Math journal accepts computer-generated nonsense paper

The peer-reviewed journal Advances in Pure Mathematics was tricked into accepting a nonsense math paper that was generated by a program called Mathgen.

To be fair, the journal did note several flaws in the paper, such as "In this paper, we may find that there are so many mathematical expressions and notations. But the author doesn’t give any introduction for them. I consider that for these new expressions and notations, the author can indicate the factual meanings of them," and requested that they be corrected prior to publication.

However, the "author" of the paper replied with a set of pat rebuttals ("The author believes the proofs given for the referenced propositions are entirely sufficient [they read, respectively, 'This is obvious' and 'This is clear']" and these were seemingly sufficient for the editors.

Sadly, the paper wasn't published, as the "author" wasn't willing to pay the $500 peer-review fee.

On August 3, 2012, a certain Professor Marcie Rathke of the University of Southern North Dakota at Hoople submitted a very interesting article to Advances in Pure Mathematics, one of the many fine journals put out by Scientific Research Publishing. (Your inbox and/or spam trap very likely contains useful information about their publications at this very moment!) This mathematical tour de force was entitled “Independent, Negative, Canonically Turing Arrows of Equations and Problems in Applied Formal PDE”, and I quote here its intriguing abstract:

Let ρ=A. Is it possible to extend isomorphisms? We show that D′ is stochastically orthogonal and trivially affine. In [10], the main result was the construction of p-Cardano, compactly Erdős, Weyl functions. This could shed important light on a conjecture of Conway-d’Alembert.

This is a nice follow-on from the Sokal hoax, wherein a humanities journal was tricked into accepting a nonsense paper on postmodernism. Goes to show that an inability to distinguish nonsense from scholarship exists in both of the two cultures.

Mathgen paper accepted! (via Neatorama)



  1. “accepting” in this case seems to be much less than the headline implies.  They are accepting it… to go on to the peer review stage, where we might presume it would have been recognized for what it was.  Do things still get published after peer review says it’s crap? Or would the “it’s crap” review not be noted at publication?

    1. My thoughts exactly. Maybe I’m missing something, but I don’t see the significance of this if no qualified persons reviewed the paper.

    2. Nope.

      The paper was accepted. Advances in Pure Mathematics is a money for resume padding scam journal, which makes this case different than the Sokal hoax.

      From the acceptance letter:

      Thank you for your contribution to the Advances in Pure Mathematics (APM). We are pleased to inform you that your manuscript: … has been accepted. Congratulations!

      Anyway, the manuscript has some flaws are required to be revised : …

        1. The journal’s email is admittedly vague, but could be interpreted as “the referee has provisionally accepted your paper, but has requested the following set of minor revisions…” (and, if you read the author’s response, that’s the assumption).

          But the somewhat sloppy style of the editor’s email is of a part with the other evidence for a vanity journal.

  2. An infinite translated mathematics of tolerance and charity among artificial memory devices is ultimately binary. Stimulating rhetoric…absolute. The theater of noise is proof of our potential.

  3. If you have to pay the journal for a peer review or pay for publication the one being tricked about it being worthwhile is you.

  4. “On August 3, 2012, a certain Professor Marcie Rathke of the University of Southern North Dakota at Hoople…”

    A fan of PDQ Bach, I see.

  5. I just ran Mathgen, and the results look SO REAL (until you actually read it).  My paper even had numbered conjectures, and a nice long bibliography of other hypothetical papers.  Brilliant!

    1. The credibility appears to be, uh, variable at best…. I just ran it and the very first sentence was “It has long been known that the Riemann hypothesis holds [18, 14]”.

  6. The difference between this and the Sokal Affair, is that journals from SRP don’t seem to be taken particularly seriously by anybody — they seem to exist mostly so people can pay to bolster resumes. Social Text (where Sokal sent his manuscript) is srs bsns for some humanities people. So this seems to be more of a critique of publishing-fee-mill “journals” than of the culture of academic math.

    1. Sokal’s paper actually made much more sense than he claimed. The physics was nonsense but the Hermeneutics Sokal wrote actually hangs together. The ‘nonsense’ was in the quotations he cited.

      Social Text is not peer reviewed either. That does not really work for what is actually a journal of aesthetics. 

      The magazine does not claim to be a scientific peer reviewed journal. So treating it as one didn’t make any sense.

      The mathgen hoax seems flawed because they didn’t get to peer review. It doesn’t count.

      The people who did the job properly were a couple of MIT students who submitted a paper generated using a Perl script to one of those affairs that accepts everything they get.

      1. Well-said.  The claims Sokal made about the meaning of his hoax didn’t hold up.  It was an apples-and-oranges situation.

        1.  yeah, apples and oranges it is. the sokal hoax was also not aimed at improving the quality of publications in any scientific field but just to show off the suposed superiority of the methods of natural sciences (to which the philosopical foundations were laid in about 1900) over those of social sciences (which are quite modern philosophically)

          long story short sokal was just beeing a dick.

    1. That’s not true for math journals.  In math, authors do not typically pay any publishing fee at all.

  7. Any mathematicians want to comment on the review policies and field impact of this journal?  It seems to have an impact factor of ~0.15.  In many fields of the natural sciences, a low impact factor like that would likely mean that there is only one reviewer, who wants to get their job done as quickly as possible and is not interested in arguing out technical points.

