Vi Hart's long essay on OpenAI's Navier-Stokes claim: a Lean-verified proof she thinks will hold, and a scoop she calls embarrassing

Vi Hart, the mathematician known for her YouTube videos, has published a long six-part essay on Patreon about OpenAI's claimed solution to the Navier-Stokes problem. Her best guess is that the result is real and will hold up. Her anger is aimed at how OpenAI got it, and at what she sees as a wider pattern in the AI industry.

The essay is called "Vi Hart's Big Navier-Stokes Post." Hart says the first five parts get increasingly intense and the sixth is a lighter treat. Everything below is her account and her opinion, as written in the post. We have not independently checked her claims, and the essay is not a peer-reviewed assessment of the proof.

Part one is about Lean, the proof assistant, which is a programming language for writing mathematical proofs that a computer can check. Hart says she briefly worked with the Lean team while at Microsoft Research. Lean is the language behind Mathlib, a large shared library of formalized mathematics, and it was used for the Navier-Stokes result.

That background gave her a lot of faith that the proof is what it claims to be. She also says the result does not surprise her. In her view, it rests on years of work by university mathematicians, students and volunteers who built Mathlib, plus all the human writing and code that AI models learn from. She asks how much work from how many people it really took.

Part two argues that AI is not about to make mathematicians obsolete. Hart says AI results look impressive because people have produced a huge number of examples for the models to learn from. She compares a library of every possible proof to the Library of Babel, an imagined library of every possible book. Almost all of it would be meaningless, she says, because mathematicians pick out the interesting parts. For her, formal proofs are a product of mathematics, not its source.

Part three is about the dispute around the result. Hart says human researchers had already made progress on Navier-Stokes. She names Diego Córdoba and Luis Martínez Zoroa for a new approach, and Tristan Buckmaster and Levent Alpöge for very recent work that followed it. She says Buckmaster and Alpöge used AI-powered methods through OpenAI's tools and were rumored to be close to a result. OpenAI then announced that it had solved the problem with its own internal models.

Hart says she has no special knowledge of the details and points readers to coverage elsewhere. She does repeat the claim that OpenAI offered one author credit in exchange for cutting out the other, who worked for a competitor. OpenAI says it was not trying to coerce, threaten or bribe Buckmaster. Hart calls the whole episode a deep embarrassment for the company. She says it spent what she guesses were millions of dollars to beat the people whose work it could see.

She also argues that the Millennium Prize problem has little practical value. In her telling, the prize is about an abstract property of the equations, not about real-world fluids. Mathematicians treat the problem like a tall mountain, she says, and the real prize is the new ideas needed to climb it. Hart compares it to P vs NP and the Riemann Hypothesis, where an answer would matter more to other work.

Part four says mathematicians who gave their work to OpenAI are now learning that they have fewer protections than they thought. Hart says mathematics has always been political. She argues there should be boycotts, closed accounts and lawsuits, and says she has seen little of that.

Part five compares AI companies today to Jeffrey Epstein's funding of researchers in 2019. Hart says she saw part of that scandal from inside MIT's CSAIL lab community. She argues that researchers who work with the companies now may regret it later. She says the point is not to shame them, because it could happen to anyone.

Part six lists seven ways the proof could still be wrong, from likely to unlikely. They include an undiscovered bug in Lean, a correct proof of the wrong statement, and AI-induced delusion among the researchers. They also include an AI-run campaign to mislead people, a clash between the bug-hunting and proof-finding work, and Lean being the wrong tool for the job. The last is simply a reason nobody has thought of yet.

On the first, Hart notes that a supposed disproof of the Collatz Conjecture was verified in Lean earlier this year despite being incorrect, which revealed a bug that was quickly fixed. She thinks another bug is unlikely, but says far more computing power went into the proof than into hunting for bugs. On the second, she says Buckmaster and Alpöge are human experts who have worked on this approach for a long time, which makes a misstated problem less likely.

Hart notes that no prize has been awarded. The Millennium Prize has a two-year minimum waiting period between a claim and an award. She says that even if her first six questions did not exist, she would not treat the result as definitive until the mathematics community has had years to review it. She adds that she may be wrong about parts of her own essay, and invites corrections in the comments.

She ends by saying that communities of experts, not lone geniuses or machines, build mathematical knowledge.