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

OpenAI released solutions to three math problems, including a refutation of the Exponential Time Hypothesis (ETH), a fundamental assumption in computer science. The lab's approach to releasing the solutions has been met with a mix of excitement and criticism, with some researchers accusing OpenAI of 'DDOS attack on mathematicians'. An open letter has been released, calling for feedback and discussion on the norms around AI contributions to mathematical work. The refutation of ETH has sparked a response from other researchers, including Anthropic, which also released its own refutation of ETH.