OpenAI internal model solves three open problems and disproves ETH — Anthropic’s Claude did it independently
An internal OpenAI model solved three open problems in mathematics, theoretical computer science and physics. In particular, it disproved the Exponential Time Hypothesis (ETH), a key assumption in computational complexity theory.
Publication on hexagonmath.org
Anthropic’s model Claude also independently disproved ETH. Anthropic says the internal Claude model found the solution on October 16. The same date appears in OpenAI’s report.
Claude spent 14 million output tokens on the solution, and there was no human participation in the discovery: Anthropic staff only helped prepare the result as a paper.
The model found a deterministic algorithm for 3-SAT running in 2^o(n) time. ETH claims that there is a fixed constant δ > 0 such that the problem cannot be solved faster than 2^(δn), so such an algorithm disproves ETH. Moreover, the model also solved the harder #3-SAT problem, counting the number of satisfying assignments.
Why it matters
AnalysisIf confirmed, the result could reshape foundational assumptions in complexity theory and show that AI models can make autonomous discoveries in hard mathematical problems.
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