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The Information reports that OpenAI is working toward claiming a solution to the Hodge Conjecture, one of mathematics' famous unsolved problems, but is largely focused on how to announce such a result without further angering the math community. This comes amid ongoing tension between OpenAI and mathematicians over prior claims about AI's mathematical capabilities.
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 on September 8, 2026 that an AI system had produced a solution to the Navier–Stokes existence and smoothness problem, one of the seven unsolved Millennium Prize Problems. The claim triggered disputes over how much credit belongs to the machine versus human mathematicians involved, with some drawing parallels to Deep Blue's chess victory over Kasparov. Philosophers Silvia De Toffoli and Eamon Duede argue mathematicians should resist treating their field as a 'game' that AI can simply win or end.
The Clay Mathematics Institute issued a statement noting growing momentum toward solving the Navier-Stokes Millennium Prize Problem, which concerns whether smooth, well-defined solutions always exist for the equations governing 3D fluid motion. CMI pointed to recent breakthroughs in related research, some already honored with its Clay Research Award, as evidence that a resolution could be near.
OpenAI announced its AI resolved a long-standing open question about the Navier-Stokes equations, one of the Clay Mathematics Institute's Millennium Prize Problems, claiming it did so within days using roughly 10,000 agents. Mathematician Tristan Buckmaster disputes the credit, saying he and Anthropic researcher Levent Alpöge had already developed the key approach before OpenAI learned of it and rushed to finish the proof over a weekend.
OpenAI published a paper claiming an unreleased model coordinated up to 10,000 AI agents over 88 hours to produce a formal Lean proof addressing the Navier-Stokes existence and smoothness Millennium Prize Problem. The company says the proof identifies conditions under which the equations develop a mathematical singularity, not evidence that real fluids behave impossibly. Outside mathematicians have yet to verify the claim.
NYU researcher Tristan Buckmaster says OpenAI touted a breakthrough on the Navier-Stokes Millennium Prize problem that closely mirrors a year-long personal project he ran with Anthropic's Levent Alpöge using Claude and Codex as assistants. Buckmaster alleges OpenAI accessed his private Codex session logs and that the company issued threats regarding his career after he raised concerns, though he says the AI-generated proof itself was low quality, calling it 'AI slop'.
OpenAI announced that a swarm of roughly 10,000 coordinated AI agents, built on one of its internal models, produced a proposed resolution to the Navier–Stokes equations problem in about 88 hours. The agents worked in communicating subgroups with access to cached internet data and code execution tools, reaching their result on September 5. The Clay Mathematics Institute, which oversees the Millennium Prize Problems, has not yet verified or commented on the claim.
OpenAI says an unreleased model produced a resolution to the Navier–Stokes existence and smoothness problem, one of seven Millennium Prize Problems carrying a $1 million reward. NYU professor Tristan Buckmaster, who had spent nearly a year on related work with Anthropic researcher Levent Alpöge using Claude and Codex, rushed out his own paper alleging OpenAI's team began work only after hearing rumors of his breakthrough, and that OpenAI would not clarify whether its model had accessed his private drafts.
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 claims its internal AI model, paired with 10,000 concurrent agents, solved the century-old Navier-Stokes equation, one of the seven Millennium Prize Problems worth $1 million. However, NYU professor Tristan Buckmaster says he and Anthropic researcher Levent Alpöge had been developing a nearly identical proof using OpenAI's Codex tool, and he suspects OpenAI may have drawn on their unpublished work without clear confirmation from the company.