Mochizuki claims a proof through his inter-universal Teichmuller theory, formally published in 2021 by the journal he edits, but Peter Scholze and Jakob Stix identified what they describe as a serious, unfixable gap around a step called Corollary 3.12 in 2018, and most number theorists have not accepted the proof as correct.
What would resolve this Either a version of the argument that resolves the Scholze-Stix objection in a way the wider number theory community accepts, or an independent proof, or a counterexample.
OpenNumber theoryErica Klarreich, Klarreich, Titans of Mathematics Clash Over ABC Conjecture (2018)