September 2018: There has been a back-and-forth in 2018 between Shinichi Mochizuki and Yuichiro Hoshi (MH) in Kyoto, and Peter Scholze and Jacob Stix (SS) in Germany, with SS spending a week in Kyoto in March 2018 to confer with MH.
SS 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 SS are missing some understanding of the background theory. It sounds like SS are still skeptical, and at minimum further clarification is needed about proving this corollary.
- SS report (August 2018 version): http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf
- Mochizuki response: http://www.kurims.kyoto-u.ac.jp/~motizuki/Cmt2018-08.pdf
- 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/