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OpenAI says it found a solution to a major math problem that has remained unsolved for around 90 years, as reported earlier by The New York Times and Wired. In a blog post on Tuesday, OpenAI announced that it discovered a solution to the Navier-Stokes problem — which relates to the flow of liquid and gas — using an internal AI model more powerful than the newly released GPT-6 Astra alongside 10,000 concurrent agents. The Navier-Stokes problem is one of seven Millennium Prize Problems, each of which comes with a $1 million reward for solving.
OpenAI says it started training the internal AI model on August 28th, which has “exhibited unprecedented performance in our benchmarks, including mathematics.” The solution is a big breakthrough for the mathematics community, but it doesn’t come without controversy.
Just one day before OpenAI’s announcement, New York University mathematics professor Tristan Buckmaster published findings on a related problem in partnership with Levent Alpöge, a researcher at Anthropic. When announcing these findings, Buckmaster claims he contacted OpenAI after learning the company had heard about their progress. However, Buckmaster found that OpenAI had produced a proof for the Navier-Stokes equation using a route he and Alpöge had been working on with OpenAI’s Codex and Anthropic’s Claude.
In his statement, Buckmaster raises concerns about whether OpenAI had accessed their Codex data to get closer to the Navier-Stokes solution. “I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project,” Buckmaster writes. “I was told the model did not look up user data. I asked again, about training, and I did not get an answer.”
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OpenAI is now attempting to squash these suspicions with its Tuesday announcement, saying “no specific user data was accessed in order to solve this problem.” It adds that “while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” When reached for comment, OpenAI pointed The Verge to its statement on X, which echoes its blog post.
Sebastien Bubeck, a member of technical staff at OpenAI, similarly said: “We did not see any of their [Buckmaster and Alpöge’s] work until they released it publicly last night. One can in hindsight see that our proofs differ significantly and even the precise results proved are different.”
Meanwhile, Buckmaster responded to this in a post on Mastodon, claiming that OpenAI is “openly admitting they used training data from a period after we found our result.”
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