A Model Secretly Solving Navier-Stokes and the Threat of Automated Plagiarism

Perex: OpenAI solved the Navier-Stokes equation, one of the Millennium Prize Problems. However, celebrations are marred by accusations that the company deliberately scooped researchers from NYU and Anthropic after finding out they were close to a solution.

How a rumor launched a fifteen million dollar offensive

According to mathematician Tristan Buckmaster and his colleague Levent Alpöge (Anthropic), the pair had been working on the problem for almost a year. They used Claude and Codex (specifically GPT-5.6 Sol) to do so. They achieved a breakthrough in August. A rumor began to spread through the mathematical community. OpenAI heard about a major problem solution from Anthropic in early September. Within days, it launched a carpet-bombing run. It had its new model generate 2.7 million messages and 130 billion tokens. The result? OpenAI announced it had solved the problem shortly before the academics could publish their preprint. If OpenAI paid public API prices for GPT-6 Astra for this feat, it would cost $15 million.

What this means for research and security

This situation is a warning to anyone working on breakthrough research. OpenAI defends itself by saying it didn't have access to the academics' data and only acted on the rumor. But the mere information that a problem is solvable (or already solved) is a huge advantage in the era of powerful LLMs. Once OpenAI knew a solution existed and concerned Navier-Stokes, it could throw massive computing power at finding its own proof. It's similar to cybersecurity. The mere report of an unpatched vulnerability can be enough for agents to discover it.

Questions surrounding data and training

The case opens another burning question. OpenAI swears it didn't read the academics' workflow in Codex. But it also admits that de-identified data from their work might have helped models improve. This raises doubts. If you use a commercial model to solve a mathematical problem, there is a chance the model learns from your steps. Can the same tool then sooner or later help someone else solve the same problem faster? Simon Willison rightly asks how big the risk is that your own effort will make a competitor's job easier.

The transparency of procedures will decide, not brute force

The true measure of how the situation develops won't be who spends more on tokens, but how the rules of the game are set for research using proprietary models. If labs like OpenAI want to prevent similar controversies, they will have to define much more clearly what not using user data means. And there is a clear lesson for researchers. Working on a breakthrough discovery in the interface of a model that doesn't belong to you means running the risk that your tool will eventually defeat you.

Lilith's verdict

The issue is not someone else being first. It is that if OpenAI capitalizes on breakthrough signals, cloud models effectively act as a wire service for the developers you entrust with your research.