OpenAI Claims Three Science Breakthroughs, Taps Expert Shepherds

OpenAI has announced three new "major" discoveries in mathematics, computer science and physics, less than a month after it released hundreds of manuscripts it said contained solutions to long-standing math questions. This time, the company says it is working with outside experts it calls "shepherds" to guide how the results are examined.

The three claims

In mathematics, OpenAI says its model produced a proof of the local smoothing conjecture in every dimension. According to the company, that also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The model output is being released directly, as in the October 6 release, and advisers suggested that researchers work out their own explanations of it. Months ago, NYU professor Hong Wang received a Fields Medal for resolving the Kakeya conjecture in three dimensions.

In computer science, OpenAI says a paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The 3-SAT case would refute the Exponential Time Hypothesis, widely believed true since it was proposed in 1999. A working group of Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof. At their request, the write-up and a Lean proof went onto GitHub immediately.

In physics, the company describes a "mathematically rigorous existence proof" of certain interacting quantum field theories with gauge fields and fermions in four dimensions, including QCD and a unified completion of the Standard Model. The details are not yet public. David Gross will lead a group with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov to shepherd the work.

A contested approach

OpenAI admits the shepherd model could have its own problems. Only a day earlier, the AGMAI panel of math advisers the company assembled recommended that AI companies not adopt the practice of giving selected people early access, citing unequal access, borrowed reputation and biased selection. The panel instead urged labs to publish on scholarly repositories with Lean-formalized proofs, details on how problems were chosen, and funding for people who work to understand the results.

OpenAI also published an open letter asking the community about early-access expectations and conflict-of-interest disclosure, how credit should reflect both discovery and the work of checking and explaining, and how to support students and researchers as methods change. Until independent experts weigh in, all three results remain claims awaiting verification.