Hundreds of papers rest on the Exponential Time Hypothesis. OpenAI says its model just proved it false — and claims Yang–Mills existence too

"An internal model at OpenAI has produced a claimed refutation of ETH!" MIT professor Ryan Williams wrote on X on Oct 26. He said he, Russell Impagliazzo and Ramamohan Paturi of UC San Diego — the two original proposers of the hypothesis — have been asked to organize an open, independent examination of the claim. The people who put the conjecture forward will now check a proof that it is wrong.

In a blog post the same day, OpenAI announced three results in mathematics, computer science and physics. The Exponential Time Hypothesis says Boolean satisfiability (SAT) needs exponential time, and hundreds of papers in graph theory, computational biology, databases and beyond use it to derive hardness results. OpenAI wrote that "our system has recently proved that the ETH is false, a result that was subsequently verified in Lean." Williams said the PDF claims 3SAT on n variables runs in about exp(n/(log n)^{1/2+o(1)}) time.

In physics, OpenAI says its models produced a rigorous existence proof for interacting four-dimensional quantum field theories including quantum chromodynamics, with pure Yang–Mills existence as a subproblem — part of a Clay Millennium Prize problem carrying a $1 million award. Nobel laureate David Gross will lead the group shepherding that work. In math, the models proved the local smoothing conjecture in every dimension, which resolves the Kakeya and Stein restriction conjectures. OpenAI says it is not seeking academic credit.

Caution followed. One mathematician (@__alpoge__) noted that Ethan Sussman has been publicly writing up 4D Yang–Mills existence via the same Balaban approach. Others (@captain_sude) pointed out that the mass gap is not claimed and the physics paper has not been released. Under OpenAI president Greg Brockman's announcement, one reply asked: "Did you get permission from the mathematicians first?"