The ETH sits within the broader P vs NP question, which asks whether any problem whose solution can be quickly verified can also be quickly solved. It holds that even the fastest algorithm needs exponentially more time to solve a certain class of tricky logic puzzles as the number of variables grows. OpenAI and Anthropic claim their models produced algorithms solving those puzzles in sub-exponential time, meaning faster than previously thought possible. If the proofs hold up, a decade's worth of papers that relied on the ETH may need revisiting, according to MIT professor Ryan Williams, who is organising his field's response.

The process looks different from OpenAI's earlier proof drops, which Williams once called a "DDOS attack on mathematicians". This time, mathematicians received their work on GitHub, while computer scientists formed a working group that asked for public proofs and an OpenAI-funded conference. Williams, along with ETH's original 1999 publishers Russell Impagliazzo and Ramamohan Paturi of UC San Diego, released an open letter seeking feedback on the result and on norms for AI contributions to research. He noted the proof contains "two or three alien-looking parts" that the whole community needs to work on together.

Not everyone is convinced the work is novel. Anthropic mathematician Levent Alpöge suggested OpenAI was building on pre-existing work, and Anthropic subsequently released its own refutation of the ETH. Williams cautioned that this is probably not the final answer, saying OpenAI's algorithm is unlikely to be the best possible, though he thinks computer scientists should put more weight on the plausibility of P = NP.