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

OpenAI announced solutions to three mathematical problems that have long troubled researchers, one of which is a refutation of the Exponential Time Hypothesis (ETH); several hours later, Anthropic also released its own refutation of ETH. ETH is part of the P vs NP problem and has long provided evidence for P ≠ NP; the two labs say their models found algorithms that solve the relevant problems in subexponential time, which, if valid, would shake this hypothesis. MIT professor Ryan Williams and ETH's original authors Russell Impagliazzo, Ramamohan Paturi and others participated in interpreting the results, and published an open letter soliciting feedback and discussing norms for AI participation in scientific research. Williams said he asked OpenAI science lead Dan Roberts whether this affects cryptographic systems; the latter said it had been checked and believed it would not lead to practical cracking.