I’ve been pretty startled by all of the publicity that Mathgen and the Marcie Rathke paper (accepted by Advances in Pure Mathematics) have recently attracted. Many people drew parallels between this incident and Alan Sokal’s 1996 hoax, in which Sokal, a physicist, got the cultural studies journal Social Text to accept a parody article which identified physics and physical reality as a social construct. I’m flattered by the comparison, but I wanted to take some space to respond and point out some essential differences between the two cases.
Basically, where Sokal attacked the intellectual standards of the entire field of cultural studies, the purpose of the Rathke paper was only to expose a particularly dismal sector of the academic publishing industry, in a field (mathematics) which I believe is essentially sound.
As Sokal later explained, he was concerned by an apparent lack of “intellectual rigor” in certain sectors of the humanities. To test this, he wrote the now-notorious article, entitled “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity”. Its aim was to put forward a thesis which he thought would “flatter the editors’ preconceptions,” by interpreting physics in terms of progressive politics, but via fatuous arguments based on nonsensical or nonexistent evidence. Social Text was, according to Sokal, a “leading journal” of cultural studies, but as a matter of editorial policy, it did not subject its articles to peer review, nor did it claim to. Thus, the article’s claims about physics were not reviewed by any physicist. The article was accepted and duly published. Later, the editors defended their actions.
By contrast, no mathematician would mistake Advances in Pure Mathematics (APM) for a “leading journal”. It may not be obvious to the outside observer, but much of the work published there is of palpably low quality, belying their claim that papers are subject to a “rigorous and fair peer-review process”. Such journals are very unlikely to be read by serious mathematicians; they exist mainly as vanity presses, whose purpose is to fatten the publication records of the authors and the pockets of the publishers. APM’s publisher, Scientific Research Publishing (SCIRP), operates over 200 other journals, and several of them have received unfavorable attention before. Unlike Social Text, APM emphatically does not represent the forefront of its field.
Journals like this have proliferated with the increased popularity of the “open access” publishing model, in which the publisher’s fees are paid by the author, not the readers. This model has its pros and cons; on the one hand, it means that published work is available to anyone without the need for a paid subscription (including the taxpayers who often funded the project). But on the other hand, it changes the financial incentive for publishers to produce a good journal (since they get paid regardless of whether anyone reads it), and can create a conflict of interest with the journal’s quality standards. There are many reputable and high-quality journals published under the open-access model (including some that are supported by volunteer and in-kind contributions and charge neither authors nor readers), but APM is unquestionably not one of them.
Some readers seem to have interpreted the present case as an indictment of mathematics as a discipline: that mathematical research is so abstruse that even professional mathematicians are unable to distinguish real papers from randomly generated nonsense. I strongly disagree. The whole point of mathematics is being able to construct, and verify, rigorously correct arguments. Yes, the field is highly specialized, and any given mathematician may be unable to understand papers in a different subspecialty — but she will know that she doesn’t understand it, and have no shame in admitting it. In the case of the Mathgen paper, the content is so egregiously absurd that any mathematician, in any field, would be able to identify it as nonsense. Indeed, from the referee’s report, it is clear that he or she makes no claim to understand it, and recognizes that the paper is junk: the abstract makes no sense, none of the notation or terminology is defined, the main theorem has no proof (the whole point of a pure mathematics paper is to present and prove a theorem). What is incredible is that, after pointing out these defects, the judgement is that the paper should be accepted! (Several readers seized on the “provisional” nature of the acceptance; I’ll comment on this in a forthcoming post.)
In short, I don’t see that there are serious problems with mathematics itself, or even with academic publishing in general; just with this particular journal and its brethren, who masquerade as serious, peer-reviewed journals when the evidence suggests otherwise.