GoKawiil
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OpenAI recently claimed its AI agents produced a solution addressing the Navier-Stokes equations, one of math's unsolved Millennium Problems, after running 10,000 agents for 88 hours. Mathematicians including Oxford's James Maynard and Brown's Javier Gómez-Serrano say the resulting proof, while apparently technically correct, is written in a form that is extremely difficult for humans to interpret or learn from.
OpenAI announced that its most advanced AI model produced a mathematical proof that the Navier–Stokes equations, which describe fluid flow, can generate a singularity — a point of physically impossible infinite speed. Mathematician George Karniadakis calculated that for air this breakdown occurs at a vortex width of about 70 nanometres, roughly the distance a molecule travels before colliding with another.
OpenAI announced it had solved part of the Navier–Stokes Millennium Prize Problem using an AI system, but the announcement via press release drew criticism for lacking transparency about verification and prior human contributions. Hours earlier, mathematicians Tristan Buckmaster and Levent Alpöge said they had reached a partial solution using AI tools from both OpenAI and Anthropic, raising questions about who deserves credit for the breakthrough.
OpenAI announced Tuesday that a swarm of 10,000 AI agents, run for 88 hours at a cost of millions of dollars, had found a scenario where the Navier-Stokes equations describe fluids reaching infinite velocity, effectively breaking the famous equations. NYU mathematician Tristan Buckmaster then publicly accused the company of producing a solution suspiciously similar to unpublished work he had been developing for years and was close to finishing.
NYU's Buckmaster and his collaborator Alpöge published a proof that a simplified version of the Navier-Stokes equations can break down, after nearly a year of work using public AI models. Hours later, OpenAI released its own proof covering the full equations using an unreleased internal model, but Buckmaster alleges OpenAI tried to pressure him into excluding his co-author, who works at Anthropic, and dodged questions about whether their models were trained on his private work transcripts.
OpenAI published a preprint claiming to show that the Navier-Stokes equations, which govern fluid motion, can break down under certain conditions, describing a spinning fluid system reaching infinite speed in finite time. The claim addresses part of one of mathematics' seven Millennium Prize Problems, but mathematicians have raised concerns over how the result was announced and over authorship disputes involving researchers connected to rival company Anthropic.
OpenAI says an unreleased internal AI model, running roughly 10,000 autonomous agents, produced a proof addressing the long-unresolved Navier-Stokes existence and smoothness problem within about 88 hours. The effort began after the company heard rumors that two Millennium Prize problems had been cracked elsewhere, prompting it to test the model on outstanding mathematical challenges. The result has not been peer-reviewed or accepted by the Clay Mathematics Institute, which oversees the Millennium Prize.
OpenAI says an internal AI model, more capable than GPT-6 Astra, generated a solution to part of the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. The proof demonstrates that three-dimensional incompressible fluid dynamics governed by these equations can develop a singularity—unbounded speed growth—in finite time, even from smooth initial conditions. OpenAI released both a written explanation of the proof and a formal verification built in the Lean proof assistant.
OpenAI announced on 8 September that its latest AI model produced a proof showing that the Navier-Stokes equations, which model fluid motion, can break down and predict a fluid reaching infinite speed in finite time. This addresses one of the seven unsolved Clay Mathematics Institute Millennium Problems, which carries a $1 million prize for a full solution. OpenAI researchers say they focused their AI on this problem after hearing that two academic mathematicians were close to solving related aspects.