OpenAI unveils three discoveries, Exponential Time Hypothesis refuted

OpenAI announced three new "major" discoveries less than a month after its mass release of hundreds of manuscripts that it said contained solutions to long-standing mathematics questions. The new results span math, computer science and physics, and OpenAI says it is releasing the model output directly, as it did in its October 6 release.

What sets this announcement apart is the use of external experts OpenAI calls "shepherds" to guide the results in computer science and physics. For the computer science claim—that the Exponential Time Hypothesis is false—verification is being guided by a group that includes Russell Impagliazzo and Ramamohan Paturi, who were part of the group that originally proposed the hypothesis in 1999, along with MIT professor Ryan Williams. They decided to release the AI output write-up and Lean proof on GitHub today and also released an open letter asking for input on norms for AI-generated breakthroughs.

OpenAI admits this approach could have its own issues: the AGMAI panel of math advisers said yesterday it recommends AI companies not adopt the practices of designating certain people to receive output first, citing unequal access, borrowed reputation and biased selection. For the math result, OpenAI says its model produced a proof of the local smoothing conjecture in every dimension and therefore also resolved the Kakeya conjecture and Stein's restriction conjecture in all dimensions—a topic that just a few months ago earned NYU professor Hong Wang a Fields Medal for resolving the Kakeya conjecture in three dimensions. The physics information has not been released in full, but OpenAI says it is a mathematically rigorous existence proof of certain interacting quantum field theories, and David Gross will lead a group to shepherd that work.