Refutation of the verified ETH in Lean, proof of local smoothing conjecture, existence of Yang-Mills theories in 4D: major announcements that now await an independent review.
On October 26, OpenAI presented three results produced by one of its models. The most spectacular concerns theoretical computer science: a refutation of the exponential time (ETH) hypothesis , on which hundreds of works of algorithmic complexity are based, from graph theory to databases. Discovered on October 16, the result was verified the next day in the Lean proof assistant.
Kakeya and Yang-Mills
In mathematics, the model would have proved in all dimensions the local smoothing conjecture formulated in 1991, which would at the same time settle the Kakeya and Stein restriction conjectures. In physics, it would have rigorously established the existence of certain quantum field theories in four dimensions, including quantum chromodynamics and the pure Yang-Mills theory, linked to one of the problems of the millennium.
Caution is still required. Russell Impagliazzo, Ramamohan Paturi (two of the ETH authors) and Ryan Williams will lead an independent review, specifying that their participation does not constitute validation. Code and evidence are published on GitHub for the mathematics and computer science components; the physics component will be written separately by Nobel laureate David Gross' team. OpenAI does not claim any academic credit and funds a Simons Foundation initiative dedicated to AI-produced research to the tune of $5 million.
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