done this before... :) Commented Jul 27, 2022 at 12:24
• Haven't encountered this type of referee comment before, but I've done a few revisions in my time.
– Ben
Commented Jul 27, 2022 at 12:47
• It seems to me the referee ought to say what it is about the proof in question that the referee had concerns about. (Of course, that doesn't answer the question of what to do when you receive the report.) Commented Aug 4, 2022 at 22:22
• Indeed, that would be preferable. Which makes it all the more reasonable to just take the comment at face value, check the proof, and report the result of your check.
– Ben
Commented Aug 5, 2022 at 1:03

As a referee, I would never purposefully put such an incredibly vague comment. However, I almost sent a referee report recently with {\color{red}\Huge Start reading at section 2.2.} because I had at some point stopped reading at that position in the article and wanted to remember where to start my refereeing work again. (Thankfully I saw it when looking at the pdf of the report.)

It's possible the referee just jotted that down to remind themselves to look at it again, then forgot to go through and check that theorem's proof.

• Hah, I put so many such comments in my drafts that, as I approach the final draft, I begin to get paranoid that I won't remember to remove them all. Commented Jul 28, 2022 at 23:11
• @LeeMosher Couldn't you just use an environment for comments which you can turn off or which creates warnings when creating the pdf? Commented Jul 29, 2022 at 8:24
• What Bruno did ("\color{red}\Huge") should work reasonably well. You most likely have some tool that can search for it. Just make sure when you start that the original doesn't contain this. Commented Jul 29, 2022 at 17:21