Overview
- On Monday, October 26 OpenAI published AI‑generated writeups and Lean formalizations claiming a local smoothing proof that it says settles Kakeya and Stein’s restriction conjectures, a refutation of the Exponential Time Hypothesis (ETH), and a mathematical existence proof for certain four‑dimensional quantum field theories while some physics artifacts remain withheld.
- A computer‑science working group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams has begun independent checks of the ETH claim and has written that their involvement is for examination rather than certification.
- Hours after OpenAI’s announcement Anthropic released its own AI‑derived ETH refutation, producing overlapping claims that multiple labs and separate review teams must now compare and vet.
- Mathematicians, AGMAI advisers and other critics have pressed OpenAI for fuller transparency on which internal models, prompts, training data and any human sources produced the outputs before the results can gain community acceptance.
- If the ETH claim holds up it would force researchers to audit hundreds of complexity results that assume ETH and could affect cryptography, but experts say practical consequences and trust in the proofs depend on broad independent reconstruction, peer review and clear provenance.