OpenAI Proves ETH Is False, and Crypto Twitter Has Questions

What it claims

OpenAI says an AI model found a deterministic algorithm that counts every satisfying assignment of a 3-SAT formula in subexponential time, meaning the running time grows more slowly than any exponential in the number of variables. Because counting solutions is harder than deciding whether one exists, the algorithm also decides 3-SAT in subexponential time. If it holds, this refutes the Exponential Time Hypothesis (ETH), which Russell Impagliazzo, Ramamohan Paturi and Francis Zane proposed in 1999. OpenAI says hundreds of papers assume ETH to argue that problems in graph theory, computational biology, databases and geometry cannot be solved quickly. Those conditional lower bounds would no longer stand on ETH.

Evidence

The article gives no algorithmic detail, running-time bound or experimental data. According to OpenAI, the model found the disproof on 16 October 2026 and the proof was formalized in Lean on 17 October 2026. Both the paper and the Lean proof are on GitHub. OpenAI used the same route for its 722 math manuscripts released earlier in October 2026, and only 162 of those came with a computer-checked main result.

Impagliazzo, Paturi and Ryan Williams (MIT) lead the independent review. In an open letter they wrote that "our involvement should not be taken as certification of the claim." OpenAI says the reviewers signed no non-disclosure agreements and are unpaid. It has also agreed to publish all raw data and to fund a conference on the result.

Anthropic posted a separate paper, "A 2^o(n) Time Algorithm for 3-SAT," dated 26 October 2026 and credited to Claude. Its repository says an internal research Claude model found the algorithm. The article does not say whether the two algorithms are the same or how they compare.

Limits

Both sources say the result is not practical. OpenAI wrote that turning it into practical improvements "will require significant further research." Anthropic's repository says the result "is purely asymptotic and says nothing about solving formulas in practice." Neither result offers a faster SAT solver to adopt.

The OpenAI paper states that the result does not show every NP problem can be solved in subexponential time, so P versus NP stays open. The claim is still under review and had not been certified as of late October 2026. This is a news article. It does not link the GitHub repositories, give the asymptotic bound, or describe the method. Anyone relying on the result needs to read the papers and check the Lean artifacts directly.