Eight years after Shinichi Mochizuki first posted his proof of the ABC Conjecture on his website it has been announced that it has been accepted for publication in Publications of the Research Institute for Mathematical Sciences (RIMS).
Before you get too excited though, there are two things you should know. One, in 2018 Peter Scholze of the University of Bonn and Jacob Stix of Goethe University released work they believe shows a “serious, unfixable gap” in Mochizuki’s work which apparently has not been addressed beyond some comments in the accepted work. Two, Shinichi Mochizuki is the chief editor of Publications of the Research Institute for Mathematical Sciences (RIMS).
While it is common for mathematicians to publish in journals they are on the editorial boards for and they say he did not take part in the review process the publication of this contentious paper through a journal he is chief editor of does raise some questions. Davide Castelvecchi posted an in-depth write-up of the situation at Nature, where you can learn much more about the background and the possible implications of the acceptance of this paper:
If the editors of the journal “waved away these criticisms” and published the paper without major revisions, it would reflect badly on them and on Mochizuki himself, says Volker Mehrmann, the president of the European Mathematical Society (EMS), which publishes the journal on behalf of RIMS. (The EMS has no editorial control over the journal’s content, Mehrmann says, and he was unaware of the upcoming announcement until contacted by Nature.)
But one mathematician who prefers to be quoted anonymously says that editors and referees handling these papers might have been in a nearly impossible situation. “If the best mathematicians spend time trying to work out what’s going on and fail, how can one referee on his own have any chance?”