OpenAI announced on October 26 scientific discoveries achieved thanks to its artificial intelligence models, in mathematics, computer science and physics. But the way the company verifies and communicates these results is drawing criticism from several researchers.
Three results in three disciplines
The first concerns the local smoothing conjecture, proposed by mathematician Christopher Sogge in 1991. It states that the most extreme concentration of waves can only be short-lived. OpenAI claims that its models have managed to prove it thanks to “a novel auxiliary partial differential equation”, without detailing their approach further. The company notes that this conjecture implies others, including the Kaleya conjecture, which amounts to rotating a needle placed on a table so that it points in all directions while covering the smallest possible surface area. Hong Wang and Joshua Zahl had found a solution in 2025, but only for its three-dimensional version. OpenAI therefore claims to have also solved the Kaleya conjecture.
In computer science, the company claims its models have proven that a widely held hypothesis is false: the Exponential Time Hypothesis (ETH), which states that certain problems would be extremely time-consuming to solve as the number of variables increases. It is related to the P=NP problem, which seeks to determine whether a problem whose solution can be easily verified can also be easily solved. Ryan Williams, a computer scientist and professor at MIT, told Techcrunch: “So this seems too good to be true”. According to OpenAI, he himself has refuted several versions of the ETH, and he will be among the experts verifying its work. On October 27, Anthropic announced that its models had also refuted this hypothesis, by developing algorithms capable of solving complex problems in “sub-exponential” time.
In physics, OpenAI certifies that its models have produced “a mathematically rigorous existence proof” of quantum chromodynamics, the theory describing the strong interaction between particles such as quarks and gluons. The result also concerns a unified extension of the standard model of particle physics, which covers three of the four fundamental forces, excluding gravity. The company also states that it has proven the existence of Yang-Mills theory.
A contested publication
OpenAI chose three modes of publication. In mathematics, it shared the result and left it to researchers to explain their work. For mathematics and computer science, it published a proof in Lean, a programming language that allows mathematical proofs to be verified computationally. For physics, the publication was postponed. “Given the length and complexity of the work, we have postponed its publication until the formalization in Lean is complete. We completed the formalization of the existence of Yang-Mills theory on October 16, 2026,” the company justified.
The AGMAI collective, composed of mathematicians who advise AI companies on the dissemination of results, was not convinced. It calls on OpenAI to immediately make the results public in natural language and in Lean. It recalls that Yang-Mills theory is one of the Millennium Prize Problems posed by the Clay Mathematics Institute in 2000. “There is therefore no longer any scientific reason to postpone publication,” the group emphasizes.
Access deemed unequal
Several researchers also criticize OpenAI for limiting access to its results to a few selected experts, tasked with verifying and overseeing its work for each discovery. “It is absurd that only a few eminent scientists can see them in the first instance,” said Constantin Kogler, a researcher at the Institute for Advanced Study, to The Verge. Andreas Karch, a physics professor at the University of Texas, for his part believes that “large labs already have enough power”. AGMAI had already advised against this approach the day before the announcement, believing that other mathematicians “may be deterred from working on it”.
