Written: Feb. 3, 2007.
We professional academic mathematicians are lucky to be paid for something we enjoy doing the most, mathematical research. Many of us also enjoy teaching, and I for one, would be willing to pay, if I had to, for the privilege to teach, even Freshman calculus.
But, of course, not everything is perfect. One annoying aspect of our life is the expectation that we submit our work to peer-reviewed mathematics journals, and for those of us that are not yet tenured, or fully promoted, there is pressure to submit to "good" journals, so that the committee could say to the dean that this is an OK guy.
So you submit your latest paper, that you worked so hard on, and are so excited about, and (usually) justly proud of, and six months later (if you are lucky, sometimes it takes a year or longer), you get the referee's (or referees') report(s). With probability 5 percent, it would be a raving acceptance, but more likely, even if it gets accepted, the report would be lukewarm, obnoxious, and often written in sarcastic or patronizing style, that the referee can afford because of his or her anonymity. That report also sometimes contains comments that truly prove that the referee misunderstood the mathematics and the main point.
Maybe I am over-sensitive, but a rejection, or even less-than-raving acceptance, ruins my day. It also makes me sad that there are so many stupid mathematicians around, who are also nasty, and of course cowards, or else why can't they reveal their identity? Myself, the few times I had to reject a paper I was asked to referee, it was on the condition that my identity will be revealed to the authors.
Let me share with you two recent rejections, and two recent "acceptances".
Most people, when they get a rejection, keep trying, and resubmit the rejected paper to another journal. This involves lots of overhead, both physical and psychological, and the risk of being insulted again, since if the paper was misunderstood the first time, there is a good chance that it will happen again. And also, most people, when their paper gets accepted, but on condition of revising it according to the referee's suggestions, try to humor the referee, and often make corrections that they don't agree with. But as for myself, luckily, I already have tenure, and am fully promoted, so I decided, regarding the above-mentioned two rejections and one of the two "acceptances" (the Basketball paper, was joint with my grad student Arvind Ayyer, that being one of his first papers) not to resubmit the rejected papers and withdraw the accepted paper. Regarding the second paper above, my two coauthors graciously agreed to keep it only on our personal sebsites (and the arxiv).
Because, hooray!, we live in the 21st century, and we have the internet. We can publish our masterpieces in our personal website and/or arxiv. It is good enough for Grisha Perelman, and the immortal Yuri Matiyashevich has his own awsome journal. I am sure that many other smart people publish lots of their papers only in the arxiv and/or their personal websites. Web-papers are much more accessible (or in case of free electronic journals, equally accessible), are free of charge, and while they won't be reviewed in MathSciNet, with the wonders of google, and especially google-scholar, they will be easily accessible and searchable for the whole wide world.
But don't think that all the papers in my (and Shalosh's)
personal journal are "rejects". Unless otherwise
stated, they have never been submitted to a "real" journal,
since it is fun to write papers, but it is (usually) not
fun to interact with obnoxious editors and stupid and nasty
referees. Of course, if you are not yet fully promoted,
you have (at present) to play the game (unless you are Grisha
Perelman), but if you are fully promoted- or don't care about these stupid things-
you can afford to minimize that
unpleasant aspect of our professional life, and tell the
editors and referees to
take their math journals and shove them.
Added Dec. 16, 2022: Vince Vatter just told me about this great critique of Peer Review by Adam Mastroianni.