Dan Rockmore’s article examines OpenAI’s September 2026 claim that it had solved the Navier–Stokes Millennium Prize Problem, one of the most famous unresolved questions in mathematics. The problem concerns whether the Navier–Stokes equations, which describe the motion of fluids, can develop a finite-time singularity or “blow-up” from initially smooth conditions. The equations are extraordinarily successful in practical applications such as weather modeling and aircraft design, yet mathematicians had never established whether their solutions always remain smooth. Rockmore explains that mathematicians Tristan Buckmaster and Levent Alpöge had independently developed important work on related Euler equations, building on earlier results by Diego Córdoba and Luis Martínez-Zoroa.
The article then describes how AI became involved in the mathematical breakthrough. OpenAI reportedly deployed its latest model against several Millennium Problems, first using roughly one hundred AI agents on the Euler equations and subsequently scaling the effort to approximately 10,000 agents for Navier–Stokes. Over about eighty-eight hours, the agents exchanged around 2.7 million messages, producing approximately 130 billion tokens of mathematical work. Human mathematicians supervised the process and used additional models to consolidate promising approaches. Although the resulting proof still requires thorough human verification, Rockmore reports that initial assessments suggested the problem had been resolved. The episode therefore represents not simply AI assisting a mathematician with calculations, but a fundamentally different model of mathematical research involving large-scale machine-generated exploration.
However, Rockmore is interested in much more than whether the proof is correct. He highlights the controversy over priority and credit, particularly because Buckmaster and Alpöge had already produced important results and published their work shortly before OpenAI announced its achievement. The episode raises broader questions about how mathematical credit should work when discoveries emerge from a combination of human researchers, previous literature, AI systems, and enormous computational resources. Rockmore argues that mathematics is particularly valuable to AI companies as a demonstration of apparent machine intelligence: unlike many real-world problems, a mathematical proof can ultimately be checked for correctness. Consequently, solving a celebrated mathematical problem becomes a powerful public demonstration of what AI systems can supposedly accomplish, as well as a way of showcasing enormous computational power.
Finally, Rockmore connects the episode to Walter Benjamin’s famous essay “The Work of Art in the Age of Mechanical Reproduction.” Benjamin argued that technologies such as photography and film changed the status of artistic works by separating them from their unique origins and “aura.” Rockmore asks whether AI is doing something analogous to human thought and mathematical creativity: reproducing the products of thinking while potentially disconnecting those products from the individual thinkers and historical processes that produced them. He acknowledges the enormous potential of AI to accelerate mathematical research and even suggests that traditional educational and research structures may eventually change dramatically. At the same time, he worries that dependence on common AI systems could make human thought increasingly standardized and concentrated around technologies controlled by a small number of companies. His central question is therefore not simply “Can AI solve mathematics?”, but whether mathematics—and human thinking more generally—loses something important when the process of discovery becomes increasingly automated.
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The article then describes how AI became involved in the mathematical breakthrough. OpenAI reportedly deployed its latest model against several Millennium Problems, first using roughly one hundred AI agents on the Euler equations and subsequently scaling the effort to approximately 10,000 agents for Navier–Stokes. Over about eighty-eight hours, the agents exchanged around 2.7 million messages, producing approximately 130 billion tokens of mathematical work. Human mathematicians supervised the process and used additional models to consolidate promising approaches. Although the resulting proof still requires thorough human verification, Rockmore reports that initial assessments suggested the problem had been resolved. The episode therefore represents not simply AI assisting a mathematician with calculations, but a fundamentally different model of mathematical research involving large-scale machine-generated exploration.
However, Rockmore is interested in much more than whether the proof is correct. He highlights the controversy over priority and credit, particularly because Buckmaster and Alpöge had already produced important results and published their work shortly before OpenAI announced its achievement. The episode raises broader questions about how mathematical credit should work when discoveries emerge from a combination of human researchers, previous literature, AI systems, and enormous computational resources. Rockmore argues that mathematics is particularly valuable to AI companies as a demonstration of apparent machine intelligence: unlike many real-world problems, a mathematical proof can ultimately be checked for correctness. Consequently, solving a celebrated mathematical problem becomes a powerful public demonstration of what AI systems can supposedly accomplish, as well as a way of showcasing enormous computational power.
Finally, Rockmore connects the episode to Walter Benjamin’s famous essay “The Work of Art in the Age of Mechanical Reproduction.” Benjamin argued that technologies such as photography and film changed the status of artistic works by separating them from their unique origins and “aura.” Rockmore asks whether AI is doing something analogous to human thought and mathematical creativity: reproducing the products of thinking while potentially disconnecting those products from the individual thinkers and historical processes that produced them. He acknowledges the enormous potential of AI to accelerate mathematical research and even suggests that traditional educational and research structures may eventually change dramatically. At the same time, he worries that dependence on common AI systems could make human thought increasingly standardized and concentrated around technologies controlled by a small number of companies. His central question is therefore not simply “Can AI solve mathematics?”, but whether mathematics—and human thinking more generally—loses something important when the process of discovery becomes increasingly automated.
ARTICLE
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