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

OpenAI released solutions to three blockbuster math problems that have long vexed researchers yesterday. One was a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science that plays a large role in how we understand what is difficult to compute. As with previous proof-drops from the frontier lab, scientific communities responded with a mixture of thrill and dismay. Anthropic mathematician Levent Alpöge suggested that OpenAI was basing its solutions from pre-existing work, and hours later, Anthropic subsequently released its own refutation of ETH. However, OpenAI’s process is evolving. This time, the lab structured its releases differently for each of the three disciplines involved: Mathematicians got the work dropped on GitHub; the computer scientists formed a working group, asked for the proofs to be shared publicly…