Claude model refutes the exponential time hypothesis

Anthropic published the preprint “A 2^o(n) Time Algorithm for 3-SAT,” in which its internal model found a deterministic algorithm on October 16, 2026, that solves 3-SAT and #3-SAT in subexponential time 2^O(n log log n / sqrt(log n)), refuting the exponential time hypothesis (ETH) — assuming the construction is correct.

Compiled by Sergey KostenchukPublished 2026-10-27Updated 2026-10-27

2026-10-27 Research OpenAI

🧪 Claude model refutes the exponential time hypothesis

Anthropic published the preprint “A 2^o(n) Time Algorithm for 3-SAT”: on October 16, 2026, its model found a deterministic algorithm that solves 3-SAT and #3-SAT in 2^O(n log log n / sqrt(log n)) — subexponentially, which refutes ETH. The proof is machine-checked in Lean 4; a human has only partially verified it.

🌍 If the result is confirmed, ETH and SETH are false: hundreds of works on computational complexity will have to be re-verified. The core of the algorithm was found without human hints — 14 million tokens.

👤 For theorists: bounds derived from ETH require revision. For everyone else — an example of how LLMs are becoming a tool for mathematical discoveries, although the benefit only appears at ~10^10000 variables.

Source 1: https://hexagonmath.org/2610.00577v1 Source 2: https://github.com/anthropics/formal-math/tree/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth

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