Scientific communication
Which of the following is the ultimate purpose of scientific communication?
- To impress expert referees and convince them that you are clever.
- To bolster your publication record.
- To get cited lots.
- To publish in top journals.
- None of the above.
In my view, the ultimate purpose of scientific communication is to communicate ideas, so that someone else, who wouldn't otherwise have thought of something, thinks of something. Anything else is more-or-less immaterial.
It's tough for early-career researchers these days, with very little in the way of job security and lots in the way of stress. Thinking of publication in terms of impressing experts/getting cited/publishing in top venues can only create more stress for you. Rather than worrying about getting a career in academia, worry about making an impact on your subject. It's more in your control, and it can only help with the former. Perhaps thinking that way, and remembering why you're really doing maths, can help you stay sane.
If someone thinks of something because of your paper, then it can have any of the above effects or none. If that person is an expert referee, they may be impressed, and you may get published in a top journal. But suppose that you went to great pains explaining something to make it clear for nonexperts, and an expert referee rejects it on the grounds that "This is all well-known to experts". Well, maybe a nonexpert will understand what you have written and have a new idea, and maybe they wouldn't have if you'd aimed it at that expert and had it accepted by that top journal. I would argue that the latter situation makes for healthier and less compartmentalised science.
What am I talking about here? Am I saying that PhD students should go against their supervisors' advice and include extra trivial details that everybody knows? No: nobody wants to read that.
I'm talking about the following. Let's suppose you have a nice proof of a folk-theorem. Or you've spent a long time thinking about a particular area which is not well-represented in the literature and you've developed some intuition for it and feel you could explain it, focusing on a couple of well-chosen examples. Or you've figured out the answer to a problem which, it turns out, was easier than you thought it would be. Any of these could fall into the "well-known to experts" category, and hence into the "difficult to publish in a good journal" category.
When a referee complains that something is well-known to experts, they may mean "the author of this paper overestimates the novelty of their work in the way they have bigged-it-up and in their choice of publication venue". So if you write such a paper, don't send it to a sequence-of-journals-of-increasing-disrepute getting more and more annoyed with the referees, just send it somewhere it's likely to get accepted.
Writing these things up would be good for you, good for the community, and good for science.
I'd (probably) read (some of) them.