Russell Impagliazzo calls AI disproof of ETH 'very shocking news'

The announcement on October 26 came in two papers: OpenAI's 67-page 'The Exponential Time Hypothesis is False' and a 49-page companion from Anthropic. Both present algorithms for 3-SAT with running time of 2^o(n), and both say the proofs were written with heavy AI involvement and checked in Lean, a program that verifies mathematical proofs line by line.

The reaction from the hypothesis's co-proposers was notably measured. Impagliazzo, Ramamohan Paturi of UC San Diego, and MIT's Ryan Williams formed a review group. Williams told TechCrunch there are 'two or three alien-looking parts, and it's exactly these parts that I saw that made me think, wow, this is something that the whole community needs to work on together.' In a joint statement, the co-proposers cautioned that 'our involvement should not be taken as certification of the claim.'

Separately, both labs tempered the practical read. Anthropic said its result does not directly address whether P equals NP, and OpenAI said its speedup does not extend to NP problems in general. Outside estimates cited by the Times put OpenAI's checked bound as improving on brute force only beyond roughly 10 to the power of 2,389 variables; Anthropic wrote its method would not beat brute force until problems exceeded 10^10,000 variables on five-clause 3-SAT formulas.