OpenAI announced earlier this month that its artificial intelligence had solved the Navier-Stokes problem, one of mathematics’ most important unsolved questions. The company framed the achievement as advancing scientific research for humanity’s benefit. However, mathematicians examining the resulting 166-page manuscript have expressed significant reservations about its practical value.\n\nThe dense proof, while believed to be technically correct by experts, has proven difficult for humans to extract meaningful insights from, according to researchers at leading institutions. Mathematicians noted the paper appears written for machines rather than human readers and would require substantial rewriting to convey actionable knowledge. This outcome disappointed many in the mathematics community who had hoped the breakthrough would demonstrate effective collaboration between artificial intelligence systems and human mathematicians.\n\nThe announcement proved particularly controversial given the timing and circumstances. Human mathematicians, including researchers at New York University and Anthropic, had been approaching a solution independently when OpenAI heard rumors of progress and launched its own intensive effort. The company deployed approximately 10,000 AI agents working for 88 hours, consuming around 130 billion output tokens at an estimated cost of $6-10 million. One mathematician accused the company of having improperly obtained knowledge of his research approach and claimed they offered authorship contingent on excluding his collaborator from a rival company. OpenAI denied using others’ work.\n\nThe Navier-Stokes equations describe fluid flow and are fundamental to physics and engineering, yet their basic mechanisms remain poorly understood. Solving the problem was designated one of the $1 million Millennium Prize Problems by the Clay Mathematics Institute in 2000. In response to criticism, OpenAI announced the establishment of an independent mathematics advisory group, though the company clarified this group would not influence the pace of its mathematical research efforts.
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