OpenAI announced three claimed major discoveries in mathematics, computer science and physics, using different release approaches for each.
In mathematics, OpenAI released raw AI model output claiming a proof of local smoothing for the Euclidean wave equation. According to the company, the proof uses an auxiliary partial differential equation to establish Sogge’s local smoothing for waves in every spatial dimension at least two, and yields the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates throughout the interior of the conjectured range. OpenAI is releasing the model output directly for researchers to develop their own explanations.
In computer science, OpenAI claims its AI has produced a proof that the Exponential Time Hypothesis is false. The company says the work presents a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, with the 3-SAT case refuting the Exponential Time Hypothesis. An independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine the proof. At the group’s request, OpenAI made the materials public immediately.
In physics, OpenAI says it has a “mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics.” David Gross will lead a group including Michael Douglas to examine this work, though the full physics materials have not been released.
OpenAI’s use of external “shepherds” to guide results in computer science and physics differs from its October 6 release of hundreds of manuscripts. However, the AGMAI panel of mathematics advisers assembled by OpenAI said that “we recommend that AI companies do not adopt” the practice of designating certain people to receive output first, citing unequal access, borrowed reputation and biased selection as concerns. The panel recommended that AI labs instead release output on scholarly repositories with Lean-formalized proofs, information on problem selection, funding for people working on understanding results, and other documentation.