Gap in Mochizuki's proof of ABC confirmed by Lean
A formalization project led by Bungen Kato has concluded that a critical argument in Shinichi Mochizuki's Inter-universal Teichmüller (IUT) theory is currently unformalizable. While the project identifies a gap in the proof of the ABC conjecture, researchers are keeping an open mind as Mochizuki continues to provide new explanations.
Why it matters
This development marks a significant milestone in the long-standing academic controversy surrounding the ABC conjecture, potentially bringing the mathematical community closer to a consensus on the validity of Mochizuki's work.
Fumiharu Kato 加藤文元（Bungen） on X: "In today's press conference, we explained our efforts over the last two years which resulted in the following conclusion: The way the argument from Theorem 3.11 to Corollary 3.12 is written in the IUT papers is unformalizable. But since Mochizuki's explanation of this point has" / X
The report summarizes a technical academic dispute and the findings of a formalization project without taking a stance on the validity of the underlying mathematical theory.
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