Frontier AI labs say their models refuted the Exponential Time Hypothesis. What does that mean?

OpenAI released solutions to three major math problems, including a claimed refutation of the Exponential Time Hypothesis (ETH), and Anthropic later released its own refutation of ETH. MIT professor Ryan Williams, working with ETH originators Russell Impagliazzo and Ramamohan Paturi, is organizing the computer science community's response, releasing an open letter calling for feedback and discussion of norms around AI contributions. Williams said OpenAI checked whether the result breaks any cryptographic systems and was reasonably confident it does not.