Nate Eldridge has written a program, Mathgen, to randomly generate a nonsense math paper. (It’s based on an older program, SCIgen, that generates random computer science papers.) While they don’t make any sense, the Mathgen papers capture the typical style of mathematical writing pretty well. The main quirk that gives it away is that a real math paper would repeat terminology, Mathgen creates new mathematical terms every sentence. (This an inevitable consequence that the algorithm used is context-free.)

Apparently it doesn’t give it away for everyone, though. A Mathgen-generated paper was submitted to a journal, Advances in Pure Mathematics, where it was accepted with revisions. I’ve never heard of this journal, so I would assume that it’s like the mathematical version of a vanity publisher that makes money from publication fees. But what’s amazing is that the paper was peer reviewed! The suggested revisions are of the form “please make this make sense”, but still, out there somewhere there’s a person who read this paper, and tried to make constructive comments. Who was this person?

As probably most of you have heard, Shinichi Mochizuki has announced a proof of the abc conjecture. At some point I decided to stop posting about announcements of solutions to famous unsolved problems, after several high-profile retractions. This time, it’s been long enough to wonder if the proof will hold up. The papers are of daunting technical complexity, so it sounds like it will be some time before we hear the verdict.

PolyMath has the definitive round-up of links on the abc conjecture and Mochizuki’s work, including this nice expository article from the Notices.