https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/
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- Corollary 3.12 is the critical step in Mochizuki's claimed IUT proof of the abc conjecture.
Supports. The article says in its own voice that the corollary is central to the proposed abc proof and that mathematicians agree it is at the core, then quotes Frank Calegari's blog post calling it a critical step without which there is no proof at all. It also reports Brian Conrad's account that several readers, Scholze among them, independently stalled at the proof of 3.12, which is evidence of the same point from the reading experience of experts rather than from either party to the dispute. Sep 16, 2026
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Posted online in 2012, Mochizuki’s papers supposedly prove the abc conjecture, one of the most far-reaching problems in number theory.
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Scholze and Stix argue that a line of reasoning near the end of the proof of “Corollary 3.12” in Mochizuki’s third of four papers is fundamentally flawed.
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But in the case of Mochizuki’s Corollary 3.12, mathematicians agree that it is at the core of the proof of abc. Without it, “there is no proof at all,” Calegari wrote. “It is a critical step.”
Supports. The article says in its own voice that the corollary is central to the proposed abc proof and that mathematicians agree it is at the core, then quotes Frank Calegari's blog post calling it a critical step without which there is no proof at all. It also reports Brian Conrad's account that several readers, Scholze among them, independently stalled at the proof of 3.12, which is evidence of the same point from the reading experience of experts rather than from either party to the dispute.
The abc conjecture (in certain forms) would offer new proofs of these two theorems and solve a host of related open problems.
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Scholze and Stix err, he wrote, in making arbitrary identifications between mathematical objects that should be regarded as distinct.
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Something more subtle is exactly what the proof does, Mochizuki contends. Scholze and Stix err, he wrote, in making arbitrary identifications between mathematical objects that should be regarded as distinct.
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History 2
- Sep 16, 2026ReadingSteward of “Corollary 3.12 is the critical step in Mochizuk…” · supports, read whole
- Aug 11, 2026Entered the graphEntered the graph; copy stored