OpenAI Seeks Outside Review of AI-Generated Proofs in Math, Computer Science, and Physics

OpenAI says its internal AI models have produced proofs in mathematics, computer science, and physics, including a claim that a central assumption in computer science is false and a claim that part of a Millennium Prize Problem has been proved. OpenAI has asked outside experts, including a Nobel laureate, to review the results and decide whether the proofs hold up.

Computer science: ETH challenged

OpenAI says one result concerns the Exponential Time Hypothesis, or ETH, which is tied to the Boolean satisfiability problem, known as SAT. SAT asks whether variables in a logical formula can be set so the formula is true. The ETH says there is no real shortcut and that worst-case computing time grows exponentially as variables are added. OpenAI says its system has proved the ETH is false. The company says this would affect hundreds of papers built on the ETH, though practical gains would still require much research.

Ryan Williams of MIT is independently checking and explaining the result with Russell Impagliazzo and Ramamohan Paturi of UC San Diego. The group says it has no nondisclosure agreements, is working unpaid, and plans to share interim findings. In an open letter, the three say their involvement is not an endorsement. OpenAI is publishing the written proof and the Lean proof, and has committed to funding a conference on the result.

Math: local smoothing in every dimension

The math result concerns the local smoothing conjecture proposed by Christopher Sogge in 1991. The conjecture says extreme concentration of waves only lasts briefly, so waves behave more smoothly when averaged over time. It had been proved in two dimensions by Guth, Wang, and Zhang in 2019. OpenAI says its models have now produced a proof for every dimension. According to OpenAI, the result also proves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. OpenAI says no dedicated group is shepherding this proof. After reaching an outside expert, it published the proof text and the Lean proof directly so researchers can decide how to check the result.

Physics: quantum field theory existence

The physics result concerns quantum field theory, which OpenAI calls the most important framework in modern theoretical physics. OpenAI says its AI has proved that certain quantum field theories exist in four dimensions. The proof covers Yang-Mills theory, quantum chromodynamics, and the simplest grand unified theory. For Yang-Mills, OpenAI says it has solved only the existence part, not the mass gap, so the Millennium Prize Problem would not be fully solved.

A group led by David Gross will shepherd the work. Gross shared the 2004 Nobel Prize in Physics. The group also includes Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. OpenAI says it has translated the Yang-Mills proof into Lean, but this group is holding back the AI materials for now and plans to write up the result itself.

Review process and credit

OpenAI says it is not claiming scientific credit and that credit should go to the groups explaining the results. It also acknowledges trade-offs, including that whoever picks the first shepherds helps decide who gets involved first. OpenAI says it is not yet clear which review approach works best.

Sources: The Decoder