Shinichi Mochizuki's 2012 claim to have proved the ABC conjecture, one of mathematics' most difficult unsolved problems, remains unverified despite over a decade of intense scrutiny. The Japanese mathematician at Kyoto University submitted a 500-page proof using novel mathematical machinery he developed, but the mathematical community has made virtually no progress determining whether his work is correct.
The ABC conjecture, formulated in 1985 by David Masser and Joseph Oesterlé, connects three coprime integers (A, B, and C where A plus B equals C). The conjecture posits that radical values of these numbers follow specific constraints. Solving it would have profound implications for number theory and related fields.
Mochizuki's proof employs "inter-universal Teichmüller theory," an entirely new mathematical framework he created. This originality compounds verification difficulties. Most mathematicians cannot read the work because they lack familiarity with his conceptual architecture. Those who have attempted detailed engagement report struggling with gaps in exposition and unclear logical connections.
In 2018, mathematician Peter Scholze and Stix Jakub identified what they considered a critical flaw in Mochizuki's reasoning regarding the theory's foundational steps. Mochizuki disputed their criticism, leading to a stalemate. Neither side has convinced the mathematical community of their position.
Journals have declined to publish Mochizuki's proof pending clearer exposition. The impasse reflects a deeper challenge in modern mathematics where increasingly abstract proofs become harder for even expert mathematicians to verify. Traditional peer review assumes sufficient shared mathematical language and context. Mochizuki's work violates that assumption.
Recent initiatives to resolve the debate by creating clearer explanations and alternative formulations have stalled. Without consensus on verification, the ABC conjecture remains officially unpr