OpenAI announced three AI-generated scientific discoveries in harmonic analysis, complexity theory, and quantum field theory. Independent experts are currently verifying the proofs, which include a claimed refutation of the Exponential Time Hypothesis.
OpenAI announced on Monday that its AI models have produced three scientific discoveries in the fields of harmonic analysis, complexity theory, and quantum field theory. The company described the AI-generated manuscripts as "raw research data" and has engaged external academic groups to verify, explain, and contextualize the findings.
According to OpenAI, its models produced a proof of the local smoothing conjecture in every spatial dimension. The company stated that this result also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The proof was generated on Oct. 18, 2026, and formalized the following day using Lean, a mathematical proof-checking system.
Alex Iosevich, a professor of mathematics at the University of Rochester, said OpenAI appeared to have "cracked" the conjecture in a "historic development." Iosevich noted that the conjecture was formulated by his PhD adviser, Chris Sogge. "Now I am filled with joy and optimism, because the scientific enterprise as a whole is going to make giant leaps as a result of the AI revolution," Iosevich told Al Jazeera.
In computer science, OpenAI claims its AI disproved the Exponential Time Hypothesis (ETH), a longstanding conjecture regarding the computational difficulty of solving certain problems. The company stated that the ETH has been "widely believed to be true" and used in hundreds of papers to derive conditional computational hardness results.
Ryan Williams, an expert in computational complexity theory at MIT, said a confirmed refutation would be a major development. "We are working to verify and examine their proof and determine if it holds up," Williams told Al Jazeera. He added that the proof proposes a "mysterious new method to more efficiently solve a variety of fundamental problems."
OpenAI has published the AI-generated explanation and the formal proof in Lean on GitHub. The work is being examined by a group including Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams.
OpenAI reported that its models developed existence proofs for certain four-dimensional quantum field theories, including quantum chromodynamics (QCD) and a unified completion of the Standard Model. The work also includes a proposed proof of the existence of pure Yang-Mills theory, which addresses part of one of the Clay Mathematics Institute's Millennium Prize problems.
Unlike the mathematics and computer science findings, the physics materials have not yet been publicly released. Nobel Prize-winning physicist David Gross will lead a group of researchers, including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov, to examine the findings. OpenAI said the group decided to defer the release to write up their own interpretation of the data.
OpenAI outlined four principles for its academic collaborations: transparency, no academic credit for the original AI discovery, recognition for researchers' explanatory work, and independence. "We do not seek academic credit for the discoveries produced by our internal models," the company said.
The company acknowledged that selecting initial academic "shepherds" creates asymmetry of information. OpenAI contributed $5 million to the Simons Foundation to support workshops and programs aimed at helping researchers understand AI-generated results. The announcements follow a previous release in October where OpenAI shared hundreds of AI-generated mathematical manuscripts.
Sources
This article was drafted with AI assistance and checked against the sources above. Company claims are reported as claims. Cover image is AI-generated.
The day's checked news, by email
One short email a day with the top stories. Free, and you can unsubscribe in one click.
Or follow for the latest news:
No comments yet. Start the discussion.
OpenAI and Oracle announced an expanded partnership on October 27, 2026, to integrate Oracle applications into ChatGPT and power new Oracle services with OpenAI models.
Google DeepMind has announced Genie 4, an updated AI world model featuring native audio generation, improved physics simulation, and longer consistency. Access will begin with Google AI Ultra subscribers and developers.