OpenAI Announces Three Scientific Discoveries in Math, Physics, and Computer Science

What happened

OpenAI has announced three major scientific discoveries involving harmonic analysis, complexity theory, and quantum field theory [1, 2]. The company is testing a new collaboration model where external experts, referred to as “shepherds,” guide the release and understanding of these results [1, 2].

According to the company, the three specific breakthroughs are:

• Mathematics (Harmonic Analysis): The AI model produced a proof of the local smoothing conjecture in every dimension. This result also resolves the Kakeya conjecture and Stein’s restriction conjecture in all dimensions [2]. The proof uses a novel auxiliary partial differential equation [2]. OpenAI obtained the AI output on 18 October 2026 and formalized it in Lean on 19 October 2026 [2]. Following expert advice, the company released the AI natural language writeup and the Lean proof to a public GitHub repository [2].

• Computer Science (Complexity Theory): The discovery claims that the Exponential Time Hypothesis (ETH) is false [1, 2]. The paper presents a deterministic algorithm that counts satisfying assignments of fixed-width CNF formulas in polynomial space and subexponential time, with the 3-SAT case refuting the ETH [1]. An independent working group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will examine and explain the proof [1]. The AI output write-up and Lean proof were released on GitHub on 26 October 2026 [1].

• Physics (Quantum Field Theory): The discovery is described as a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics [1]. David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov to shepherd this work [1]. The physics information has not been released in full [1].

OpenAI stated that these manuscripts are intended as raw research data [2]. The company’s external collaborations follow four principles: transparency (no nondisclosure agreements required), no academic credit sought by OpenAI for the discoveries, recognition for the work of the understanding groups, and independence for voluntary, unpaid participants [2].

However, the AGMAI panel of math advisers recently recommended that AI companies should not designate specific people to receive output first, citing concerns about biased selection and unequal access [1]. They suggested that labs should instead release output to scholarly repositories with Lean-formalized proofs and funding for researchers [1].