In the span of a single week, two of the world’s leading AI companies announced results that have jolted the mathematical community. OpenAI says it has solved a 90-year-old, million-dollar math problem, while Anthropic revealed that its Claude AI formalized one of history’s most famous proofs. The rapid-fire announcements have left mathematicians oscillating between wonder and dread.
On Tuesday, September 8, OpenAI announced that roughly 10,000 AI agents, running on an unreleased model more powerful than its GPT-6 Astra, had solved the Navier-Stokes existence and smoothness problem in 88 hours. The problem, one of six remaining Millennium Prize Problems designated by the Clay Mathematics Institute in 2000, asks whether the equations governing fluid motion can produce sudden infinities, or “blow up.” OpenAI’s agents concluded that they can. The solution, pending independent verification, builds on work by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa, who developed the underlying technique over a year of research. But the announcement was immediately shadowed by a dispute. Hours before OpenAI’s release, NYU mathematician Tristan Buckmaster posted a statement claiming that he and Anthropic researcher Levent Alpöge had been working on the same problem using Córdoba and Martínez-Zoroa’s approach, and that OpenAI had moved to publish after learning of their progress. Buckmaster alleges OpenAI attempted to influence credit for the work.
Days earlier, Anthropic disclosed that Claude had produced the first complete, computer-checked formalization of Fermat’s Last Theorem in the Lean proof assistant. Working largely autonomously over 11 days, the system generated roughly 13 million lines of code and proved 29,500 intermediate theorems along the way. Kevin Buzzard of Imperial College London, who has led a parallel multi-year effort to formalize the same proof, called it an extraordinary autoformalization achievement. The result does not constitute a new proof. Andrew Wiles proved the theorem in 1995. Rather, it is a machine-verified encoding of an existing one, a task that mathematicians expected would take years.
The breakthroughs have prompted soul-searching among researchers. In an interview published Saturday, Cornell University mathematician Steven Strogatz described himself as really terrified by the pace of change. The science is exhilarating, he said, but it comes with a lot of human discord. Strogatz, co-author of Big Math, a forthcoming book on mathematics moving beyond human comprehension, framed the race between corporate labs as driven partly by the prospect of lucrative IPOs. As AI accelerates mathematical discovery, the implications for researchers who have devoted entire careers to these problems remain uncertain.
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