The Million-Dollar Math Problem AI Didn’t Solve: A Rumor, a Fight Over Navier-Stokes, and the Trust Crisis Nobody Wants to Talk About

As of September 10, 2026, the BSD Conjecture has not been solved. Neither OpenAI nor Anthropic has released any official result on it.

The claim that it was “possibly solved” began with a post on X by a user named Leo in early September. The gist: he had heard that the Hodge Conjecture was about to be verified by OpenAI, and that the BSD Conjecture was about to be handled by either OpenAI or Anthropic. The post included no paper, no institutional statement, and no checkable link. It was a “heard.”

Timing made the rumor spread. BSD itself did not.

On September 8, OpenAI announced that it had used roughly ten thousand AI agents over 88 hours to crack the existence and smoothness problem for the Navier-Stokes equations. The Navier-Stokes equations describe fluid motion. They are one of the seven Millennium Prize Problems, each carrying a one-million-dollar bounty from the Clay Mathematics Institute. OpenAI’s announcement was quickly buried under a controversy.

Tristan Buckmaster, a mathematician at NYU, publicly alleged that he and Levent Alpöge, a researcher at Anthropic, had been working on the problem for nearly a year. They had started from the work of Diego Córdoba and Luis Martínez-Zoroa, pushed along the “forcing” route, and reached a breakthrough on August 15. All of their drafts during the project were stored in OpenAI’s Codex platform.

Buckmaster directly asked Sébastien Bubeck, an OpenAI researcher, whether the model had been trained on or had accessed those Codex sessions. Bubeck’s answer was that “the model does not look up user data.” When the question turned to “training,” there was no follow-up.

OpenAI’s official statement included this sentence: “While unlikely, we cannot rule out that de-identified data derived from their use of our products helped improve our models.” The sentence acknowledges an indirect data pathway while refusing a definitive denial.

Buckmaster also alleged that OpenAI offered him a deal: he could publish the joint result as the sole author, but Alpöge had to be excluded. The reason: Alpöge works at Anthropic, and his name would “mess up the headline ‘OpenAI solves Millennium Prize Problem.’” When he refused and said he would make the matter public, he was allegedly told: “Why do you want to destroy your career?”

OpenAI denied all allegations, calling Buckmaster’s claims “false and inflammatory.” Terence Tao called Buckmaster and Alpöge’s work “a remarkable achievement.” He said nothing about OpenAI’s conduct.

That silence weighs more than any accusation.

The rumor began to move. If OpenAI could “follow up” within a week on a problem someone else had chewed on for a year, what comes next? Leo’s post offered no evidence, but it offered a narrative: OpenAI and Anthropic are racing toward the next Millennium Prize Problem. BSD and Hodge were named, not the Riemann Hypothesis or P vs. NP.

That is not random.

The Navier-Stokes problem has a particular structure: it is extremely hard, but its target is a relatively clear existence/regularity statement. Once a proof strategy exists, a large part of what remains is heavy, technical estimation and construction. For that kind of problem, the pattern of “swarm thousands of agents, then verify line by line in Lean” can, in principle, make progress.

BSD is different.

The BSD Conjecture, the Birch and Swinnerton-Dyer Conjecture, says: for an elliptic curve EE defined over the rational numbers, the rank of the group of rational points equals the order of vanishing of its L-function L(E,s)L(E,s) at s=1s=1.

rank⁡(E(Q))=ord⁡s=1L(E,s)rank(E(Q))=ords=1​L(E,s)

The left side is an algebraic object: how many “independent” rational solutions the curve has. The right side is an analytic object: the behavior of a function from complex analysis and modular forms at a specific point. The equation demands a bridge between two worlds in number theory that have almost no traffic with each other.

Over the past sixty years, each step has cracked only the rank 0 or rank 1 cases. Coates and Wiles proved the rank 0 partial case in 1977. Gross and Zagier established the relation between the canonical height of Heegner points and the derivative of the L-function in 1986. Kolyvagin then developed the Euler system method. By 2017, the work of Wei Zhang and Skinner-Urban on the Iwasawa main conjecture pushed the refined BSD formula to rank 1 in the ordinary case. Wan Xin extended the result to the non-ordinary case.

