OpenAI on Monday announced three new results it describes as major discoveries in mathematics, computer science and physics, less than a month after releasing hundreds of manuscripts that it said solved long-standing mathematics problems. The company said outside experts it calls shepherds guided the computer science and physics work, while mathematicians advised it to publish the math output directly so researchers could develop their own explanations.
The computer science result claims to disprove the Exponential Time Hypothesis, long widely believed to be true. OpenAI said its paper presents a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, and that the 3-SAT case refutes the hypothesis. Russell Impagliazzo of UC San Diego and Ramamohan Paturi, both part of the group that originally proposed the hypothesis in 1999, are among three experts guiding verification, and at the group's request OpenAI released the writeup and Lean proof on GitHub today.
In mathematics, OpenAI said its model produced a proof of the local smoothing conjecture in every dimension, which it said also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The proof uses an auxiliary partial differential equation to establish Sogge's local smoothing for waves in every spatial dimension of at least two. OpenAI is releasing the model output directly, as it did in its October 6 release, after advisers recommended that approach.
The physics work has not been released in full. OpenAI described it as a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics and a unified completion of the Standard Model of particle physics. David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov that will shepherd the work.
The shepherd approach carries its own risks, the company acknowledged. The AGMAI panel of math advisers OpenAI assembled said yesterday that it recommends AI companies not adopt the practice of designating certain people to receive output first, citing unequal access, borrowed reputation and biased selection. The panel instead recommended that labs release output on scholarly repositories with Lean-formalized proofs, information on how problems were chosen, and funding for people working to understand the results.
The announcement follows OpenAI's October 6 release of hundreds of mathematics manuscripts and its October 15 pledge of $5 million to help mathematicians make sense of AI-generated research. Mathematicians have said they will need years to work through the earlier drop.
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