On August 3, 2012, fictional professor Marcie Rathke from the non-existent University of South North Dakota sent an article to the scientific journal
Advances in Pure Mathematics , one of many journals published by
Scientific Research Publishing .
An article entitled “Independent, negative, canonical Turing arrows in equations and problems of applied formal PDE” (
pdf ) was accompanied by an intriguing annotation: “Let ρ = A. Is it possible to extend the isomorphism region? We show that D ′ is a stochastic orthogonal and trivial affine correspondence. In [10], the main result was the construction of the Cardano set, the Erdos function, Weil, which can shed important light on the Convey-D'Alembert hypothesis ”.
Both the abstract, and the entire text, and the
bibliography in this “scientific article” were generated by the
Mathgen program, which was written by the mathematician Nathan Eldridge (Nate Eldredge). He proudly stated that the article was eventually
accepted for publication .

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The editors of
Advances in Pure Mathematics reviewed the article, and after 10 days sent a congratulatory letter: the text was adopted.
However, they found a number of flaws in the article, which they asked to correct. In particular, the editors advised to rewrite the annotation for a clearer understanding and send a list of keywords. In addition, the text of the article contains “many mathematical expressions and notations for which the author does not give a preface,” and the second section in section 2.4 presents a theorem without proof. The editors asked for a more detailed description of the specific process of the proof for statements 3.3 and 3.4, and also to send the scientific work in a standard format file.
Nathan Eldridge had to write his own answer to the editors of the journal; he could not trust such a thing to the generator. He redid the annotation, but otherwise tried to protect the authenticity of the work. He replied that "there are indeed many mathematical expressions in scientific work, but readers of appropriate qualifications can understand their context (or lack thereof) from the context."
Regarding a more detailed process of proofs 3.3 and 3.4, the author wrote: “I believe that the evidence presented for these provisions is quite sufficient [for paragraphs 3.3 and 3.4 it is written, respectively,“ This is obvious ”and“ This is understandable ”]. Nevertheless, the author respects the opinion of the reviewer and adds a few additional details. ”
As for the format, there are no complaints at all: “the work is generated in the LaTeX format, which is a generally accepted standard for scientific articles, which cannot be said of
the APM magazine template made in Microsoft Word”.
In the end, the editors approved the article and allowed the publication. As is well known, scientific journals of a lower level, like this one, require payment of a fee for “article processing” before printing. In this case, it required $ 500, which Nathan Eldridge decided not to pay, so on paper we will not see the product of the Mathgen generator, unfortunately.