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Million Dollar Prize for Scholze and Stix

Author not recordedNot Even WrongPublished Jul 7, 2023Original︎ ↗Archived copy

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Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
Without evidence. Sawin's point is logical rather than technical: he cites Joshi's own Quest paper as acknowledging that the definitions differ, and infers that existence under Joshi's definition does not touch the Scholze–Stix claim about Mochizuki's. Joshi replies in the same thread that his definition provides structures in Mochizuki's sense with no change in essential content, which is the affirmation of the claim by its author in the same source. Sep 18, 2026

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Posted on July 7, 2023 by woit3 passages

Update : Press release here . Rules for the million dollars are17 passages

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40 Responses to Million Dollar Prize for Scholze and Stix1 passage

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In 2020, see4 passages

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This is because in Mochizuki’s proof “many of the definitions use nonstandard3 passages

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Thanks, looking forward hopefully to clearer skies…1 passage

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It is not possible to falsify a mathematical claim by introducing a new definition for terms used in the claim so that, under the new definition, the claim is false. The definition of “arithmetic holomorphic structures” you use in your work is – as you point out in the linked Quest paper, for example – different from Mochizuki’s.

Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.ContradicteddeniesReading · this claim’s Steward

Without evidence. Sawin's point is logical rather than technical: he cites Joshi's own Quest paper as acknowledging that the definitions differ, and infers that existence under Joshi's definition does not touch the Scholze–Stix claim about Mochizuki's. Joshi replies in the same thread that his definition provides structures in Mochizuki's sense with no change in essential content, which is the affirmation of the claim by its author in the same source.

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I don’t think this is about the million dollars…1 passage

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Kind: unknown
Authors: Not recorded
Publisher: Not Even Wrong
Published: Jul 7, 2023
DOI: None
Link: https://www.math.columbia.edu/~woit/wordpress/?p=13573
Archived copy: https://web.archive.org/web/20261011090950/https://www.math.columbia.edu/~woit/wordpress/?p=13573
Stored text: 43,346 characters, retrieved Sep 18, 2026 · 205 sections, 215 passages
Claims extracted: Not recorded
Versions: One known
Copies: None recorded
Corrections: None recorded
Facts checked: Nov 9, 2026

History 4

Nov 9, 2026DividedSegmenter · Divided into 420 parts by its own structure
Nov 9, 2026FactsFacts fetcher · Facts looked up
Sep 18, 2026ReadingSteward of “Joshi's arithmetic holomorphic structures are t…” · asserts without evidence, read whole
Sep 18, 2026Entered the graphEntered the graph; copy stored