On October 17th, from the IT community, it was reported that OpenAI published a 166-page proof related to the Navier-Stokes equations ( Navier – Stokes equations ) this September, claiming that their internal AI system solved this millennium-old problem in about 88 hours.
However, as the mathematical community further reviewed the related work, researchers began to question the methods used in the proofs, the relationship with existing research, and to what extent the large-scale AI intelligentsia played a role.
Mathematician Gonzalo Cao-Rabola ( Gonzalo Cao - Labora ) pointed out that OpenAI might have rushed to publish a paper without even fully understanding it himself.
He stated that the proof details of OpenAI follow a different approach compared to the methods previously proposed by Spanish mathematicians Diego Cordova (Diego C or rdoba) and Luis Martínez-Zoroya (Luis Mart í nez-Zoroa), and any similarities between them may be more superficial.
Multiple groups of experts involved in the review all stated to Scientific American that there are increasingly many signs indicating that the proof for OpenAI does not follow the "Spanish route." This means that when OpenAI published this result, they did not seem to fully understand what their model actually did.
Note from IT: The Navier-Stokes equations, used to describe fluid motion, are one of the Millennium Prize unsolved problems established by the Clay Mathematics Institute. OpenAI released related research on September 8th, stating that its internal model had completed the mathematical proof, and simultaneously published the proof written using the Lean formal verification language. OpenAI stated that its research team used approximately 10,000 AI agents, obtaining the result in about 88 hours, and then spending approximately 17 hours completing the formalization and verification work.
Lean is capable of checking whether the logical deductions in formal proofs conform to established rules, but passing formal verification does not necessarily mean that the problems solved by the proof correspond to the scientific issues that researchers were originally concerned about, nor does it imply that the reasoning behind the proof is easily understandable to humans. OpenAI The published proof is 166 pages long, and the mathematical community is still reviewing its specific methods and conclusions.
One of the disputes this time is about how closely the research of OpenAI is related to the research paths previously explored by Cordova and Martinez-Zoroya.
Scientific American points out that the proof for OpenAI utilizes the external force term in the Navier-Stokes equations to construct a scenario where fluid velocity increases indefinitely within a finite amount of time.
Mathematicians have different views on the significance of this result: it fits one of the scenarios permitted by the original problem statement of the Clay Mathematics Institute, but it does not address the more pressing question of whether the solutions to the three-dimensional Navier-Stokes equations remain smooth without the application of external forces.
In terms of the attribution of research findings, Tristan Buckmaster, a mathematician from New York University ( Tristan Buckmaster ), questioned whether the research of OpenAI might have benefited from related studies conducted by him and Levent Alperge ( Levent Alp ö ge ), an employee of Anthropic, using public models.
In response to this, OpenAI denied the use of巴克马斯特's relevant data and stated in an official statement updated on September 10th that, after investigation, it was impossible for the keywords entered by巴克马斯特 in Codex over the previous two months to have any impact on this research, including through model training. However, as of now, there is still disagreement between the two parties regarding the relationship between the research methods and the results.
Another question that has not yet received a clear answer is exactly how much contribution these agents' collaboration has provided. OpenAI officially states that their research involved about 10,000 agents running in parallel, sending approximately 2.7 million messages in total, and using around 130 billion outputs Token. However, these numbers only reflect the scale of computation and the process of operation; they do not directly indicate the actual contribution of the multi-agent architecture to the final results.
Researcher Norm Brown ( Noam Brown ) also pointed out that currently, researchers are not clear about exactly how much additional benefit such a large-scale agent cluster has brought. Due to the high cost of conducting systematic controlled experiments with thousands of agents, researchers have not fully compared the time required for a single agent to complete the same task, nor is it easy to accurately measure the advantage of 10,000 agents over 1,000 agents. Brown estimates that the contribution of multi-agent collaboration architecture to this success may be less than 10%.
In his view, due to the novel nature of AI intelligent entity technology and its tendency to attract widespread attention, it is easy to gain recognition that exceeds one's actual contributions; the truly critical factors may be the capabilities of the underlying model itself, as well as the model's ability to handle tasks continuously over a long period and to explore multiple solutions in parallel.
At the beginning of October, OpenAI made public approximately 400 mathematical research results. The mathematics community generally stated that it would take several years to digest this amount of information.
These results are published in a relatively loose form on GitHub, which has also caused dissatisfaction among some mathematics researchers. They worry that the concentrated publication of a large number of results without sufficient explanation, organization, and academic exchange may reduce the readability of mathematical research findings and may also blur the distinction between rigorous research verification and large-scale automatically generated results.
Currently, the mathematical community is still evaluating the relevant research on OpenAI. This controversy involves not only whether AI can generate formal proofs, but also whether the research methods have truly solved the target problems, how the results should be attributed, and how the actual contributions of multi-agent systems should be measured.
