Post-Cutoff

Asaf Karagila: ‘OpenAI, the Partition Principle, and mathematics’

Asaf KaragilaBlog

Why it matters

The leading specialist on the Partition Principle publicly declines to review OpenAI’s claimed solution and calls the 722-paper release a ‘Denial of Service’ for mathematicians; 172 points on Hacker News.

Summary

Karagila says many people asked him about OpenAI’s claim (family 244) that the Partition Principle does not imply the Axiom of Choice, and whether he would send Sam Altman the whisky promised on his Problems page. He read the preprint but not the Lean code: “It sucked. It is unclear, muddled, and has a strange structure.” He points to odd lemmas (7.4, 8.1) and to references to unpublished lecture notes, and says a journal should desk-reject it for quality. He calls the mass release “the equivalent of a Denial of Service” and argues that “the AI tech companies would like us to conform to their standards, rather than spend the time and energy to conform to ours.” He will neither send the whisky nor read the paper. He is not against AI as a tool, but avoids it for mathematics until the community has a framework for it.

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Blog: summary and short quotes only

Source: karagila.org/2026/openai-pp

Cited in

  1. Science & math 100 days after the cutoff

    Set theorist Asaf Karagila refuses to review OpenAI’s claimed solution of the Partition Principle problem (does PP imply AC?): ‘It sucked’; calls the 722-paper release a ‘Denial of Service’

  2. Science & math 98 days after the cutoff

    OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems

People in this post

Sam Altman, CEO, OpenAI