OpenAI and Anthropic AI Models Disprove ETH Hypothesis

🤖 OpenAI and Anthropic AI Models Disprove ETH Hypothesis

On October 26, both companies published preprints with machine-checkable proofs in Lean: their algorithms solve #3-SAT in 2^{o(n)} time, compared to the previous 1.328^n. Peer review is still ahead, and this does not prove P = NP.

🌍 Hundreds of works on hardness (Clique, Vertex Cover, Independent Set) are built on ETH—if confirmed, they will need to be reconsidered. Ryan Williams' group at MIT is verifying the formulations by Impagliazzo and Paturi; OpenAI states there is "reasonable confidence" that current cryptography will not be broken.

👤 For the first time, two frontier labs independently found a single disproof with Lean proofs: correctness is checked by a machine, while the bottleneck is the fidelity of the formulation to ETH. Watch for the verification of "strange" parts and reductions to other NP problems.

Source 1: https://raw.githubusercontent.com/openai/math/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf