OpenAI claims solution to Navier–Stokes problem; researcher raises questions about data
OpenAI said it had found a solution to the Navier–Stokes problem, which concerns the movement of liquids and gases, using an internal artificial intelligence model. According to the company, it used a model more powerful than the recently released GPT-6 Astra, as well as 10,000 agents operating simultaneously. The Verge reports.
The Navier–Stokes problem is one of the seven Millennium Prize Problems, with a $1 million reward offered for solving each of them. OpenAI said it began training the internal model on August 28. According to the company, it showed unprecedented results in its tests, including in mathematics. OpenAI also said it does not plan to claim the reward.
Work by other researchers
A day before OpenAI's announcement, New York University mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpoge published results on a related problem. Buckmaster said he contacted OpenAI after learning that the company had heard about their progress.
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According to Buckmaster, OpenAI obtained a proof for the Navier–Stokes equation through an approach that he and Alpoge had been working on using OpenAI's Codex and Anthropic's Claude. He questioned whether the company had access to their Codex sessions, where the researchers uploaded all drafts of the project. Buckmaster says he did not receive an answer to a repeated question about the possible use of those data for training the model.
OpenAI's response
OpenAI said it had not accessed specific user data to solve the problem. At the same time, the company noted that, although unlikely, it cannot completely rule out that anonymized data derived from the use of its products may have helped improve the models.
OpenAI technical team member Sébastien Bubeck said the company had not seen Buckmaster's and Alpoge's work before its publication. According to him, the proofs differ substantially, as do the specific results. In response, Buckmaster wrote on Mastodon that, in his view, OpenAI acknowledges the use of training data from the period after he and Alpoge obtained their result.
