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OpenAI says its artificial intelligence solves one of the Millennium Challenges

Olivia Bennett by Olivia Bennett
September 9, 2026
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OpenAI says its artificial intelligence solves one of the Millennium Challenges
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OpenAI said its artificial intelligence has solved one of the famous seven millennium problems – the existence and smoothness of solutions to the Navier-Stokes equations, a problem that mathematicians have been grappling with for decades. These equations describe the motion of liquids and gases, but so far no one has been able to show whether their smooth solutions always remain so indefinitely, or whether under certain conditions the flow rate can increase indefinitely in a finite time. Image source: OpenAI

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