Key Takeaways
- OpenAI says its models produced three new results in mathematics, computer science and physics.
- No outside verification is reported. OpenAI says Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will verify its Exponential Time Hypothesis claim.
- OpenAI has posted writeups and Lean proofs for two results on GitHub. Lean is software that checks proofs by computer. The physics materials are not public.
- By WYDE's calculation, OpenAI's $5 million contribution to the Simons Foundation equals 1.04% of the foundation's 2024 charitable disbursements. The ratio sets a 2026 gift against 2024 disbursements. Euronews reported that the initiative totaled $15 million in combined funding and resources from the Simons Foundation, Anthropic and OpenAI.
OpenAI said on October 26, 2026 that its AI models produced three new scientific results in harmonic analysis, complexity theory and quantum field theory. OpenAI says academic groups will explain two of them.
Greg Brockman, OpenAI's president, wrote in a pinned X post: “Announcing three major scientific discoveries, one each in mathematics (harmonic analysis), computer science (complexity theory), and physics (quantum field theory).” Neither post reports verification by outside experts.
By WYDE's calculation, OpenAI's $5 million contribution to the Simons Foundation equals 1.04% of the $481,607,180 in charitable disbursements the foundation reported for 2024 on its Form 990-PF, listed on ProPublica. The ratio sets a 2026 gift against 2024 disbursements. Euronews reported that the initiative totaled $15 million in combined funding and resources from the Simons Foundation, Anthropic and OpenAI. The post says the money will fund workshops, conferences and special programs. Euronews reported on October 16, 2026 that OpenAI had announced the gift on X on Thursday. The Association pour les mathématiques humaines (AHM) said mathematicians had not asked for this work to be done and that OpenAI showed total contempt for the standards of scientific research, according to Euronews.
What OpenAI says each result shows
In mathematics, OpenAI says its models proved the local smoothing conjecture in every dimension. OpenAI says this also resolves two related problems in mathematical analysis, the Kakeya conjecture and Stein's restriction conjecture, in all dimensions. Sogge proposed the conjecture in 1991. OpenAI says it obtained the AI output on October 18, 2026 and formalized it in Lean the following day.
In computer science, OpenAI says its system proved the Exponential Time Hypothesis (ETH) is false. The ETH is a longstanding conjecture about the computational complexity of Boolean formula satisfiability. OpenAI says its AI found the disproof on October 16, 2026, and that OpenAI formalized the result in Lean on October 17. OpenAI wrote: "This work will be verified and shepherded by a group led by Russell Impagliazzo (UC San Diego), Ramamohan Paturi (UC San Diego), and Ryan Williams (MIT)." For the Exponential Time Hypothesis result, OpenAI says it agreed to the group's requests that all raw data be made public and that OpenAI fund a conference on the work's implications for the field.
In physics, OpenAI says its models produced a mathematically rigorous proof that certain quantum field theories in four dimensions exist, including quantum chromodynamics (QCD), the theory of the strong force. The post calls the pure Yang-Mills existence proof a subproblem that is part of the Clay Mathematics Institute's Millennium Prize problem. OpenAI dates its Yang-Mills proof to September 9, 2026, and its QCD proof to September 18, 2026.
Who will check the claims, and what is public
This article cites no independent coverage of the three results. The arXiv preprint linked here, submitted September 24, 2019, is the 2019 paper by Guth, Wang and Zhang that proved the two-dimensional case of the local smoothing conjecture. It predates OpenAI's claims and does not check them. The post also says all three approaches involve tradeoffs. It says the collaborations “empower experts to foster unpacking the results,” and that choosing initial shepherds (the outside experts who organize each group) “necessarily shapes who gets involved first and creates asymmetry of information.” For physics, OpenAI wrote: "For the physics collaboration, the group has decided to hold off on releasing the AI-produced artifacts and instead work on writing it up themselves." OpenAI says David Gross will lead that group. OpenAI says it does not seek academic credit for the discoveries its internal models produced.
Why the dates and release choices matter
OpenAI says it finished the Lean formalization of Yang-Mills existence on October 16, 2026, 37 days after its September 9 natural-language proof. Outside readers cannot check the physics proof from OpenAI's materials, because those artifacts are held back. OpenAI says the math release followed the same strategy as its October 6, 2026 release, which WYDE covered in OpenAI's Math Release Reaches 719 Manuscripts, and 58% Lack Lean Checks.
People Also Ask
Has OpenAI's Exponential Time Hypothesis result been verified?
The post reports no outside verification yet. OpenAI says its system proved the Exponential Time Hypothesis is false, and a group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will verify the work.
What is the local smoothing conjecture?
The local smoothing conjecture concerns how waves behave as they become focused, and Sogge proposed it in 1991. OpenAI says its models proved it in every dimension. Guth, Wang and Zhang proved the two-dimensional case in 2019, according to the post.
How much is OpenAI's Simons Foundation contribution?
OpenAI announced a $5 million contribution to the Simons Foundation for workshops, conferences and special programs. By WYDE's calculation, that $5 million equals 1.04% of the foundation's 2024 charitable disbursements. The ratio sets a 2026 gift against 2024 disbursements. Euronews reported that the initiative totaled $15 million in combined funding and resources from the Simons Foundation, Anthropic and OpenAI.
Sources: OpenAI, arXiv, Greg Brockman on X, Euronews, ProPublica.