IT之家 reported on October 17 that in September this year OpenAI published a 166-page proof related to the Navier–Stokes equations, claiming its internal AI system solved this Millennium Prize Problem in about 88 hours.
However, as the mathematical community scrutinizes the work further, researchers have begun to question the method used in the proof, its relationship to existing research, and how much role the large-scale AI agents actually played.
Mathematician Gonzalo Cao-Labora pointed out thatOpenAI may have rushed to publish the paper without understanding it itself。
He said the details of OpenAI's proof present a different route from the approach previously proposed by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa, and the similarities between the two may be more superficial than substantive.
Multiple groups of experts involved in reading the work told Scientific American that mounting evidence suggests OpenAI's proof did not follow the "Spanish route." This means that when OpenAI released the result, it seemingly did not fully understand what its model had actually done.
Note from IT之家: the Navier–Stokes equations describe fluid motion and are one of the Millennium Prize Problems established by the Clay Mathematics Institute. OpenAI released the related research on September 8, saying its internal model completed the mathematical proof, and simultaneously published the proof written in the Lean formal verification language. OpenAI said its research team used about 10,000 AI agents and obtained the result in about 88 hours, then spent about 17 more hours on formalization and verification.
Lean can check whether the logical derivations in a formalized proof conform to the set rules, but passing formal verification does not mean that the problem the proof solves necessarily matches the scientific question researchers originally cared about, nor does it mean the proof's reasoning is easy for humans to understand. The proof OpenAI published runs 166 pages long, and the mathematical community is still examining its specific methods and conclusions.
One point of this controversy is how much connection OpenAI's research actually has to the research path previously explored by Córdoba and Martínez-Zoroa.
Scientific American noted that OpenAI's proof exploits the external force term in the Navier–Stokes equations to construct a scenario in which fluid velocity grows without bound in finite time.
Mathematicians hold differing views on the significance of this result: it fits one of the scenarios allowed by the original statement of the Clay Mathematics Institute's problem, but it does not solve the more closely watched question of whether solutions to the three-dimensional Navier–Stokes equations always remain smooth when no external force is applied.
As for attribution of the research results, New York University mathematician Tristan Buckmaster questioned whether OpenAI's research may have benefited from related work he and Anthropic employee Levent Alpöge conducted using public models.
In response, OpenAI denied using Buckmaster's related data, and in an official statement updated on September 10 said that after investigation, the prompts Buckmaster had entered into Codex over the previous two months could not in any way have influenced this research, including through model training. But as of now, the two sides still dispute the relationship between the research methods and results.
Another question that has not yet been clearly answered is how much these collaborating agents actually contributed. OpenAI officially said its research involved about 10,000 agents running in parallel, sending about 2.7 million messages in total and using about 130 billion output tokens. However, these figures only reflect the scale of computation and the running process; they cannot directly indicate the actual contribution of the multi-agent architecture to the final result.
OpenAI researcher Noam Brown also pointed out that researchers currently do not know how much additional benefit such a large-scale agent cluster actually brings. Because systematic controlled experiments with thousands of agents are costly, researchers have not yet fully compared the time a single agent needs to complete the same task, making it hard to accurately measure the advantage of 10,000 agents over 1,000 agents.Brown estimated that the multi-agent collaboration architecture may have contributed less than 10% to this success。
In his view, because AI agent technology is novel and prone to attracting wide attention, it easily receives recognition exceeding its actual contribution; the truly crucial factors may be the capability of the underlying model itself, and the model's ability to keep working on tasks for long periods and explore multiple solutions in parallel.
In early October (10月初), OpenAI also publicly released about 400 mathematical research results.The mathematical community generally says that merely digesting this material will take years。
These results were published on GitHub in a relatively loose, centralized form, which again drew dissatisfaction from some mathematics researchers. They worry that publishing a large volume of results in bulk without adequate explanation, organization, and academic exchange will reduce the readability of mathematical research outputs, and may also blur the distinction between rigorous research verification and large-scale automatically generated results.
Currently, the mathematics community is still evaluating OpenAI's related research. The controversy involves not only whether AI can generate formalized proofs, but also whether the research methods genuinely solved the target problems, how the results should be attributed, and how the actual contributions of multi-agent systems should be measured.
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