Compute Polynomials Twice as Fast -
Here's a fun result, done entirely without AI.
That because we proved it years ago, but it ran a hundred pages and we weren't quite sure enough to publish. Now AI verified it in Lean.
A fun fact about polynomials is that
P(x) = x⁴ + a₃x³
Jakub: "we believe we could make the models better at specifically mathematics research with additional focus, but we do not prioritize this direction" (2 days ago.)
Noam: "We have not pushed it to its limits on math and science." (5 days ago.)
Seb: (today)
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem
Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help.
Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of
I want to prevent a race into unmonitorability kicked off by confused reporting. The depth of the computation graph for our present frontier models, including Astra, is within a factor of two of GPT-4.
OpenAI has worked to preserve and utilize chain-of-thought monitoring since
