OpenAI and Anthropic claim their AI models refuted a long-standing computer science assumption, but the field is still working out what it means

OpenAI released solutions to three major math problems, including a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science about what is hard to compute. As with earlier proof drops, researchers reacted with a mix of excitement and dismay. Anthropic mathematician Levent Alpöge suggested OpenAI built on pre-existing work, and hours later Anthropic released its own refutation of ETH.

OpenAI handled each discipline differently this time: mathematicians got the work on GitHub, while computer scientists formed a working group that asked for public proofs and a funded conference. MIT professor Ryan Williams, who once called an OpenAI proof dump a "DDOS attack on mathematicians," agreed to help interpret the result alongside UC San Diego's Russell Impagliazzo and Ramamohan Paturi, who first published the ETH in 1999. The group released an open letter seeking feedback and discussion of norms around AI contributions.

The ETH sits within the broader P versus NP question: whether every problem whose solution is quickly verifiable can also be quickly solved. Most scientists assume P ≠ NP, and ETH supported that by holding that the fastest algorithms need exponentially more time as variables grow in a class of logic puzzles. OpenAI and Anthropic claim their models found algorithms solving those puzzles in sub-exponential time - potentially refuting ETH. Williams said every computer scientist should put a little more weight on the plausibility of P = NP, but added, "I don't think that OpenAI's algorithm could possibly be the best algorithm you can get."

Williams said many papers relying on ETH's durability may need revisiting, which is why he pushed for a conference. On security, he asked OpenAI science lead Dan Roberts whether any cryptographic systems were affected; OpenAI checked and was reasonably confident the result implies no breaks. Williams remains optimistic despite concerns, saying AI is forcing researchers to be more ambitious about the questions they ask.

Source: TechCrunch