A while back, we mentioned a new mathematics journal with an unusual twist on peer review. Rejecta Mathematica was founded with the mission of publishing articles that had actually been rejected by journal editors and peer reviewers, based on the reasoning that even mistakes can contain valuable information. The risk, of course, is that the journal would be nothing more than an outlet for cranks and the bile of scorned authors. The first issue is now out, and there's no shortage of bile, but there's also some fairly solid research and glimpses of how the online world has changed publishing.

Rejecta Mathematica, which is online only and open access, has some simple rules for publication. Papers had to be submitted for peer review at one or more other journals, and they had to have been rejected, either by the journal's editors or the paper's reviewers. The papers authors could then send a letter that describes the reason for rejection, along with the paper itself, to Rejecta, which would publish both as a single document.

There is an obvious tension at work in academic publishing. A number of significant papers have been rejected through some combination of political maneuvering, editorial misapprehension of whether the research was sufficiently compelling, and basic misunderstanding of the work on the part of reviewers. At the same time, researchers can always be counted on to overestimate the significance of their own work. There is also no shortage of crackpots with a PhD, pursuing ideas that can be unnecessary or fundamentally erroneous, all while railing against the powers that be in their field. The question is which of these would dominate the virtual pages of Rejecta.

Although I'm not in any position to evaluate advanced mathematics, the answer appears to be "neither." There's plenty of bile that hints at crackpottery; for example, one author invites everyone to "Read the Narrow-Minded and Ignorant Referee's Report and my response." In paraphrasing the response from a reviewer, another admits that he is "Quoting from memory, since I had rejected his rejection letter."

This latter author seems to have some serious issues with his field, writing, "Where did I go wrong? Perhaps I should not have called professional mathematicians, in the first paragraph, 'meaning-imposers' who generate 'inconsistencies and confusions.'" In fact, the term "Meaning-Imposers" appears in his title.

There's another author who is apparently attempting to derive masses for particles using quantum mechanics without having a functional theory of quantum gravity. I can't speak to the validity of the approach, but the author cheerfully admits that a string theorist has called the group using this approach "F-ing Crackpots" in a blog comment.

But there are also a couple of papers that appear to occupy a middle ground. In one case, an author is apparently convinced that his work is novel, while the two journals he sent it to were not. The math appears to be reasonable, however, as the authors noted that "one reviewer suggested a simplification of our proof, which we gladly used in our revision, which was also rejected." In another case, a group of researchers developed an algorithm that could perform halftoning (an image transformation used for print) via the well-understood mathematical approach of deconvolution. It was rejected in part because the reviewers didn't find the image results very compelling.

There's at least one article, however, that appears to be real, quality material. It was submitted to a journal that took 8 months to reject it based simply on the fact that it ran too long. In the meantime, the author had written a follow up, which has since been published and received a number of citations. The first manuscript, languishing on the arXiv preprint server, has also started receiving citations, and has now accumulated more than a work the author actually published in the Journal of the American Mathematical Society. So, it appears to be a quality piece of work that's finally found a home in Rejecta.

Probably the least important lesson of Rejecta's first issue is that there are mathematicians at war with their field, and using outrageous language in campaigning for their pet ideas. I certainly knew they existed in the sciences, so the surprise would have been if math didn't have its share. Nor is it a shock that the process of peer-reviewed publishing has its issues. To paraphrase Churchill, editorial discretion and aggressive reviewers can make it the worst system, except for all the others.

Instead, the real lesson is that the Internet era has allowed researchers to recover from some of the problems with peer review. The approach to quantum mass derivations may indeed be "F-ing crackpot," but its adherents are getting the word out (even if it is only via blog). Meanwhile, the arXiv has managed to keep a valuable bit of research from disappearing down the memory hold. Rejecta may be doing a service by putting these things in one place, but the work itself has clearly already found an audience. The journal itself, in fact, represents a logical outcome of the low cost of hosting and the growth of open access research.