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I submitted a paper to a decent mathematical journal more than six months ago. Later, after communicating with several people, I have come to find the notation that I used in the paper very confusing, and thus fear that people may have serious difficulty in understanding my work.

I have since revised my paper by eliminating some notations and adding more examples and explanations. I think the revised version is much better than the previous one, even though there are no changes affecting the results of the paper, and I haven't found anything wrong in the proof.

I am worried that the referees will be annoyed by the notation that I previously used, and thus lose interest in my paper. So, I am considering submitting the revised paper to the editor to help the referees better understand my work. But some people say the referees would be unhappy to see the revision if they do not ask me to submit one.

Two weeks ago, I got a reply from the editor saying the paper is still under review, but he did not say when the review would finish, saying something like "it is difficult to put excessive pressure on the reviewers." So, I guess the review may still require some time to finish.

Should I submit the revision or not?

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    Please note that we had to make an enormous number of corrections to the text. If this is the quality of the writing you submitted, that will also not help your case, and will slow down the review process as well.
    – aeismail
    Commented Jan 14, 2015 at 19:30

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You should not submit your revised version at this time. If it had been just a day or two since you submitted, it would be a different matter. However, more than six months later, it is quite likely that the reviewers will be angry to receive a new version of the paper, particularly since you have made a great deal of changes. This will be even more so if they are a substantial portion of the way through the review process. (It is also unfair to the reviewers and editors if the author can keep changing and revising the paper while it is under review.)

Your best bet will be to wait until the reviews have been returned, and use your revised version of the paper to "jump-start" the revision process.

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  • As long as the changes are minor, I don't see a problem with updating the arXiv version however. There's a chance the referees will see it, and help them understand the current version better.
    – Kimball
    Commented Jan 15, 2015 at 7:18
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I'm a mathematician who sometimes referees papers for math journals. If I were the referee for your paper, I would prefer to receive the revised and improved version. Quite possibly your referee has not started yet. If they have started, they can choose to ignore the new version, or use the new version to make the refereeing process easier.

(For what it's worth, a shorter version of this answer received at least six up-votes on mathoverflow in the brief time before the question was moved to here.)

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