OpenAI internal model reportedly solved three open problems in math, theoretical CS and physics
The claimed breakthroughs include a disproof of the Exponential Time Hypothesis, proofs for Kakeya and local-smoothing conjectures in all dimensions, and existence results for Yang-Mills theory and full QCD.
OpenAI's internal model reportedly solved three open problems in mathematics, theoretical computer science and physics.
Among them, the model allegedly disproved the Exponential Time Hypothesis (ETH) — a central assumption in computational complexity closely connected to the P ≠ NP millennium problem.
ETH states that Boolean satisfiability cannot be solved substantially faster than exhaustive search. For decades, researchers have used it as a foundation for results in graph theory, computational biology, databases, geometry and other areas.
Hundreds of papers rely on ETH. If ETH is false, questions such as “how much faster can these problems be solved?” reopen.
The result is considered significant enough that a verification group led by Russell Impagliazzo and Ramamohan Paturi — the scientists who formulated ETH — will examine it. OpenAI has also promised to fund a conference to discuss the outcome.
Two other notable results:
- Kakeya conjecture and local smoothing. The problem concerns waves that focus at a single point. Sogge’s 1991 conjecture says that the strongest focusing cannot persist for long. The Kakeya conjecture and Stein’s restriction conjecture follow from it.
This is one of the central problems of harmonic analysis. Mathematicians worked on it for decades, but proofs previously existed only in low dimensions, typically two or three. The OpenAI model reportedly produced a proof for arbitrary dimensions, thereby also settling Kakeya and Stein restriction in all dimensions.
- Existence of QCD and Yang-Mills theory. The model is said to have rigorously proved the existence of Yang-Mills theory, which is part of one of the seven Millennium Prize Problems. It also reportedly proved the existence of full QCD, where quarks are added to gluons, and of a unified theory containing Standard Model particles. A group led by Nobel laureate David Gross will review the result.
Something extraordinary appears to be happening.
Why it matters
AnalysisIf verified, the result could reshape fundamental complexity bounds, reopen major research programs in harmonic analysis, and change how some Millennium Prize problems are understood.
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