Claude disproves the Exponential Time Hypothesis, says Anthropic
Why it matters
Anthropic posted a preprint, "A 2^o(n) Time Algorithm for 3-SAT", credited to Claude and deposited on Hexagon on 27 October 2026. It claims a deterministic algorithm that solves 3-SAT on n variables in 2^o(n) time, refuting the Exponential Time Hypothesis (ETH) proposed by Impagliazzo and Paturi in 2001, and that also counts the satisfying assignments. Anthropic says the core algorithm was found on 16 October by an internal Claude research model using 14M output tokens and no human input, after which Anthropic researchers worked with Claude on the presentation. The Lean 4 formalization is public on GitHub, and the repository's CI re-checks the proofs with a second, independently written kernel. The result is purely asymptotic and says nothing about solving formulas faster in practice, it does not settle P vs NP, and the preprint is not yet peer reviewed. OpenAI separately claims a similar result.
Read the source: hexagonmath.org (opens in a new tab)
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