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For mathematical manuscripts, what makes the editor opt for a rejection rather than major revisions and vice-versa?

Usually, the editor determines the gravity of the mistakes within the manuscript. If they can be corrected in time, the authors are given the chance to revise and resubmit (major revision). But, if the mistakes can't be corrected in time. Then, a rejection decision is made.

The issue is that in the mathematical field, it is usually hard to determine whether the manuscript can be corrected in time or if the mistakes made are unfixable. Indeed, one can try a slightly different approach and fix the "grave" mistake in a short period of time. So, my question is what do editors rely on to decide that a mathematical mistake in unfixable no matter what and doesn't deserve a chance for a major revision.

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    Time to correct issues is not the only factor in rejections.
    – Ed V
    Jul 16 at 14:23
  • I think they rely on the authors and reviewers. Let's say a reviewer says a proof is flawed. Then it's up to the authors to admit that the reviewer is correct and thus a new proof is required (if possible). Otherwise, the authors provide a response to counter the reviewer's assertion. If a proof is critical and cannot be corrected, then the authors will withdraw the manuscript. Otherwise, it's up to reviewers to check the responses or revised proof provided by the authors. Jul 25 at 23:11

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For journal publication, time is of little importance other than for special issues. For conferences, time is of the essence. But if a paper isn't completed for the next issue or so, there is always the issue after that.

The main reasons for rejection are:

  • Not consistent with the journal's policies or focus.

  • Not sufficiently novel/interesting to publish (here). Or, these results are known already.

  • Probably not fixable at all. Serious and fundamental issues.

A few others, I'd guess.

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Rather than a direct answer to the question, the following is more of a frame challenge. I think the assumption in the question about why a mathematical manuscript can be rejected ingores a number of very relevant reasons.

First of all:

  • The editor might come to the conclusion that the results or techniques in the manuscript are not sufficiently innovative to warrant publication in the journal to which the manuscript was submitted.

  • On a similar note, the editor might consider the topic of the manuscript to be not sufficiently "interesting" (however the editor interprets this word) to warrant publication in this specific journal.

The above two cases will often result in desk rejection of the manuscript rather than peer review. It might, however, still be likely that the manuscript can be published in a different venue.

If, however, the manuscript makes its way to peer review, then the reviewer(s) will typically be asked to recommend whether the paper should be accepted, or revised, or rejected. The final decision will, of course, still be within the discretion of the editor, but in my experience, editors will often follow this recommendation.

Now, there are many potential reasons why the reviewer(s) might recommend rejection, even if they do not find an unsalvageable mistake in it:

  • They could find that the results are not sufficiently "substantial", i.e. they might be more or less clear to experts in this particular field.

  • The results and proofs might be written in a very sloppy way, which makes it extremely difficult to even determine if they are correct.

  • The writing of the paper might just be outright bad, thus making it a real burden to even read the paper.

  • It might turn out that the authors are completely unaware of large parts of the relevant literature.

The last three points might, in principle, be fixable, assuming that the authors take them seriously and put sufficient effort into it. However, this does not imply that the reviewers were necessarily obliged to recommend a revision of the paper instead of a rejection in such a case. A good reason to actually suggest rejection in some of these cases if the following experience that I made quite often when got the first requests to review papers:

The manuscript suffered from several of the issues mentioned above; I wrote a very lengthy report where I pointed out in detail all the problems that I encountered and suggested a major revision of the manuscript. The authors apperently took this as an encouragement that there paper were "close to acceptance", and instead of thoroughly improving the manuscript, the tried a "minimally invasive" approach to superficially deal with the issues I had raised, but did not make a real effort to substantially improve the paper - leading thus to yet another long report in the second round of review.

After I had become more experienced and already used to this pattern, I changed my recommendation practice. If a paper exhibits too many issues of the types mentioned above, I will typically point out several of them, include some general recommendation to the authors how they should improve their paper if they plan to submit it elsewhere, and recommend to reject the paper.

In such a case, recommendation for rejection (rather than for a major revision) clearly signals to the authors that, from my perspective, that paper is not close to being publishable - so much more work is needed to improve it than would be the case during a "major revision". For the majority of papers which I, as a reviewer, recommend to reject, the reason for my recommendation is actually this "not close to being publishable" issue rather than non-fixable mathematical errors.

TL;DR: Apart from mathematical errors that cannot be fixed (or cannot be fixed within a reasonable time frame), there are many more potential reasons why a math paper can be rejected by the editor or recommended for rejection by the reviewer(s).

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Journals do not accept all submitted papers which are correct. I find this a bit silly, but they continue to produce a fixed number of pages per year, and are trying to put the "best" articles they can manage in that number of pages. So, in general, editors will ask for a revision if they think that it is likely that the paper will be accepted after the revision, and will reject if they think it is not likely.

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    Why do you say "silly"? And, editors don't do this on their own. They use the advice of reviewers in almost all cases.
    – Buffy
    Jul 25 at 17:37
  • @Buffy The silly part is the restriction on the number of pages. There's plenty of room on the internet for as many articles as they want to accept. I don't understand your point about reviewers; I agree, they will either ask for a revision or reject (usually) with a report in hand and using that to inform their decision. Jul 26 at 18:31
  • Page limits lead to better, tighter, writing. Ask a writing professor. Imagine the workload on reviewers without page limits. Imagine the workload on reviewers if journals would accept an unlimited number of articles and/or pages. And even web hosting has costs, not just in space but, more importantly, in maintenance. A higher standard than "correctness" is appropriate, actually.
    – Buffy
    Jul 26 at 19:31
  • @Buffy I feel like you are reading a huge number of things into this that I didn't say; you're arguing with a strawman. I was just trying to explain the fact of page limits to the OP, and made an off-hand side comment, not a detailed description of my plan for fixing journals. Jul 27 at 3:39

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