Alexander Wissner-Gross, a computer scientist and founder of Reified, broke into a discussion about frontier labs on Moonshots with Peter Diamandis to get something out: "Please, please, please, let me say something about Navier-Stokes." He had been sending the host red alerts by text that morning. At the time of recording, he said, the news was about six hours old.
The claim was that OpenAI had made progress on one of the Clay Mathematics Institute's Millennium Prize problems — the best-known list of open challenges in mathematics — using a model the panel described as not the publicly known GPT-6 Astra but a more advanced internal system. Wissner-Gross had predicted at the end of 2025 that AI would solve one of them this year.
The problem, and which part of it was answered
The Navier–Stokes equations describe how fluids move. They are the mathematics behind aircraft and submarine design, and, as one panelist pointed out, behind questions like how blood flows through an artificial heart without clotting. The equations work; what nobody could settle is whether they always behave.
The prize problem, as Charles Fefferman set it out for the Clay Institute, concerns three-dimensional incompressible flow and offers four acceptable targets. Alternatives A and B ask for a proof that smooth flow, left to itself with no outside push, stays smooth forever — in open space and in a repeating box. Alternatives C and D go the other way: they allow a smooth external force and ask for an example where the smooth solution breaks down. Fefferman's description also notes that results in two dimensions do not settle the three-dimensional case, and that numerical instability makes it hard to conclude much from simulations alone.
OpenAI's announcement places its result in that second category, C and D. It describes a fluid that starts at rest and is driven by a smooth force into an ever narrower, more elongated vortex, with the velocity growing without bound while the total energy stays finite. That is a singularity in finite time: the mathematics stops making sense at a point, under a force the problem's own rules permit. A separate Euler result in the same announcement concerns unforced flow — the Euler equations are Navier–Stokes with the viscosity, the fluid's internal stickiness, removed.
On the podcast this became a joke about coffee. Can you stir a cup "in such a way that you get a black hole out of it?" In the continuum limit, Wissner-Gross said, the answer appears to be yes. He then took it back where it belonged: the conjecture "hinges on whether it's possible in finite time with continuous initial conditions to achieve a singularity in an idealized fluid," and in the real world there is no idealized fluid. Will anyone make a black hole in a cup of coffee? "No. But it teaches us something. Don't worry about black holes in cups of coffee yet."
He did offer one speculative application, crediting Terence Tao: if you could engineer the right initial and boundary conditions, you might in principle get a fluid that builds smaller and smaller copies of itself — "a fluid-based nanotech." What Tao actually proposed, in a 2019 research note, was a route toward proving blowup by constructing fluid dynamics that repeat computational behavior at ever smaller scales — a proof strategy, not a manufacturing plan.
Eighty-eight hours, then seventeen more
OpenAI reports roughly 10,000 agents running at once, 88 hours to the result and another 17 hours to formalize and verify it in Lean, the proof-checking language in which every step must follow from earlier steps by rules the software enforces. The Navier–Stokes work consumed about 130 billion output tokens — tokens being the fragments of text, usually a word or less, that a model produces. Across all the problems attempted, the figure was about 300 billion. The agents passed intermediate findings to one another, and researchers swapped them onto a further-trained model partway through.
Emad Mostaque, founder of Intelligent Internet, read the timeline off the announcement: training on a new model that became very good at mathematics began on 28 August, and on 1 September it was pointed at this problem. The same day training started, he said, an OpenAI researcher had publicly waved off a question about whether a Millennium Prize had been solved. One panelist summed up the method: "It's bitter lessened. You used to be able to get AI better by applying more compute to it. Now it seems like you can do that for any verifiable domain."
The $6.5 million figure that opened the episode is an outside estimate of the inference cost — the compute spent producing answers, not training the model — which the panel relayed as coming from at least one such estimate rather than the company. A panelist immediately argued the number should not intimidate anyone, on the group's forecast of roughly hundredfold price-performance gains by the end of the year: "it could be six bucks within a year and a half to do that exact same thing."
The fight over who gets the credit
Within hours, the story was about attribution. One panelist described a letter from researchers working on the related Euler blowup problem, saying OpenAI had approached them about priority and offered lead authorship on condition that a collaborator from Anthropic be dropped. Sebastian Bubeck, who leads the work at OpenAI, then posted his account, which the same panelist read as "just seems like a misunderstanding." As he paraphrased OpenAI's reasoning, the company had been willing to let the Euler researchers be lead authors because they would have got there anyway, but not to include the Anthropic collaborator, "because that would be weird because it's our model."
OpenAI's published account credits Levent Alpöge and Tristan Buckmaster with priority on the forced Euler result and says the company will not claim the Millennium Prize.
The sharper worry was contamination. At the time of recording, Wissner-Gross said he had found a caveat at the bottom of the announcement conceding that OpenAI could not rule out other teams' work having entered the training of the model that solved Navier–Stokes. The announcement's current text says an investigation excluded influence from the two months of Buckmaster's Codex prompts that preceded the result, including through training. What Wissner-Gross wanted was a world "where researchers benefit from frontier capabilities without worrying that the frontier platform is going to compete with them." Another panelist went further on the assurance that such work had been anonymized: "anonymizing someone else's research and then potentially scooping them is insufficient." He added that he was "not sure what the ground truth is," and that he had reviewed both approaches and found them genuinely different.
Generalists beat the specialists
The result also settled an internal argument about method. Google DeepMind, the panel said, had a team working toward Navier–Stokes with physics-inspired neural networks — models built around the equations themselves — and had been publishing incremental progress. "And they got trounced by a generalist model," one panelist said: no fine-tuning that he could see, just a general system reasoning for 88 hours.
That inverts the usual route to scientific glory, another noted. Everyone at Google wants to be the next Demis Hassabis, who built a specialized system for protein folding and won a Nobel Prize. But here "the prompt to solve this is like, give me thousands of GPUs and solve the problem. No one's going to give you a Nobel Prize for writing that prompt."
Closing the segment, Salim Ismail put it as a change in how science scales. For 500 years, he said, science grew with the number of brilliant people you could train and point at problems; now "we can spin up 10,000 researchers on a Tuesday afternoon," moving from staff on demand to "breakthroughs on demand."
Asked which prize falls next, two panelists agreed on Yang–Mills, a conjecture in particle theory about the existence of a mass gap. The reasoning was not about the mathematics. "It's just because that's the next chosen target," one said. "You know, you choose a different target. It'll be the next to fall." Before Navier–Stokes, he added, the targets had been Riemann and P versus NP.