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I submitted my paper on mathematics to a journal 8 months ago but I have no received any reports or comments yet. I sent an email to the editor asking him about the manuscript, he just replied that it is still under review. What shall I do?

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    What shall I do? Wait, I guess. – user102 Oct 8 '14 at 13:42
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    An eight month wait is not at all unusual in mathematics. – Shane O Rourke Oct 8 '14 at 13:43
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    It is a bit weird that your question's title does not align with the question you ask in the body. Both questions are interesting, but you should choose which one you really want to ask and write your text and title accordingly. – Benoît Kloeckner Oct 8 '14 at 18:40
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    I've had plenty of papers take more than a year; one of my papers has currently been at a journal for 2.5 years. It takes a long time to referee a paper, and people who do a good job at refereeing get tons of requests. My usual policy is to ask the editor if there has been any progress in refereeing the paper at 9 months, at 1 year, at 15 months, and then every 2 months thereafter. – Andy Putman Oct 8 '14 at 22:32
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    IMHO, since most journals require copyright transfer, it would be ethical from their part, at the very least, to guarantee authors some time frames for their actions, specifically, maximum review time. – Aleksandr Blekh Jun 9 '15 at 3:06
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Mathematics tends to have a long refereeing process. It's nice when it can be completed in a few months, but eight months is not especially worrisome. The editor should be sending the referee(s) periodic messages to make sure they aren't just forgetting, and you can send status inquiries to the editor every once in a while if you'd like (it shouldn't be necessary, but it can't hurt and could conceivably help). I tend to ask for a status update every six months or so.

One reason it takes so long is that refereeing a mathematics paper is difficult. The referee has to read and understand the proofs, which is one of the slowest and most painstaking forms of reading. Another issue is that there is no expectation that it should be done quickly: a referee who takes eight months isn't generally considered problematic by the journal or the community at large.

In practice, the lengthy refereeing times are not a problem. Mathematics papers are typically circulated publicly (for example, on www.arXiv.org) long before they are accepted for publication, so the publication process isn't holding up progress in the field. And the mathematics community is well aware of how long it takes to get papers officially published and takes this into account in career evaluation (hiring, tenure, etc.). For example, if you're applying for a job, nobody will expect your papers from the last year or two to be published yet. If they are at least on the arXiv and submitted for publication, then everything is as it should be.

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    And that's just the process to get accepted. After the lengthy process of getting a referee's report, making corrections, and getting those accepted and your article officially put in line for publication, with some (reputable) journals you can still wait years for it appear in the actual print journal. Thankfully, a lot of them have caught onto publishing articles online, so you usually get a DOI soon after it's fully accepted. But the actual print version could take a long time, indeed. – zibadawa timmy Jun 9 '15 at 4:39
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To reiterate the other good answer and comments... do nothing. It is unfortunate, yes, and frustrating, yes, and inconvenient, yes, that refereeing takes so long... but it is both understandable and inevitable.

Ironically, but understandably, the more original your work is, the more effort will be required of referees... who are paid nothing, and will acquire no status/raises/funding/whatever from their efforts to appraise or improve your writing.

As in other answer/comments, hiring committees and funding agencies are aware of the time-lags... although, yes, true, it's better to have gotten through this gauntlet than have to explain that one is enduring it.

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