OpenAI’s Navier-Stokes Proof Faces Scientific Scrutiny
Questions arise over methodology and the 'black box' nature of AI research.
Scientific Skepticism
In early September, OpenAI released a 166-page document claiming to provide a solution to the Navier-Stokes equations, one of the most complex problems in fluid dynamics. The company stated that its proof was based on the work of Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. However, independent experts disagree with this assessment.
Gonzalo Cao-Labora, a mathematician at EPFL, argues that OpenAI’s approach differs fundamentally from the methodology of these mathematicians, with any similarities remaining purely superficial. While the proof is written in the Lean programming language—which verifies logical steps—it remains exceptionally difficult for humans to read or comprehend. The Clay Mathematics Institute (CMI) is currently reviewing the work.
Disputes Over Copyright and Methods
The controversy within scientific circles extends beyond the content of the proof. Tristan Buckmaster, a mathematician at New York University, accused the company of basing its proof on his own work and that of Levent Alpoge. OpenAI denied these allegations, stating that the mentioned data was not used. The core issue is that modern language models function as "black boxes," making it nearly impossible to fully decipher their internal processes.
The situation intensified in October following the release of an additional 400 results, which appeared scattered across GitHub. Some mathematicians have criticised this approach, viewing it as a devaluation of the field.
An Opaque Technological Process
Perhaps most striking is the fact that OpenAI itself cannot fully explain how it reached these results. For this task, the company utilised approximately 10,000 model instances over 88 hours, processing 130 billion tokens. According to OpenAI researcher Noam Brown, no one knows exactly what contribution this large-scale "team of agents" made to the final result.
Brown suggests that the contribution of multi-agent systems to the success is less than 10%. These systems are new and popular, which often leads to them being given disproportionate importance. In reality, the primary driver is the base model itself, capable of processing complex tasks in parallel and over extended periods. This case highlights once again that the development of artificial intelligence often outpaces our understanding of how this technology truly functions.