OpenAI Announces Three Major Breakthroughs: AI Proves a Century-Old Conjecture, Refutes the ETH Hypothesis, and Tackles a Millennium Problem

OpenAI announced today that its models have made major discoveries in three fields: mathematics, computer science, and physics. This may be the first time an AI has stood at the forefront of basic science as a primary contributor.

The three discoveries fall into harmonic analysis, computational complexity theory, and quantum field theory—each one tackling a hard problem.

The first discovery comes from harmonic analysis. The model produced a proof of the local smoothing conjecture, and along the way resolved the Kakeya conjecture and the Stein restriction conjecture in all dimensions. The Kakeya conjecture is a classic problem in geometric measure theory: in n-dimensional space, any set containing a unit line segment in every direction must have sufficiently large dimension. The conjecture has deep connections to Fourier analysis and wave equations, and had remained unsolved for a long time. OpenAI has posted both the AI-generated natural-language report and the Lean proof to a GitHub repository.

The second discovery comes from computational complexity. The model proved that the Exponential Time Hypothesis (ETH) is false. ETH states that NP-complete problems like 3-SAT cannot have algorithms that run much faster than exponential time. This hypothesis had been treated as true for decades, with hundreds of papers using it as a condition to derive hardness lower bounds. If ETH is false, all those conditional results lose their foundation. OpenAI has handed the work to a team of experts led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams for verification, and the Lean formal proof is also publicly available on GitHub.

The third discovery comes from quantum field theory. The model provided a mathematically rigorous existence proof for a class of interacting quantum field theories in four-dimensional spacetime. This class includes gauge fields and fermions, and encompasses a unified completion of quantum chromodynamics (QCD) and the Standard Model of particle physics. A subproblem also includes a proof of the existence of pure Yang-Mills theory, which is part of the Clay Mathematics Institute's Millennium Prize Problems. This effort was carried out jointly with a group of physicists led by David Gross, including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. The group has left a public email address, YANGMILLS4D@gmail.com, for academic discussions.

To support independent review by the external academic community, OpenAI donated $5 million to the Simons Foundation to fund related workshops, conferences, and special projects.

None of these results have yet undergone formal peer review. OpenAI's announcement is a starting point; the final verdict will have to wait until human experts finish their verification. The Lean formal proof can check every step of reasoning, but the machine does not have the final say on whether the overall framework is directionally correct.

The significance here goes beyond the three results. OpenAI is attempting a new model of scientific publication: AI generates results, verification is public, and experts confirm. If this path works, the way basic research is produced could be rewritten.