OpenAI Claims Three Scientific Breakthroughs: ETH Refuted, Kakeya Solved, Yang-Mills Existence Proved

OpenAI announced on October 26 that its models produced three major results across mathematics, computer science and physics — claims that, if independently confirmed, would mark a turning point in AI-assisted science. The math and computer-science results come with Lean formalizations published on GitHub; the physics materials are being withheld at the reviewing group's own decision, and the company is explicit that all three await independent verification.

Mathematics: local smoothing in every dimension

The company says its models proved the local smoothing conjecture, proposed by Sogge in 1991, in every dimension. The conjecture concerns how energy in wave equations concentrates over time, asserting that the most extreme focusing must be brief.…