On September 8, 2026, OpenAI announced that it had discovered a solution to a challenging problem concerning the "Navier-Stokes equations," one of the Millennium Prize Problems in mathematics. According to the company's announcement, using a multi-AI agent system powered by internal models more capable than GPT-6 Astra, they obtained a proof that a solution starting from smooth initial conditions develops a singularity within a finite time. It was reported that this proof has also been verified using Lean, a formal language for mathematical descriptions.
During the proof process, the AI agents sent 2.7 million messages and generated approximately 130 billion tokens. OpenAI researcher Noam Brown noted that while computational costs reached millions of dollars, he expressed the view that scaling up computational resources will eventually create an environment where anyone can solve advanced mathematical problems.
On the other hand, suspicions regarding the misappropriation of research results have arisen after it became clear that OpenAI had obtained information prior to the announcement that Levent Alpoge of Anthropic and Tristan Backmaster of New York University were working on the same problem. Backmaster stated that while they were conducting research using Codex, OpenAI sent prompts after obtaining information about their work.
In response, OpenAI denied that its researchers or agents directly referenced the work of the two individuals or accessed specific user data. However, the company also stated that it cannot completely rule out the possibility that anonymous data derived from product usage contributed to the improvement of the model.
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