Less than a month after publishing several hundred papers containing what the company claims were solutions to long-standing mathematical problems, OpenAI has presented three additional major results achieved through artificial intelligence in mathematics, physics, and computer science. Notably, the company approached the verification of each result differently. In physics and computer science, OpenAI has engaged external experts to accompany the presentation process, while mathematicians who advised the company recommended publishing the AI-derived results directly so researchers can analyze the proofs independently and offer their own explanations. This approach continues the line initiated on October 6, when similar papers were made publicly available.
Mathematics: Sogge's Conjecture and Its Consequences
The AI-driven discovery in mathematics relates to the local smoothing of the wave equation in Euclidean space. Using an auxiliary partial differential equation, the model proved Sogge's conjecture for waves in spaces of dimension at least two. According to OpenAI, this proof has also confirmed several Kakeya conjectures and Stein estimates. The company decided to publish the results directly, as was done on October 6. Experts, in turn, recommended that future AI research results be published in scientific repositories accompanied by formalised proofs in the Lean system, information on task selection criteria, and funding mechanisms for researchers tasked with analyzing the findings.
Computer Science: Refutation of the Exponential Time Hypothesis
In computer science, OpenAI claims the AI has refuted the exponential time hypothesis. The paper presents an algorithm that allows for the exact counting of the number of solutions in a certain class of logical problems in sub-exponential time with limited memory. An independent group of scientists will study and explain the proof; at their request, the company immediately opened access to the materials so other specialists could review them.
Physics: Four-Dimensional Quantum Field Theories
Detailed information about the physics work has not yet been published. It is only known that it concerns "a rigorous mathematical proof of the existence of certain interacting quantum field theories involving gauge fields and fermions in four-dimensional space, including quantum chromodynamics and a unified extension to the Standard Model of elementary particle physics." Consequently, the full text and methodology of this result remain confidential pending the completion of external oversight.
Open Letter and the Issue of Trust
In parallel, OpenAI published an open letter to the scientific community calling for a discussion on approaches to verifying such claims and establishing norms for working with AI scientific breakthroughs. Three questions have been put forward for discussion concerning how the community should validate results generated by models. The context for these statements is set by earlier announcements: back in September 2026, the company claimed its internal AI system had solved one of the seven Millennium Prize Problems—the existence and smoothness problem for the Navier-Stokes equations, as reported by various outlets. The combination of these announcements makes the current series of discoveries part of a broader OpenAI campaign to demonstrate the research potential of its models, although independent verification of most of them, including the physics result, is still ongoing.
