OpenAI's Navier-Stokes Millennium claim rests on a proof outsiders have not seen
OpenAI said 1,000 agents found Euler blow-ups in 50 hours and 10,000 agents extended them to Navier-Stokes in 11 hours, at a customer cost of about 15 million dollars. The Clay prize is 1 million dollars. Nature and Quanta Magazine date the same announcement to 8 September; the proof was checked in Lean, though New Scientist wrote that nobody outside has seen it.
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1,000 agents took 50 hours, 10,000 agents 11 hours; customer cost 15 million dollars
OpenAI told a press conference that 1,000 agents took 50 hours to find blow-ups in the Euler equations, and that 10,000 agents extended them to Navier-Stokes in 11 hours. It put the compute cost for a customer at about 15 million dollars. It did not name the model, saying only that it is significantly more capable than GPT-6 Astra. Nature reported that the company announced on 8 September a computer-generated solution to the Navier-Stokes Millennium Problem, and that the model first answered a simplified version in 50 hours using 1,000 AI agents.[1], [2]
The Clay prize is 1 million dollars; Chandrasekaran said infinite speed in finite time
The Clay Mathematics Institute prize attached to the problem is 1 million dollars. Nature reported that OpenAI computer scientist Ven Chandrasekaran said the proof shows there exist fluids which start out perfectly normal and under the Navier-Stokes equations achieve infinite speed in a finite amount of time. Martin Bridson, president of the Clay Mathematics Institute, called it an exciting day for the human understanding of mathematics. Quanta Magazine reported that 10,000 autonomous agents found a singularity in three dimensions and that the result has been formally checked in the programming language Lean.[2], [3]
The announcement came hours after Buckmaster and Alpöge; OpenAI said its proof differs
The announcement came hours after Tristan Buckmaster at New York University and Levent Alpöge at Anthropic reported blow-ups in the Euler equations. Quanta Magazine put that gap at 12 hours. Buckmaster then published a note saying he had asked OpenAI for clarification and was given no hard details about how the result was reached. OpenAI said its Euler proof differs from theirs and denied using their work or prompts. Mark Chen said that was also the company's understanding for the thousands of agents.[1], [3]
