OpenAI’s AI-Generated Proofs Face Outside Review in Math, Computer Science and Physics

OpenAI says its internal AI models produced proofs for open questions in math, computer science and physics. The company describes the manuscripts as raw research data that still needs expert interpretation, not as settled discoveries.

The results are being handled differently by field, with outside specialists asked to act as “shepherds” for review. OpenAI also says it translated the math and computer science proofs into Lean, a language that can check formal proof steps but cannot by itself confirm that the formalized statement captures the intended problem.

The computer science result centers on the Exponential Time Hypothesis, or ETH, a widely accepted assumption about the difficulty of solving Boolean satisfiability problems in the worst case. OpenAI says its system has proved the ETH false.

If that proof holds, hundreds of papers that rely on ETH would lose their foundation, though their conclusions would not automatically become false. Ryan Williams, Russell Impagliazzo and Ramamohan Paturi are checking and explaining the result; Impagliazzo and Paturi originally proposed ETH with Francis Zane.

The math result concerns Christopher Sogge’s local smoothing conjecture, which OpenAI says its models proved in every dimension. According to OpenAI, that would also settle the Kakeya conjecture and Stein’s restriction conjecture in all dimensions.

The physics result targets the mathematical foundations of quantum field theory. OpenAI says its AI proved the existence of certain four-dimensional quantum field theories, including the existence part of Yang-Mills theory, but not the mass gap portion required to fully solve the related Millennium Prize Problem.

A group led by Nobel laureate David Gross will shepherd the physics work, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov also involved. OpenAI says the Yang-Mills proof has been translated into Lean, but that group is holding back the AI materials for now and plans to write up the result itself.

The broader issue is not just whether the proofs are correct, but how AI-generated scientific breakthroughs should be verified, shared and credited. OpenAI says it is not claiming scientific credit for the discoveries and has pledged $5 million to the Simons Foundation to support workshops and conferences on AI results.