GoKawiilOpenAI claims proof that Partition Principle does not imply Axiom of Choice
OpenAI released a preprint, accompanied by Lean formalization code, asserting a resolution to a long-standing open problem in set theory: whether the Partition Principle implies the Axiom of Choice. The announcement prompted widespread attention from mathematicians, including a blogger known for offering a whisky bottle reward for a solution to this exact problem.
GoKawiil's interpretation of the reporting above, not reported fact.
The blogger's skeptical response suggests the mathematical community may not yet accept AI-generated proofs at face value, especially for results in foundational areas like set theory where rigor and peer verification are paramount. The episode highlights unresolved questions about how mathematics should credit, verify, and formally incorporate AI-assisted or AI-generated proofs, including whether chat logs or full reasoning traces should be disclosed to reviewers.
- OpenAI published a preprint and Lean code claiming the Partition Principle does not imply the Axiom of Choice.
- A mathematician who had offered a reward for solving this problem says he will not pay out, voicing skepticism about the claim.
- The incident raises broader unresolved questions about verifying AI-generated mathematical proofs and disclosure standards in academic publishing.
Source: karagila.org, 2026-10-08
Published there as: “OpenAI, the Partition Principle, and Mathematics”
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