For the general case of rank greater than or equal to 2, there is still no publicly accepted attack framework. Computation is not the obstacle. A conceptual framework is missing.

That means even if someone, human or model, claimed “it’s proved,” judging whether the proof holds would itself require top number theorists months or years. Lean verifies the correctness of logical steps. The core of a BSD proof, those conceptual bridges between algebra and analysis, whether they exist and whether they work, requires human mathematical intuition to judge.

On preprint platforms like Zenodo and figshare, several 2026 BSD “proofs” are already sitting there. One has a core mechanism called a “Tamesis Kernel Hamiltonian,” paired with a claim that “information conservation implies the finiteness of the Tate-Shafarevich group.” Another brings out a “fractal correction engine” and claims that pi is “the mechanism generating lattice structures.” Their common feature: they decorate themselves with terms from the literature, such as Iwasawa main conjecture, Skinner-Urban, and Kato, piled onto a self-made framework with no mathematical content. Then they use “we match all 500,000 curves in the LMFDB database” as evidence.

Numerical agreement proves nothing. Numerical verification of BSD has been going on since the 1960s. Birch and Swinnerton-Dyer themselves derived the empirical pattern from computer calculations. Numerical agreement is the starting point of the conjecture, not the end.

These preprints show one thing: in the AI era, the cost of producing a text that looks like a proof has fallen to nearly zero. Large models have a particular texture: terminology correct, reasoning hollow. They can accurately use words like “Iwasawa theory,” “Selmer group,” and “Euler system.” They can construct argument structures that look plausible at the syntactic level. They cannot judge whether those arguments touch the core of the mathematics.

An August 2026 study found that as many as 1,655 academic records on Zenodo contained fabricated author names generated by large language models. Other work has begun tracking the network structure of AI-generated mathematical proofs, trying to understand how machine-generated “proofs” enter the academic communication system. Journal editors are already complaining about a flood of AI-generated papers that look plausible but are wrong.

The nature of the problem has changed. Before, the bottleneck in mathematics was “writing the proof.” Now the bottleneck is “judging whether the proof is real.” The latter is exactly what AI currently cannot do. It is good at generating. It is not good at judging.

Back to Buckmaster’s question. He asked Bubeck: has your model been trained on our Codex sessions, or did it read the drafts we stored in Codex? Bubeck said “the model does not look up user data.” Buckmaster followed up: “What about training?” No answer.

These are two different questions. Reading user sessions in real time and training a model on de-identified historical usage data are two different things. OpenAI’s official statement answered the first, no real-time reading, but on the second it said only “cannot rule out.”

On a million-dollar problem, after a direct question, that answer leaves the key issue open.

A second number theorist, Andreas Thom, later raised a similar concern. He found that OpenAI’s result on “non-sofic groups,” which OpenAI called “one of ten mathematical advances we announced this month,” built heavily on his and Gábor Kun’s prior work. OpenAI’s initial announcement did not adequately credit them. Thom said he was struck by “how detailed OpenAI’s grasp of our techniques was,” techniques that “at the time were neither the most obvious nor the most promising route.”

He emailed OpenAI researchers asking whether his interactions with ChatGPT “formed part of the training data, or could be accessed by the reasoning process.” He did not get a satisfactory answer. OpenAI answered only whether the conversation could be directly accessed, not whether it entered the training data.

Thom’s conclusion was direct: “I think this is at least dishonest.”

As of September 10, 2026, the BSD Conjecture has not been solved. Neither OpenAI nor Anthropic has released any official result. Leo’s post remains a rumor on X.

But the reach of that rumor exposes something concrete.

It exposes the trust fracture left by the Navier-Stokes controversy. The company provides research tools to users and holds computing power and resources far beyond those users. It can hear a user’s research progress and then quickly follow up. It answers questions about data use with ambiguity. Under those conditions, “will the next hard problem also be solved this way” stops being an absurd guess and becomes a reasonable concern.

It also exposes a deeper dilemma: in an era when the cost of AI-generated content approaches zero, mathematics, a discipline built on rigorous proof, is facing a question it has never faced before. The question is no longer only “is this proof correct.” It is also “how do we know whether this proof is worth judging at all.”

The BSD Conjecture needs a bridge that does not exist. The rumor around it needs a certainty that does not exist.

Neither has arrived.