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I received the following rejection email today :

Dear Prof. XXX,

This message concerns the manuscript

XXXX by XXX

submitted to XXXXX journal.

Informal consultations with possible reviewers have persuaded me that your article is too specialized for our journal, and therefore I am sorry to say we cannot accept it for publication.  We have elected not to review it fully so as not to cause undue delays in its eventual publication.

I advise you to submit it to a journal more narrowly focused on number theory, and I do wish you success in publishing it elsewhere.

Now, my question is:

Are there any positives/negatives that can be taken from this email ? or, it is just a desk rejection ?

Note that I received this email 20 days after the submission.

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    Submit it to a more specialized journal that is pertinant to this article. This journal seems to be more general and accept articles that are of sufficient interest to a more general audience. It says exactly what it says. Submit it to a specialized journal. I am telling it from experience. There are no negatives in this email. Prima facie, positive is their advice to submit to a specialized journal. – Rajesh Dachiraju Oct 9 '20 at 3:15
  • Being very specialized is good. So that's good in what they say. Just not good for publication in that journal. – Philosopher of science Oct 9 '20 at 11:10
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    This is the default desk rejection text for journals of the American Math Society. I received the exact same rejection from Transactions of the AMS in the past. – the L Oct 9 '20 at 11:20
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    If it was from the Journal of Number Theory then I would be disheartened. Otherwise, we can call it a positive. – Strawberry Oct 9 '20 at 12:57
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    If I understand this correctly, your paper has now been rejected at two journals that experienced members of this site called a “top journal in the field.” My advice is to make sure you don’t ask your adviser what great journals you could submit your result to, but which journals they believe you have a realistic shot at publishing it in. Maybe you already did. – gnometorule Oct 9 '20 at 14:43
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This is a desk rejection. There's not much more to say about it - I suppose you could say that they haven't outright said your paper is incorrect, which is a positive; on the other hand they did also say that they are not considering your paper and you should submit elsewhere, which is effectively the same as rejection and certainly a negative thing.

There's nothing to do but submit elsewhere.

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    +1, but I wouldn't claim That is effectively the same as rejection, usually considered the most negative outcome, since your article is too specialized for our journal, which is an out-of-scope desk reject. Perhaps a negative is that you shouldn't have submitted, then again, journals are rarely clear on what they want. – user2768 Oct 9 '20 at 8:22
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    @user2768 I don't understand what you mean. In the event of a rejection, they are not considering the paper and one should submit elsewhere. In the event of a desk rejection, that's the same result, except accelerated since no reviewers needed to be invited. – Allure Oct 9 '20 at 10:26
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    @Allure He is saying that being too specialized is much better than being wrong. – Philosopher of science Oct 9 '20 at 11:12
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    @Allure I meant they, I don't know user2768's gender identity. – Philosopher of science Oct 9 '20 at 11:53
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    It hasn’t got any negative implications about the quality of the work. In fact, the paper may even be above the average, it is just not in the scope of that journal. – NearIR Oct 9 '20 at 12:16
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From the letter, it simply seems that you did not submit to the right journal, which can happen to anybody and can be usually known only afterwards. They did not do a classical review process with reports so nothing can be deduced about the quality of the paper.

The good new is that they replied rather quickly so that you can start the submission in an other journal without having to wait for months.

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There is a great positive in this letter: they are telling you that your work is too specialized. Being specialized is good in science and in academia, and, as Thomas Kuhn indicated, is the common tendency in the sciences. You usually need to be specialized in any higher education field. Just look for a more specific journal. They even tell you which kind you should look for.

The negative aspect is obviously that it was desk rejected.

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    Being "too specialized" here likely means that it's just not that interesting, except to maybe a few people. Not being interesting to a wide audience is not a positive thing. – glougloubarbaki Oct 9 '20 at 12:16
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    @glougloubarbaki "Wide audience" is relative, and, I think, not that important. On one extreme, 99% of academic peer-reviewed publications are not interesting to the general public. On the opposite extreme, many of the most prestigious work in science is only understandable by a handful of people. – Philosopher of science Oct 9 '20 at 12:20
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    I mean a wide portion of the journal's intended audience, i.e. in this case researchers in mathematics. A prestigious and non-specialized journal will probably not consider publishing a paper that is only of interest to a very specialized audience, as opposed to a stronger result that is relevant to a wider community. For instance, the resolution of Fermat's conjecture is interesting a much wider audience than number theorists, but there are papers in number theory that are only interesting to a small fraction of all number theorists. – glougloubarbaki Oct 9 '20 at 12:27
  • @glougloubarbaki Yes, good point. – Philosopher of science Oct 9 '20 at 12:30
  • I would love to publish on Science, which is not at all a specialized journal – carlo Oct 9 '20 at 19:10

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