Shinichi Mochizuki published a claimed proof of the ABC conjecture in 2012 using his own highly complex framework called Inter-universal Teichmüller (IUT) theory. In 2020, the Publications of the Research Institute for Mathematical Sciences (RIMS) in Kyoto — where Mochizuki himself is a professor — formally published the proof. However, this publication carries a significant conflict of interest, and the broader mathematical community has never endorsed it.
The core problem is a gap identified by two highly respected mathematicians, Peter Scholze and Jakob Stix, who reviewed the proof in person with Mochizuki in 2018. They concluded there is a "serious, unfixable gap" in a key step of the argument. Mochizuki disputes this, but has not produced a resolution that satisfies the wider community. Quanta Magazine and the Columbia Math Department blog (Not Even Wrong) have extensively documented this ongoing impasse.
As of early 2026, subsequent attempts to rescue the proof — including papers by mathematician Kirti Joshi — remain explicitly conditional on the community accepting new enhancements that have not been endorsed. The situation is unchanged: the ABC conjecture is an open problem in mainstream mathematics, with no consensus proof in sight.