OpenAI announced on October 26 three results produced by internal models in mathematics, computer science, and physics. The claims are extraordinary: a purported disproof of the Exponential Time Hypothesis (ETH), a proof of the local smoothing conjecture with consequences for Kakeya and Stein restriction, and a rigorous construction related to the existence of quantum field theories in four dimensions. None should yet be treated as an accepted scientific result. The company itself describes the materials as raw research data that still require explanation, checking, and evaluation by specialists. [1]

The computer-science claim has the clearest review process. ETH broadly holds that the 3-variable Boolean satisfiability problem cannot be solved in subexponential time. OpenAI says its model produced a disproof on October 16 and that the result was formalized in Lean the following day. Lean is a proof assistant that checks whether a chain of reasoning follows specified logical rules. The company released both the model-generated write-up and the formal artifact for examination. [2]

Three researchers—Russell Impagliazzo and Ramamohan Paturi of the University of California, San Diego, and Ryan Williams of MIT—will coordinate scrutiny of that claim. Two of them helped formulate ETH. Their participation is not an endorsement. In a letter quoted by independent coverage, they warned that a claim of this significance requires careful scrutiny. They also said that they signed no nondisclosure agreements and will not be paid by OpenAI for the review. [3]

The second result concerns the local smoothing conjecture proposed by Christopher Sogge in 1991. OpenAI says it obtained a solution in every dimension on October 18 and formalized it in Lean the next day. If correct, it would also settle the Kakeya and Stein restriction conjectures in every dimension. The company released the model output and formal code, while leaving the mathematics community free to organize the work of interpreting and verifying it. [1]

The third case is being handled more cautiously. OpenAI says its models constructed a mathematical existence proof for certain quantum field theories in four dimensions, including pure Yang–Mills theory and a rigorous formulation of quantum chromodynamics. Rather than immediately releasing all materials, the company formed an external group and said it would defer to that group on how and when to disclose them. Without public access to the complete argument, outsiders cannot yet verify the claim. [1][2]

Formalization in Lean improves traceability, but it does not automatically turn a claim into scientific consensus. A verifier can establish that a file conforms to a chosen logic and definitions. Specialists must still determine whether those definitions faithfully represent the stated problem, whether inappropriate assumptions were introduced, and whether the conclusion has the scope being claimed. The uncertainty is greater for the physics result because the full material is not public.

OpenAI’s scientific publishing experiment also changes how credit is allocated. The company says it will not seek academic credit for discoveries produced by its internal models. External researchers should instead receive recognition for the explanations, papers, and context they develop. That is a meaningful position, although it does not settle broader questions about authorship, responsibility, and reproducibility.

For now, the news is not that three historic problems have been definitively solved. It is that an AI laboratory has put forward three high-impact claims, two accompanied by public artifacts and a third under controlled disclosure, and has invited independent experts to try to convert them into scientific understanding—or reject them. The decisive result will be what survives that review.

Sources

[1] Read More — Working with academic communities to build scientific understanding — OpenAI
[2] Read More — OpenAI says its AI model has disproved the Exponential Time Hypothesis — The Next Web
[3] Read More — OpenAI Hands ETH, Kakeya, Yang-Mills Proofs to Reviewers — AI Weekly