OpenAI's math breakthrough claim sparks credit dispute with rival researchers

On September 8th, OpenAI announced that researchers working with an unreleased internal model had solved the Navier-Stokes equations, one of mathematics' most formidable unsolved problems. The announcement arrived with immediate complications: two mathematicians claimed the company may have built its solution on their unpublished work without attribution.

The Navier-Stokes equations describe how fluids move through space—how water flows, how air currents form. The Clay Mathematics Institute designated it one of seven "Millennium Prize Problems" in 2000, attaching a $1 million bounty to any proof. For more than two decades, only one of those seven problems had fallen. OpenAI's claim, if verified, would represent a watershed moment in both mathematics and artificial intelligence.

But Tristan Buckmaster, a professor at New York University, and Levent Alpöge, a researcher at Anthropic, had spent much of the preceding year pursuing the same problem through independent work. They were building on research by mathematicians Diego Cordoba and Luis Martinez-Zoroa, attempting to prove a related equation—the Euler equation—as a stepping stone toward the larger prize. Buckmaster alleged in a statement that after OpenAI learned of their progress, the company accelerated its own effort using a nearly identical approach.

According to Buckmaster's account, he contacted OpenAI after hearing rumors that Anthropic had solved the problem. During a subsequent call, OpenAI researcher Sebastian Bubeck told him the company was also working on Navier-Stokes, pursuing what Buckmaster described as a strikingly similar path. Buckmaster asked whether the model had been trained on or had access to sessions in Codex, OpenAI's coding tool, where he and Alpöge had stored their drafts throughout the project. He said he was told the model had not accessed user data. When he pressed the question about training data, he received no answer. Bubeck then proposed releasing their findings jointly, but with a condition: Alpöge would not be listed as an author.

Bubeck later disputed this account on social media, saying he had offered access to OpenAI's internal model so Buckmaster and Alpöge could complete their own proof. He framed his hesitation about including an Anthropic employee as a matter of navigating intellectual property concerns, not an attempt to erase Alpöge's contribution.

OpenAI issued a categorical denial of the core allegation. In a statement, the company said its researchers "did not see any of their work through any means until they released it publicly." The company acknowledged, however, that user feedback and data—including individual chats with ChatGPT and interactions with Codex—are incorporated into its model training. "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models," OpenAI wrote. CEO Sam Altman added that the two approaches "appear to be different" and noted that the company's latest model can solve many other mathematical problems.

Buckmaster's statement was careful in its framing. He said he had not seen OpenAI's proof, did not know what the model had done or how, and could not confirm whether his data had been used. He was not accusing anyone of intentional wrongdoing. He was, instead, documenting a sequence of events and a proposal he believed the public should know about—a record against what he saw as a false narrative taking shape. The dispute raises a question that will likely outlast this particular disagreement: as AI systems become tools for solving humanity's hardest problems, who gets credit, and how do we ensure that credit flows to those who earned it?