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 , 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.