Publication: an author’s view

One of the few positives about this strange year is that I have done a lot more mathematics than usual. Sitting on the sofa with nothing to see but occasional people walking along the wynd outside has given me time to think, though I admit I felt a bit like the Lady of Shalott at times.

More papers written, more papers submitted, and a higher proportion of papers rejected. If everyone is writing more papers and the capacity of journals has not increased the result is to be expected.

I am beginning to think that I am not very good at judging the quality of my own papers. Some that I consider fairly routine are accepted by journals, while others that I consider quite groundbreaking are turned down so quickly that the editors can hardly have had time to think about them.

Now, at my age, it doesn’t matter a great deal if I publish papers or not; and I could save myself a lot of trouble by simply putting them on the arXiv and encouraging people to read them there.

There are a few arguments for not doing that.

• The standard argument is that the refereeing process is a guarantee of quality; referees will catch the mistakes and you have a chance to put them right before the paper gets published. There are a couple of things wrong with this. First, often mistakes are not spotted by referees but are pointed out by readers after the paper has appeared. Second, referees do more than just point out mistakes. Once I had a fairly positive referee’s report on a paper which, at a certain point, said “page 13, line 5: This is wrong.” The referee gave no indication of why it was wrong; I read it carefully and wrote to the editor saying “I stand by what I wrote”, and the paper was published without any change to that point. Another more recent referee’s report, one of the most positive I have ever had, ended by saying “The open questions that the authors state: I think they could probably answer some of these.” The editor took this to mean that the paper could not be published without major revisions. We wrote back inviting the referee, if (s)he knew how to answer these questions, to be a co-author – we certainnly couldn’t do it – and heard nothing for two years, after which there was no alternative but to withdraw the paper.
• An argument that does carry weight with me is that many of my papers have coauthors, many of whom are researchers at the start of their careers, and for their sake the paper should be published in the best journal that will accept it. Yes, that is true, and that is the main reason why I still submit papers to journals.
• The final reason is that universities are judged by the quality of their research, and the rules of the game specify that this research must be published in journals; conference proceedings essentially don’t count. Why? Because the people who judge the quality are incompetent to do it themselves, and rely on the gold standard given by refereeing (but see the first point). So while I am in employment, I have no choice.

On the last point, when you put a paper in the St Andrews repository, the first question, before any details of the paper itself, is: Peer reviewed or not? This is clearly the most important piece of information for the bureaucrats. The difference in attitude is reflected by the fact that almost inevitably I forget to answer it and when I try to upload the form I am told to go back and answer that question.

Some of my papers which have been turned down by journals have stood the test of time and are now among my most cited papers. Back in the days when submitting a paper to a journal meant printing it out and putting it in an envelope with a covering letter, one paper came back from a journal appearing not even to have been taken out of the envelope and unfolded. This paper is now sometimes cited as a pioneering document in the theory of mutually unbiased bases in quantum computing (although we had no idea about this at the time).

Thinking about all this has led me to a theory. It is the interdisciplinary papers that are most likely to be rejected by journals without proper scrutiny. (The paper referred to above was so interdisciplinary that we felt it necessary to include a “road map” of the concepts discussed.) A paper which is simply an incremental improvement of already known results is more likely to be taken seriously. This despite the fact that journals claim that the opposite is the case. And of course I much prefer finding unexpected links between very different areas.

Sad. But maybe true, and maybe inevitable. And I must make clear that, as hinted above, I find no fault with journal editors, who have been facing huge difficulties with the every-increasing pressure to publish.