Summary
“OpenAI says its models have produced mathematical proofs that challenge established theories in harmonic analysis and computer science. The work also…
“OpenAI says its models have produced mathematical proofs that challenge established theories in harmonic analysis and computer science. The work also includes a claimed existence proof for quantum field theories, including quantum chromodynamics (QCD). Researchers will now examine the results, verify their implications and explain their significance to the wider scientific community.
The company has adopted different release strategies for the three projects. It has published the mathematical and computing proofs, while an external physics group will prepare its own account of the research.
One proof addresses the local smoothing conjecture, a problem in harmonic analysis proposed by Christopher Sogge in 1991. It describes how waves behave when they concentrate, suggesting that extreme focusing cannot persist for long periods.
OpenAI says its models proved the conjecture across every spatial dimension. The result also resolves the Kakeya conjecture and Stein’s restriction conjecture, according to the company…
OpenAI also says its models disproved the Exponential Time Hypothesis (ETH), a longstanding conjecture in computational complexity. The hypothesis concerns the difficulty of solving Boolean satisfiability problems and underpins conditional hardness results across numerous research fields…
The physics work concerns the mathematical foundations of quantum field theory. OpenAI says its models produced existence proofs for interacting theories involving gauge fields and fermions in four dimensions. The results include QCD, which describes the strong force governing interactions between quarks and gluons.
The work also addresses pure Yang-Mills theory, a key component of a Millennium Prize problem from the Clay Mathematics Institute. That problem concerns the mathematical existence of quantum Yang-Mills theory and the presence of a mass gap.”
Jeremy Horpedahl — Jul 21, 2026
Marian L. Tupy — Mar 3, 2026
Gale L. Pooley — Jul 14, 2025
May 7, 2025
Source: Human Progress
