September 2018: There has been a back-and-forth in 2018 between Shinichi Mochizuki and Yuichiro Hoshi (MoHo) in Kyoto, and Peter Scholze and JacobJakob Stix (ScSt) in Germany, with ScSt spending a week in Kyoto in March 2018 to confer with MoHo.
ScSt have released a report saying they believe there is a gap in the proof of Corollary 3.12 in IUTT-3, and Mochizuki has posted a reply saying that ScSt are missing some understanding of the background theory. It sounds like ScSt are still skeptical, and at minimum further clarification is needed about proving this corollary.
- ScSt report (August 2018 version, slightly updated from May 2018 version): http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf
- Mochizuki response:
- http://www.kurims.kyoto-u.ac.jp/~motizuki/Cmt2018-05.pdf (to StSc May 2018 version)
- http://www.kurims.kyoto-u.ac.jp/~motizuki/Cmt2018-08.pdf (update for StSc August 2018 version)
- Further discussion and links on Mochizuki's site: http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html
- Somewhat drama-ish Quanta magazine write-up by Erica Klarreich: https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/