    Even though the paper is “peer reviewed”, there may be the implicit assumption that papers in that journal will not be cited for any wide-reaching conclusions.  Anyone in academia can point to a few published papers in their field that are incorrect or nearly valueless – it’s unavoidable even with the best of intentions by all parties.  Generally, these papers will either be ignored (not cited much) or later papers will specifically refute their conclusions.

    1. As others have pointed out, this is a vanity journal.  0.15 vastly overrates its impact.  That’s why it was targeted for this exercise.

    2. I had never heard of the journal “Advances in Pure Mathematics” and, as far as I can tell, it seems to be trying to masquerade as the well respected “Advances in Mathematics”. A quick look at their contents shows that it’s pretty much junk and only started in 2011. The fee to publish is highly suspect as well. This isn’t something that happens in mathematics journals.
      No respectable reviewer would even take a look beyond the gibberish abstract, except for curiosity.

  8. I keep getting spammy requests for papers from these guys. Apparently I have magically acquired a doctorate! A related journal publishes some wonderful pieces. I recommend “Some Examples to Show that Objects be Presented by Mathematical Equations,” “Base-X Notation and Tri-Value Logic,” and “Efficient Use of Cloud Computing in Medical Science.” The first one presents a bunch of pictures the writer drew in Mathematica; the second presents something that’s been around for at least 50 years if not more; the last is gobbeldegook that doesn’t say anything at all except “Doctors should use THE CLOUD to share diagnoses. Also make sure it’s encrypted.”

  9. “Goes to show that an inability to distinguish nonsense from scholarship exists in both of the two cultures.”

    The importance difference is that the mathematical nonsense paper was rigorous.

  10. Always bugged me when a tech article never listed what the variables were in the formulas given. Then I found out even the author didn’t know. The math was ghost written.

  11. As has been noted by others, this is important, but shouldn’t be overblown.  I publish in the Computer Science literature, not Mathematics, but things will be somewhat similar. (One CS specific weirdness is the importance of conferences.  Ours are peer reviewed, whereas they’re not in most fields.  For this reason, I’ll talk about ‘publications’, not ‘journal articles’.)

    There are a number of ways of classifying publications:
      – Peer reviewed vs. not peer reviewed
      – How much respect they hold in the field
      – How much they charge for publication
      – For profit vs Not for profit
      – Requiring ‘important’ research vs. requiring ‘valid’ research (i.e. do the reviewers have to think it is a useful contribution, or just that you didn’t do anything obviously wrong.)

    The Sokal affair pointed out that a highly respected journal in a field was accepting papers that they perhaps shouldn’t have been.

    This pointed out that a journal that charges for publication (most don’t charge much), and which was apparently not well respected, was doing a poor job of peer review.

    Both are useful.  It is really great to know which journals to avoid.  But I don’t think this is an indictment of mathematics in the same way that the Sokal affair was an indictment of postmodernism.

    If you want other instances, see 

  12.  Indeed – I’ve never heard of any reputable journal asking an author to pay to have an article reviewed. I certainly do not review for any journals that require payment. This is a “vanity” publication, and I’m sure it’s seen as such by the mathematics community.

    1. They’re not asking the author to pay for having the article reviewed (Cory is, as far as I can tell, wrong to call it a “peer review” fee); the charges are for publication if the article is accepted (and the author still wants to go ahead with it).

      This is actually the usual approach for author-pays scientific journals. Whether or not such journals are “vanity” journals (as this one appears to be) depends on the journal itself, and the field. (For example, three of the top five journals in astronomy are author-payment-based, and have been for decades.)

  13. I ran the generator program. My article began:

    It is well known that there exists a Wiener, trivial, semi-projective


  14. Dear Cory,

    Mathematician here. To echo comments by Roy Wiggins and Alex Rudnick (and to somewhat address metacalifragilistic’s comment), this is, pretty blatantly, a vanity journal. I get a spammy email from them at least once a day (which is frustrating, because they [intentionally?] have a name very similar to a top math journal). No serious pure math journal (with the exception of very recent experimentations with open access journals, which are kind of unnecessary due to the arxiv) charges for publication. And, randomly browsing their publications (so, say, 5 data points), the published papers have pretty clearly not been vetted, let alone edited for correct english, and are generally non-sensical.

    (In particular, this is really rather different than Sokal.)

  15. This paper is less full of nonesense, omission and cryptic maths than most papers on computer graphics. Author should definitely consider submitting a computer graphics paper.

    1.  Reminds me of a comment by Tom Duff, “90% of computer graphics research is mathematical archaeology.”.  I might not’ve remembered the words exactly by that’s the gist of what he said.

  16. I’m also a mathematician, and I second everything that David Zureick-Brown said. I just wanted to add that I don’t like the line:

    Goes to show that an inability to distinguish nonsense from scholarship exists in both of the two cultures.

    You’ve missed the point. It’s not that journal reviewers can’t distinguish between nonsense and scholarship, it’s that this particular “journal” isn’t interested in the distinction. They are only interested in the publishing fees.

  17. Sokal absolutely exposed the vacuousness and intellectual pretensions of the post-modernists, who are a particularly egregious example of the political corruption which aflicts modern American academia.

    Those who are just learning about the “Sokal Affair” for the first time will benefit from reading the Wikipedia article about it:

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