In 2012, Shinichi Mochizuki posted a 500+ page proof of the ABC conjecture using his own invented framework called Inter-Universal Teichmüller (IUT) theory. The proof was so novel and self-contained that the broader mathematical community struggled for years just to read it. In 2018, two leading mathematicians — Peter Scholze (a Fields Medalist) and Jakob Stix — traveled to Kyoto specifically to work through the proof with Mochizuki and returned unconvinced, publishing a document identifying what they called a "serious, unfixable gap" in a core step.
Mochizuki disputes this characterization and maintains his proof is correct. When RIMS (the Research Institute for Mathematical Sciences in Kyoto, where Mochizuki works) published the proof in its own journal in 2021, critics noted an obvious conflict of interest. As Quanta Magazine and the Columbia Math Department blog (Not Even Wrong) documented, the publication did not resolve the dispute — it simply formalized the divide.
As of early 2026, the situation remains unresolved. Kirti Joshi published papers attempting to rehabilitate the proof, but his defense is explicitly conditional on acceptance of new enhancements the community has not endorsed. The result is a phrase that has become shorthand for the controversy: the ABC conjecture is "a theorem in Kyoto, a conjecture everywhere else."