Nobody Cares About Your Paper

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?