I have received the following referee comment:

This paper is well-written and the results appear to be correct. But I don't think the research is significant enough to warrant publication in ....(math journal name). Perhaps it would fit better with ......(another math journal name)?

How could I know that my article is significant enough?

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    Some of this (as in other answers and comments-to) is code-language for "status". Some status-enhancing things can be understood: solving old, important problems, for example. Beyond the obvious, status-determination depends on many things external to the literal mathematics. E.g., if you were already a big-shot, and your paper were merely-reasonably-good, publication would "add-status" for all but the top journals. I daresay that the same result from a lesser-status person would be treated differently... – paul garrett Feb 4 '16 at 23:38
  • @paulgarrett "the same result from a lesser-status person would be treated differently" if this is my case, how can I overcome this stumbling block. – Semsem Feb 5 '16 at 8:20
  • It is not really a stumbling block for people with less reputation. It just means that they don't get a free ride but have to first produce some research of a higher quality. – Tobias Kildetoft Feb 5 '16 at 9:38
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    The only way to see if your submission is significant enough is to submit it and see what response you get. – Stig Hemmer Feb 5 '16 at 9:45
  • @TobiasKildetoft agree. It seems that is the only way. – Semsem Feb 5 '16 at 11:41

Significance may be a very subjective judgement. Of course, for old, famous problems such as Fermat, any proof would count as significant, but the question becomes much more dodgy when one enters a side alley. As heuristic, ask yourself: is the result solving an old, unsolved problem? Is it connecting two unconnected or loosely parts of the field? Is it a beautiful, unexpected result? Is it generalising existing concepts?

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  • Thank you. I read many articles. Some of them contains only new and non-trivial results and just generalizing existing concepts to higher dimensions or different spaces. I thought that my article is better than those articles. – Semsem Feb 4 '16 at 19:25
  • @SamehShenawy Better in which sense? Could you be more specific? Is the journal they recommended perhaps a better fit? If you get an algebraic result which you submit to a functional calculus journal, the readers may not appreciate it, so readership matters. – Captain Emacs Feb 4 '16 at 19:35
  • The number and quality of results, as I and the second article author think, are better than those of the articles we motivated by. – Semsem Feb 4 '16 at 19:42
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    Try somewhere else then. And be prepared for the long haul. Don't forget, the legend says that Newton introduced journals for the purpose of keeping his competitors out :-) – Captain Emacs Feb 4 '16 at 19:46
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    @SamehShenawy An issue with "the number and quality of results... are better than those of the articles..." It's possible that you've gotten much better results, but that for an expert they are relatively obvious generalizations of the originals. I've run into this issue several times in my own work - someone might publish something that in my opinion is pretty low quality and obvious, but that to publish the better result I need to show that there are important things that the original can't do that my approach can. – Joel Feb 4 '16 at 23:33

"Good enough for journal X" is not a mathematical claim. Operationally speaking, it is precisely a matter of collective opinion. Math journals group themselves into rough, approximate equivalence classes (which is also entirely a matter of collective opinion), and you should take this negative referee result as one data point that your paper is not good enough for a journal of that class. If your prior belief was that the paper was roughly equal or better in quality to other papers published in journals of the same class, you should try at least once more at a different journal of about the same level.

A good referee report reveals something about why the referee thinks the quality of the paper is not sufficient, either in absolute or relative terms. This may give you something to improve: either actual mathematical improvements or improvements in the exposition to make referees believe your work is more valuable.

In summary: it doesn't necessarily mean much on its own. Revise if applicable and resubmit. Good luck.

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  • Thank you. I agree with you. One more thing, I have noticed that the IF of the suggested journal is more than the referee journal IF. I want to re-evaluate my work. How can I know that my work is significant enough for a certain journal. I want to avoid this report type. – Semsem Feb 4 '16 at 19:15
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    "I want to avoid this report type." - if you wish to publish, you will have to live with a lot of this type of reports. Take the messages on board - sometimes you can ask the journal editors whether papers of the present kind are of interest for the journal, before you submit for review. – Captain Emacs Feb 4 '16 at 19:40
  • @SamehShenawy Impact Factors are statistically meaningless. – David Roberts Feb 4 '16 at 21:53
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    @DavidRoberts, or, to be more precise, impact factors are commercially-motivated products... cf. "conflict of interest", etc. – paul garrett Feb 4 '16 at 23:35
  • @paulgarrett ga.lsu.edu/blog/andrewsluyter/2015/01/27/… – David Roberts Feb 5 '16 at 0:19

In a comment to @PeteLClark's answer, you state "I want to avoid this report type". We all do, of course. But remember that good journals reject around 2/3 of all submitted papers. You will not be able to avoid having at least some of your papers rejected if you continue to publish, simply based on statistics and the fact that the reviewing process has a random element to it. It's just part of the process. Go with the flow -- take the reviewer comments serious (they are typically written by people with a good amount of experience), address them in your manuscript, find a different journal one rung down the ladder, and resubmit.

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    An additional point here - if you're not sometimes getting rejected that means either all of your papers are being published in the highest possible journal or you are publishing in much lower quality journals than you should be. – Joel Feb 4 '16 at 23:35
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    @DavidRoberts I don't think the OP has the reputation needed to get people to read his articles if they are published in an obscure Iranian journal, do you? A good paper in an obscure journal will be ignored unless the author is so famous that people automatically read everything he/she writes. A mediocre paper in a good journal will at least be skimmed if it seems relevant, even if the author is unknown. – Joel Feb 5 '16 at 1:06
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    It's not really controversial that academics should publish, is it? If you "should" publish, then you "should" publish in a venue that isn't massively too obscure for your work. If you always aim too low, and taking things to extremes, you might as well just stick a few flyers to lampposts. Atiyah can holler proofs into a thunderstorm if he likes, he's a free man, but on the whole what he should do, as an academic, is publish in venues suited to the significance of the work. Which may or may not be the Ukranian Mathematical Bulletin depending on the paper :-) – Steve Jessop Feb 5 '16 at 3:51
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    @DavidRoberts Even if we forget about job prospects (which obviously is an issue), if the OP produces major results but publishes in obscure journals they won't get noticed. Sure, it would be great if there were some other filter that got the important works through to readers. But so many papers are published these days that I can't read them all, and I'm simply going to ignore papers published in lower journals. – Joel Feb 5 '16 at 7:03
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    Thank you all for this useful discussion. How can I overcome this stumbling block, I mean reputation. – Semsem Feb 5 '16 at 8:45

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