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

Three frontier AI labs have recently submitted solutions to three significant math problems that have long troubled researchers. One of these solutions involves a surprising rejection of the Exponential Time Hypothesis (ETH), a long-standing assumption in computer science that impacts our understanding of difficult computations.

The ETH assumes that even the fastest computer algorithm will require exponentially more time to find a solution as the number of variables grows in a particular class of challenging logic puzzles. If OpenAI and Anthropic's solutions are accurate, they could disprove the ETH and potentially lead to faster algorithms for solving these problems.

The AI labs approached the announcement of their findings differently, depending on the discipline involved. For mathematicians, the solution was posted on GitHub, while computer scientists formed a working group to discuss the proofs publicly and fund a conference to delve deeper into the matter. Physicists, on the other hand, established a working group to determine the appropriate release of their results.

MIT Professor Ryan Williams, who specializes in computational complexity and helped interpret the solution, agreed to collaborate with the AI labs. He praised the labs for their openness to feedback and discussion, stating that some parts of the proof were routine, but a few sections were novel and required further exploration by the scientific community.

The ETH is part of the broader P vs NP problem, which has captivated computer scientists and other fields for decades. P vs NP questions whether any problem whose solution can be easily verified (NP) can also be easily solved (P). If OpenAI and Anthropic's solutions are correct, they could potentially prove that P = NP, which would have significant implications for cryptography and other fields.

While the AI labs' findings are promising, there are still questions to answer. Williams emphasized the need for further research and discussion within the scientific community to determine the next steps and potential impacts on existing research. Despite concerns, Williams remains optimistic about the role of AI in advancing scientific discovery.