Shinichi Mochizuki

After spending a week in Kyoto in March 2018 discussing the proof directly with Mochizuki, Scholze and Stix concluded in a report titled Why abc is still a conjecture that there is a serious, in their view unfixable, gap in the argument, centered on a step called Corollary 3.12. Stix described the problem as an inequality where the measuring stick is shrunk by a factor nobody controls, so that control over what the inequality actually means is lost; the situation has also been compared to M.C. Escher's winding staircase, where local steps look consistent but fail to close up around the loop. Scholze has said he was entirely unable to follow the logic of the proof past a specific figure in Corollary 3.12, and that he still considers the abc conjecture open. Mochizuki has responded that the criticisms stem from fundamental misunderstandings of his theory. The papers were nonetheless accepted for publication in 2020 by the journal Mochizuki himself edits, without the disputed mathematics being changed, and most number theorists have not accepted the proof as resolving the conjecture.