OpenAI announces three results from its models: disproof of ETH, local smoothing and Yang–Mills
Prepared by Sintelligent with the help of SI. Published in SI: . Updated: .
The results remain OpenAI's claim: independent mathematicians and physicists have been asked to assess them, and that assessment will decide whether they become established.
On October 26 OpenAI reported three results from its models. An internal model, the company says, disproved the Exponential Time Hypothesis (ETH) on October 16, and the proof was formalized in Lean on October 17. The models also, according to OpenAI, proved the local smoothing conjecture in all dimensions — which would also settle the Kakeya and Stein restriction conjectures — and produced proofs of the existence of quantum chromodynamics and pure Yang–Mills theory in four dimensions; the existence of Yang–Mills theory is part of one of the Clay Mathematics Institute's Millennium Prize problems. The ETH result will be checked and explained by a group of Russell Impagliazzo and Ramamohan Paturi (UC San Diego) and Ryan Williams (MIT); they stressed: "Our involvement should not be taken as certification of the claim." The physics group will be led by Nobel laureate David Gross; it decided not to publish the SI-produced material for now and will write the work up itself. OpenAI said it does not seek academic credit for the discoveries, gave $5 million to the Simons Foundation for workshops and conferences on SI-produced results, and published the model's write-up and the proof in Lean.
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