If a reviewer makes significant contributions to improving a paper, may he/she suggest becoming a coauthor? I was asked by the editor of a mathematical journal to review a submission by an author (unknown to me) which heavily relies upon some of my earlier work. I do not have much experience with writing peer reviews, but I have a good grasp of the topic of the submission.

The new results in the submission build heavily on earlier results in my published work; they are interesting and, in my opinion, worth publishing. However, while reading the mathematical proofs, I couldn't shake the feeling that they were overly complicated. Indeed, after thinking about it some more, I found that the proofs can be dramatically shortened by using insights that the author may not have had. For instance, one proof would go from roughly three pages to around half a page. For another proof, it seems that it can be reduced to a more standard situation, again drastically shortening it.

My work-in-progress report on the paper now 1) sketches the shortened proof for the first situation, 2) describes the needed insight to reduce the proof in the second situation to the more standard situation. At this point, the suggested changes seem to amount to a significant contribution to the paper since they touch not just minor parts of the paper, but the bulk of it.

At this point, I wonder what the best way to proceed is. Should I just submit the report with these suggestions? Or may it be appropriate in this situation to suggest to the editor that, if the original author is interested, he may contact me so that we can co-author a revised paper together? Or would that be considered unethical?

I do not want to overstep my bounds as a reviewer, but on the other hand I don't know how common it is for reviewers to contribute significant improvements to a paper anonymously.
At this point, I wonder what the best way to proceed is. Should I just submit the report with these suggestions?


This is indeed the high road to take here. As a reviewer, you explain your ideas on how the paper can be improved. The authors will or will not take all or some of them into account.

Asking for co-authorship in return for your service would likely be perceived as very cocky and unprofessional. I doubt that either the editor or the authors would be pleased about this or seriously consider taking you up for your offer.