OpenAI posted 372 mathematical results produced by an unreleased frontier model, a volume that mathematicians say will take months to check.
The big picture: Each result resolves or makes substantial progress on a major open question in mathematics or theoretical computer science, the company says. OpenAI published them in a GitHub repository with protocols for paper revisions and citations.
- Among the claims are a solution to the four-dimensional Kakeya conjecture, improvements to some of the world's most important computer algorithms, and progress toward the Riemann hypothesis.
By the numbers: The average result used the equivalent compute of roughly three hours of ChatGPT Pro thinking, OpenAI said, and the company released 10 summaries of the model's reasoning alongside the proofs.
Zoom in: OpenAI is also sharing formalizations of many proofs in Lean, a programming language that lets a computer check a proof's logic, which makes those particular results all but certain to be correct.
The other side: A spokesperson told Scientific American that the model produced almost every result from a single prompt handed to a single agent, a claim that mathematicians want tested before they accept it.
- "Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified," said Andrew Sutherland, a mathematician at MIT. "We should ask for receipts."
Yes, but: An independent advisory group that OpenAI assembled in September recommends that a company publishing such results make public the model, the exact prompt and the compute time behind each one. OpenAI released average compute time and no prompts.
Why it matters: A single agent reproducing hundreds of research results in hours would put mathematical firepower once reserved for large funded teams within reach of anyone holding a subscription, which is exactly why the field is asking for receipts.
