OpenAI and Anthropic claim to refute the Exponential Time Hypothesis
In brief
- OpenAI and Anthropic claim to refute the Exponential Time Hypothesis (ETH) with proofs formalized in Lean.
- The proposed algorithms only become advantageous from 10^10000 variables onward, with no immediate practical application.
- The proofs are under review by researchers, with no official certification yet.
OpenAI and Anthropic announced on October 26 and 27 that they had refuted the Exponential Time Hypothesis (ETH), a major conjecture in theoretical computer science formulated in 1999 by Impagliazzo and Paturi. Both labs date their discovery to October 16 and have published proofs formalized in Lean, an automated verification language.
The proposed algorithms, while very close, only outperform brute force starting from 10^10000 variables, making them impractical for real-world use. Both algorithms suggest a sub-exponential complexity of around 2^n / √log(n), directly contradicting ETH. Anthropic notes that its proof was generated and reviewed by AI models without initial human validation. OpenAI also claims results on the Kakeya and Yang-Mills conjectures.
Researchers Impagliazzo, Paturi, and Williams are organizing an open review to validate the proofs, though without official certification. No immediate impact is expected on cryptography or industrial SAT solvers, but the community is questioning the reliability of AI-generated proofs and the ability to verify them.
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