I handle quite a few papers (though far fewer than other editors I know) as an associate editor at Mathematische Zeitschrift. Since the acceptance rate at Math Zeit is something in the neighbourhood of 20%, there are certainly good papers which I have to reject. What papers “make the cut” through the first round depends, to some extent, on how “interesting” the paper is. Naturally, this is a somewhat subjective judgement. I make the determination (in part) on quick opinions I solicit from experts. But there is also a second possible mechanism available. Suppose I decide to send the paper out for a thorough review, but then I can’t find anyone to review it. If I email 10 people in the immediate field (not at the same time of course; usually requests to review come with a request for alternative suggestions for reviewers) and they all say no, does that indicate that nobody cares about your paper and it should be rejected? What if it’s twenty people? I haven’t (yet) ever rejected a paper on these grounds. But I have started to form opinions on certain specific subfields of number theory which seem to generate many pages of material but very few people willing to review anything. If they don’t care enough about their own subject to bother reviewing each other’s papers, why should anyone else?
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Meta
I think if a whole field doesn’t want to review, this is a problem and perhaps the best response is exactly to start rejecting (explicitly) because no suitable referee could be found.
Probably, though, in every field there are some people who dependably write papers with excellent ideas, which will benefit the community, but whose writing style is sufficiently atrocious and whose resistance to change is sufficiently great that no-one wants to referee because they will face a choice between either rewriting the paper one preliminary report at a time, or letting through an unintelligible mess. I don’t see a good solution to such papers – blocking them from publication is a loss to the community (especially if there are no arxiv preprints), allowing publication encourages degradation of standards.
I feel like this is a general problem with pure mathematics: there is a tendency to encourage: (1) citations to existing papers and (2) generalizations. These days math is getting pretty specialized, and in any subfield (no matter how popular), it’s hard to see how diminishing returns won’t take place. I think this will probably happen for most fields eventually…
At some point, as mathematicians, we should probably figure out how to restructure the reward system of math so that publishing new papers and endless generalizations isn’t the sine qua non of academic promotion and recognition.
Don’t get me wrong, I love math, but I think we are at a sufficiently advanced stage that we need to focus on other areas like exposition of existing material and a change in the way research functions in order to remain healthy as a discipline.
Interesting thought. I am from a different discipline (Chemistry) and I review around 30-40 papers per year, but as far as I know it rather rarely happens that requests to review are declined in our field. I think I did it only about 3 times in my life. It feels of kind of a duty to do this work, especially since I am obliged to others also reviewing my work.
How long are these papers, and how long does it take to read and review them?
I’m in a different field, but (sadly) my primary consideration when deciding if I’ll accept a review request is whether or not I need a tenure letter from the editor asking me…
There are a surprisingly large number of junior people (postdocs and some non-tenured faculty) who don’t even bother responding to referee requests.