OpenAI Claims Breakthroughs in Math and Physics, Sparks Controversy Over Release Strategy

IT Home reported on October 28 that OpenAI announced on Monday (local time) significant breakthroughs in mathematics, computer science, and physics, while also stating that it is adjusting how it communicates its findings. However, despite this apparent shift in strategy, researchers interviewed by The Verge expressed growing frustration with the company's approach.

IT Home noted that tensions between OpenAI and the mathematical community have persisted over the past few months. In early October, the company released hundreds of preprints at once, overwhelming mathematicians. This time, OpenAI stated it would collaborate with domain experts serving as "guides" to determine the appropriate method for releasing its latest results.

The three achievements address some of the most critical unsolved problems in mathematics, computer science, and physics. Some continue OpenAI's previous research directions, while others open new avenues. Based on recommendations from these "guides," each result employs a distinct release strategy:

• Mathematics: The AI-generated derivation is released directly, "leaving it to academic researchers to organize their own efforts to interpret the conclusion."

• Computer Science: OpenAI will assemble an external research group responsible for interpretation.

• Physics: The result remains unpublished for now; OpenAI states that an external expert team will decide the subsequent format for release.

• The mathematical result is described as stunning, reportedly proving the Kakeya conjecture across all dimensions. Simply put, this problem investigates the minimum space required to rotate a needle or pencil in every direction. Earlier this year, mathematician Hong Wang won the Fields Medal, among other reasons, for proving the three-dimensional version of this conjecture. Brendan Hassett, a professor of mathematics at Brown University, stated that OpenAI's conclusion "appears well-founded," but emphasized that he has not yet verified the Lean formal proof—the system used to validate conclusions via computer checking.

• The physics result centers on the Standard Model, the most mature and complete theoretical framework in physics. The research focuses on Quantum Chromodynamics (QCD), which describes the strong nuclear force—one of the four fundamental forces—and its relationship with Yang-Mills theory. Yang-Mills theory is also a cornerstone of modern particle physics and one of the seven Millennium Prize Problems. However, OpenAI's study does not resolve the outstanding "mass gap" problem.

• The final result claims to disprove the Exponential Time Hypothesis (ETH). This is a widely accepted assumption in theoretical computer science stating that certain problems cannot be solved significantly faster than brute-force enumeration. ETH is closely related to the P vs NP problem—another Millennium Prize Problem and one of the field's most famous unsolved questions—which explores whether problems whose solutions are easy to verify can also be solved quickly.

Due to varying levels of disclosure and the extremely high barrier to verification, researchers find it difficult to fully evaluate these conclusions. Even with access to all materials, the verification process requires substantial time. Nevertheless, experts interviewed acknowledged that these results deserve serious consideration, with many describing them as "enormous," "major breakthroughs," and "profoundly significant."

While researchers are excited about these scientific advances, they are also annoyed by OpenAI's methods. After receiving a flood of AI-generated research conclusions over the past several months, this fatigue is already familiar. Many researchers hope the entire academic community can focus its energy on the heavy lifting of verification, questioning why OpenAI adds further barriers by personally selecting experts to control the process.

Most experts interviewed approved of OpenAI consulting external researchers, but argued that publishing research conclusions implies making relevant materials available to everyone for verification. Constantin Kogler, a researcher at the Institute for Advanced Study, said, "I appreciate this release cadence—publishing only three results instead of dumping hundreds at once as before." However, he disagreed with restricting access to experts selected by OpenAI. He stated, "There is no reason to initially limit content access to a small number of prominent scientists."

Andreas Karch, a professor of physics at the University of Texas at Austin, remarked, "It is very bad for them to hand-pick the expert team. Large labs already wield sufficient influence; they should not decide who qualifies to participate and who is excluded." Karch initially suggested using a selection mechanism to choose researchers but admitted that those ultimately chosen would likely still be top-tier scholars. He then questioned why supporting evidence couldn't be released simultaneously, accompanied by an expert interpretation group. "This would allow everyone access to the content while demonstrating their desire for the results to be understood and taken seriously."

Just one day before OpenAI's announcement, the Advisory Group on Mathematics and Artificial Intelligence (AGMAI) published a statement specifically warning against such information control. The group stated, "We do not recommend AI companies adopt this model." They argued that prioritizing access for specific groups is unnecessary, borrows the prestige of selected researchers, and introduces risks such as unequal access, biased selection, and unjustified delays. AGMAI proposed that AI labs should upload results to academic preprint servers, include formal proofs and topic descriptions, and provide funding and support to help the academic community interpret these conclusions.

Following the release of these new results, AGMAI urged OpenAI to "immediately publish the natural language manuscript and Lean formal proof corresponding to this physics result":

These are core problems in both physics and important mathematical questions. The existence of quantum Yang-Mills theory is a Millennium Prize Problem, and the construction of interacting quantum field theories in four dimensions has been a goal in mathematical physics for decades. We deeply respect the scientists invited by OpenAI to lead this work. But as stated in our previous declaration, interpretation of results should proceed in a public environment where everyone has equal access. OpenAI claimed the delay was to complete the Lean formalization. According to their own account, this work is now finished, so there is no scientific justification for continuing to withhold publication.

Hassett believes that fully disclosing the results benefits scientific progress and helps foster broader acceptance of new tools like AI. "Multiple research teams around the world working together on these conclusions will enable researchers who need them to get up to speed with these new tools more quickly."

Finding a communication approach that satisfies researchers across the various disciplines OpenAI is entering may be inherently unrealistic. OpenAI states it is experimenting with different strategies and acknowledges that each method involves trade-offs. Jared Duker Lichtman, a mathematician at Stanford University, noted: “My sense is that no matter which option we choose, someone will inevitably be dissatisfied. We are simply trying to find the path of least contention.”

Xiaoyu He, a mathematics professor at Georgia Tech, believes the issue runs deeper than just the format of publication. “The results themselves are impressive, but in my view, they are merely performing responsibility and caution while avoiding the core contradiction: these fundamental problems are being rapidly solved by AI without any contribution from human researchers, and the resulting proof texts are difficult to read and verify.”