Claude autonomously discovered a 2o(n) 3-SAT algorithm, refuting the Exponential Time Hypothesis
__alpoge__ · x · 2026-10-27
Anthropic has released the paper "A 2o(n) Time Algorithm for 3-SAT" along with code: an internal Claude research model, with no human input, autonomously found a deterministic subexponential-time algorithm for 3-SAT on October 16, using 14 million output tokens — directly refuting the Exponential Time Hypothesis (ETH) in computational complexity. The algorithm actually solves the harder #3-SAT (solution counting) problem in time 2O(n log log n / √log n).
Anthropic researchers then worked with Claude to polish the paper's presentation, and the Lean 4 formalization was also written by AI models. Caveat: the result is purely asymptotic and says nothing about solving formulas in practice. Anthropic positions it as a research artifact, not accepting contributions.
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