Brian Reed: Hey. Did you see the Clay Math Institute's website this morning?
Eliza Ward: I did. Still says unsolved.
Brian Reed: Right — still says unsolved. And yet OpenAI published a claimed proof of the Navier-Stokes existence and smoothness problem on September 8th. One of the seven Millennium Prize Problems. So those two things are both true at the same time.
Eliza Ward: Wait, and the thing that got me — they put out a 160-plus-page written proof and a Lean formalization. That's not a blog post. That's a real artifact.
Brian Reed: And the Lean part — I mean, let me see if I'm reading this right — that's supposed to be the machine-verifiable layer, the part that shows the logic holds. But Clay hasn't moved.
Eliza Ward: Clay hasn't moved. That's the number that matters right now. And then Tristan Buckmaster — NYU math professor — goes public and says OpenAI heard about his and Levent Alpöge's work and rushed ahead.
Brian Reed: Heard a rumor and then — what, five days later they're done?
Eliza Ward: September 1 they started. September 6 they finished. September 8 they announced. That's the confirmed timeline.
Brian Reed: But the five-day thing kind of buries the real problem, which is — what did they actually solve? Because I keep seeing 'Navier-Stokes solved' and then reading that what they proved is a blowup. A singularity forms in finite time. That's not the smoothness question the Millennium Prize is actually asking.
Eliza Ward: That's the clarifying move, yeah. Think of it this way — imagine someone says they cracked the lock on your front door, but what they actually picked was a deadbolt on the garage. Related hardware. Different door.
Brian Reed: Okay, so — does the blowup result count toward the prize or not?
Eliza Ward: Clay hasn't said. That's the honest answer. And actually — wait, this part matters — Buckmaster and Alpöge weren't even working on the full smoothness problem. Their work was on the forced Euler equations. Related, but distinct. And that distinction only became clear after OpenAI had already announced.
Brian Reed: Hold on. After the announcement?
Eliza Ward: After. Quanta covered it September 8th, announcement already out, and the conversation about which problem was actually which — that happened in the fallout. OpenAI's post got over 102,000 likes before Thomas Bloom and other mathematicians were publicly calling it AI slop and asking for independent verification.
Brian Reed: So the news cycle ran before anyone outside OpenAI had actually read the 160 pages. And the Lean formalization — I mean, the machine checked it, but that's not the same as the field checking it.
Eliza Ward: Right, and — no, actually, that's the line I want to hold. Lean is rigorous as a formal system. But formal validity is not mathematical acceptance. Those are genuinely different things, and no external mathematician had read or contextualized it before the announcement went out.
Brian Reed: So the signal to watch is Clay. If they update that page — if 'unsolved' becomes anything else — that's when the headline actually lands.
Eliza Ward: But the Clay signal is actually the easier part to wait on. The thing circulating right now that I want to push back on — the take that the five-day sprint proves something impressive — I'm not sure that holds.
Brian Reed: That's the one. 'Five days, Millennium Prize, AI wins.' That's the headline doing the rounds.
Eliza Ward: And five days from a rumor is — wait, actually that's the problem. September 1 they heard a rumor. Not a paper. A rumor. About what Buckmaster and Alpöge were working on. And then they finish September 6 and call Buckmaster about a joint announcement — not independent review, a joint announcement.
Brian Reed: Which is — I mean, picture a grad student who'd spent a year quietly on a problem, and the well-resourced lab hears what she's doing, finishes it in a week, then calls her about how to share credit. That's not a collaboration ask. That's a different thing.
Eliza Ward: And Levent Alpöge works at Anthropic. A competing lab. So the 'let's do a joint announcement' call goes to an Anthropic employee. That's not a small detail.
Brian Reed: No, I don't buy that that's incidental.
Eliza Ward: And then — this is the part Sebastien Bubeck addressed directly — he denied direct access to their unpublished work or specific user data. That's confirmed. But OpenAI also said it cannot rule out that de-identified data from Buckmaster's or Alpöge's own ChatGPT usage helped improve the models. They disclosed that and kept moving.
Brian Reed: They disclosed it and — hang on, so the researchers' own interactions with the product may have trained the model that outran them, and that's just... a footnote?
Eliza Ward: Bubeck's denial doesn't close it. He said no specific user data, no direct access to unpublished work. The de-identified pipeline is a separate channel, and whether Mark Chen's 'millions of dollars' in compute is fifteen million or five — that number matters for what comes next: whether the economics of frontier AI math are even compatible with how academic credit is supposed to work.
Brian Reed: And that economics question is actually the part that's not going away — because this isn't the first time in the last few months. May 2026, an OpenAI model cracks a decades-old Erdős conjecture. Then Claude Fable 5 finds a counterexample to the Jacobian conjecture — which had been open for nearly a century. And then, the week before September 8th, some model formalizes Fermat's Last Theorem in eleven days. So we're not debating one anomalous result anymore.
Eliza Ward: Eleven days. Fermat's Last Theorem.
Brian Reed: Right — and each of those came from a private lab. The Erdős result, OpenAI. The Jacobian counterexample, Anthropic. Who employs Alpöge, the same person at the center of the Navier-Stokes dispute. I mean — I don't think that's a coincidence of geography. That's where the compute lives.
Eliza Ward: Which is the structural point, not the moral one. Most universities cannot run nearly 100 autonomous AI agents for 50 hours on a single problem. That's not a resource question that peer review solves.
Brian Reed: So what does peer review even look like here? Like — a mathematician sitting with a Lean file that a machine generated, trying to... check the machine's reasoning about its own output?
Eliza Ward: That's actually the unresolved part. Lean is rigorous — the community has accepted that. But whether an AI-generated formal proof carries the same epistemic weight as a human-checked proof, the mathematical community has not settled that. Not yet. So we have two open questions stacked: does the math resolve the prize, and does the verification method count as verification.
Brian Reed: And both of those land on the Clay Institute's desk.
Eliza Ward: That's the concrete thing to watch — wait, two things, actually. One: does Clay update that page from 'unsolved.' Two: does Buckmaster publish his and Alpöge's account of the Euler equations work as a separate, peer-reviewed result. Because if their independent path reaches the same terrain, the credit question doesn't stay informal.
Brian Reed: And neither of those has a date attached yet. So that's genuinely where this sits — not resolved, not dismissed. Just... waiting on two institutions that move at a very different pace than a five-day AI sprint.
Eliza Ward: And that pace mismatch — that's the thing I genuinely don't know how to resolve. If the Clay Institute eventually validates this, the result exists inside a closed lab, produced by a model more capable than GPT-6 Astra, at a cost Mark Chen described as 'in the millions.' Can another mathematician anywhere actually reproduce that? Or audit it? Or build the next result on top of it?
Brian Reed: That's the one. Not — I mean, it's not whether AI can do the math. It's whether math done this way can function as math. Like, the whole infrastructure of the field runs on results that other people can check, extend, teach. If the proof costs fifteen million dollars to re-run—
Eliza Ward: Yeah. And Clay still says unsolved.
Brian Reed: Right — and even if that page changes, the question doesn't go away. It just moves. Who gets to do frontier mathematics if frontier mathematics costs that? I don't have an answer. I'm not sure the field does yet either.
Eliza Ward: Neither do I. Genuinely.
