Claude Refuted ETH Too: Anthropic's 3-SAT Paper Explained (cellcog.ai)

Anthropic announced on October 27, 2026, that its AI model, Claude, has independently refuted the Exponential Time Hypothesis (ETH) with the publication of the paper "A 2^o(n) Time Algorithm for 3-SAT." This groundbreaking result follows a similar claim from OpenAI, both of which emerged on the same day. Claude's algorithm effectively solves the 3-SAT problem more efficiently than previously thought possible, demonstrating a deterministic approach with a time bound of 2^O(n log log n / sqrt(log n)) for the counting problem #3-SAT, marking a significant theoretical advancement in computational complexity. The implications of this discovery are profound for the AI/ML community and theoretical computer science, as it challenges long-standing assumptions underpinning algorithmic limits. Although the results are mostly asymptotic and do not translate into practical improvements for current SAT solvers, they open the door to subexponential algorithms for other complex problems like Independent Set and Clique. By confirming the likelihood that ETH is false, this research invites further exploration into faster theoretical algorithms, potentially shifting approaches in computational theory. Both models (Claude and OpenAI's) highlight a trend toward automated discovery in theoretical adjustments, pointing to a new era where AI contributes to critical advancements in science.