AI's Real Math Wins Get Overshadowed by an Unverified Claim It Solved a $1 Million Problem

Two real breakthroughs, and one that isn't confirmed

AI has had a genuinely good year in mathematics. It's also had a very confusing week.

On May 20, 2026, OpenAI announced that one of its general-purpose reasoning models had disproved a conjecture tied to the planar unit distance problem, a question Paul Erdős first posed in 1946 about how many pairs of points in a plane can sit exactly one unit apart. The prevailing assumption since Erdős's time was that "square grid" arrangements were essentially the best possible answer. OpenAI's model produced an infinite family of counterexamples showing a polynomial improvement over that assumption. The proof was checked by outside mathematicians, and Fields medalist Tim Gowers wrote in a companion paper that the result is "a milestone in AI mathematics." Princeton's Noga Alon has called the unit distance problem "one of Erdős' favorite problems." That result is real, reviewed, and dated.

Then, according to a post on X by Anthropic on September 4, 2026, the company's Claude model spent 11 days formalizing Andrew Wiles's 1995 proof of Fermat's Last Theorem into Lean, a language computers can check line by line. That's a different kind of achievement than the Erdős result. Claude didn't discover new math. It translated an existing, already-verified proof into roughly 13 million lines of machine-checkable code, building on a formalization project that Imperial College London mathematician Kevin Buzzard started in 2024, according to Decrypt. Buzzard's own project outline runs 86 pages and has funding secured through 2029. Claude reportedly did the translation in 11 days, mostly on its own, per Anthropic.

The claim nobody can actually see

The third story is the one that's generating the most noise, and it's the least solid.

On Tuesday, September 8, 2026, mathematician Tristan Buckmaster published a statement comparing the moment to "Deep Blue-Kasparov," the 1997 chess match where IBM's supercomputer beat world champion Garry Kasparov, according to Scientific American. Buckmaster alleges that he and Levent Alpoge, a mathematician who works at Anthropic, had made significant progress last month toward proving the Navier-Stokes equations, which govern fluid motion, break down under certain conditions. That would resolve one of the six remaining Clay Mathematics Institute Millennium Prize problems, worth $1 million.

Buckmaster alleges that before he and Alpoge could publish, word of their method reached OpenAI. OpenAI's researchers used their large language model to finish the proof with a single prompt sent "in the past few days." OpenAI did not respond to Scientific American's request for comment. Scientific American's own headline hedges, saying AI "may have" solved the problem, but its body treats Buckmaster's account with far more certainty than the underlying record supports. There is no published paper, no proof text, and no independent expert review available anywhere in public.

A separate viral post on X by user Andrew Curran, which has drawn more than 2.5 million views, claims it's actually Anthropic's Claude, not OpenAI's model, that cracked Navier-Stokes, and speculated the company would time an announcement to its initial public offering. Fields medalist Terence Tao posted a hypothetical scenario about AI solving the problem. Some readers interpreted this as a hint he had inside knowledge. Tao has publicly clarified he does not.

So as of today, two different unverified narratives are circulating, crediting two different companies with the same unproven result. The Clay Mathematics Institute still lists Navier-Stokes existence and smoothness among its unsolved problems. Under rules the institute adopted in September 2018, it won't even consider a submission until it's published in a peer-reviewed journal, has sat for at least two years after that, and has won general acceptance in the mathematics community. A proof announced today, even a real one, wouldn't be eligible for the prize for years.

A fair concern about how AI labs are doing this

Tao has raised a broader point worth taking seriously: if AI companies keep their iteration process private and only publish finished proofs, mathematicians lose almost everything of value. The failed attempts, dead ends, and intermediate insights are often where the real mathematical understanding lives, not just the final answer. That's a legitimate methodological critique, not a dismissal of AI's capabilities, and it applies whether or not the Navier-Stokes claim turns out to be true.

None of this proves fraud or wrongdoing by anyone. Buckmaster's allegation is his own account, unconfirmed by OpenAI, and there's no evidence yet that anyone acted in bad faith. What's missing is simple: a paper, a proof, and outside mathematicians willing to put their names on a review. Until one of the two companies publishes something checkable, the honest label for the Navier-Stokes claim is unverified, not solved.