# When Artificial Intelligence Claims a Mathematical Breakthrough: Questions of Credit and Creativity
In September 2026, OpenAI declared it had cracked one of mathematics' most stubborn puzzles—a problem that had defied human insight for nearly two centuries. The announcement should have been cause for pure celebration. Instead, it ignited a fierce debate about authorship, data ethics, and whether machines can truly be credited with intellectual discovery.
The Navier-Stokes problem concerns equations describing how fluids move, formulated by Claude-Louis Navier and George Gabriel Stokes some two hundred years ago. Mathematicians have spent generations investigating whether these equations always produce smooth solutions or whether some theoretical scenario exists where part of the fluid moves infinitely quickly and the mathematics "blows up." The Clay Mathematics Institute deemed the question so fundamental that it designated Navier-Stokes one of seven Millennium Prize Problems, each carrying a one-million-dollar reward.
OpenAI's approach involved deploying roughly ten thousand artificial intelligence agents that worked largely autonomously for eighty-eight hours, using computational power that likely cost millions of dollars. The company claimed its system identified a specific blowup scenario involving a vortex of fluid spiraling inward and stretching out like spaghetti. They verified the work using a programming language called Lean.
But timing raised uncomfortable questions. remove this sentence
In a public statement, Buckmaster revealed that he and Alpöge had made significant progress on the Navier-Stokes problem but had not yet published their findings. Crucially, they had used large language models during their research, including OpenAI's Codex. In a conversation with employees of OpenAI, he asked whether the model had been trained on, or had access to, their sessions in Codex.
"I do not know whether our data was used," Buckmaster wrote. "I am not accusing anyone of anything."
OpenAI maintained that its researchers and agents had not seen the mathematicians' work until it became public. The company stated that no specific user data was accessed to solve the problem. However, the blog post included a notable caveat: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." Later, the company issued a stronger statement to media, declaring it "impossible" for Buckmaster's recent Codex prompts to have influenced the system.
The controversy extends beyond questions of data access. Buckmaster credited earlier foundational work, with Buckmaster stating his belief that Martínez-Zoroa deserved a Fields Medal for contributions. He and Alpöge had used large language models to build on their ideas, with Buckmaster stating his belief that Martínez-Zoroa deserved a Fields Medal for the foundational contributions.
Timothy Gowers, a mathematician at the Collège de France, acknowledged the symbolic significance of artificial intelligence solving such problems, calling it "the next in a natural chain of big moments." Yet the episode reveals thorny questions about attribution when machine learning systems, trained on vast datasets that may include human researchers' work, produce breakthroughs in areas where those same humans are actively laboring.
OpenAI announced it would not claim the million-dollar prize. Who ultimately receives credit for solving the Navier-Stokes problem remains uncertain.
**Sources:**
Smithsonian Magazine. "A.I. May Have Solved a Longstanding Math Problem With a Million-Dollar Prize. It Ignited a Controversy Over Who Gets Credit." September 10, 2026. https://www.smithsonianmag.com/smart-news/ai-may-have-solved-a-longstanding-math-problem-with-a-million-dollar-prize-it-ignited-a-controversy-over-who-gets-credit-180989472/