Mathematicians Rebut OpenAI's Navier-Stokes Proof as Solving the Wrong Problem
A new proof shows OpenAI's forced-fluid loophole can never be extended to the real Millennium Prize problem, reviving a dispute over AI-generated math.
What to know
- OpenAI's headline claim of solving Navier-Stokes rests on a version of the problem that includes an external force, which most mathematicians consider outside the scope of the real Millennium Prize question.
- Independent formal verification by 8Braid confirmed OpenAI's Lean proof checks pass, but stressed that passing formal checks does not settle whether the result addresses the intended physical problem.
- A newly posted proof by three mathematicians shows OpenAI's forced-fluid method can never be extended to the unforced case, closing off the loophole permanently absent a new approach.
- The dispute has sharpened tension between the mathematicians who built the underlying forced-blowup method and OpenAI, which released its result less than a day after their preprint.
OpenAI AI companyLuis Silvestre Mathematician, University of ChicagoDiego Córdoba MathematicianLuis Martínez-Zoroa Mathematician8Braid Independent verification team
How it unfolded 3 developments, newest first · click a bar or a number to jump articlesposts
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Scientific American asks whether OpenAI solved the wrong problem
The outlet reported that OpenAI's proof solves a forced variant of Navier-Stokes that most experts consider disconnected from the real, unforced problem mathematicians care about, quoting several mathematicians who argue the core question remains open.
“The most important problem is unsolved. The Clay problem is settled, but the main problem for the Navier-Stokes equations is not.”
— Luis Silvestre -
first by Scientific American, 2d ago
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> In a sense, the LLM found and exploited a loophole in the framing of the question. they tend to be very good at that.
2 more of the top 3 · 27 posts in this stretch
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«In yet another sign of # AI ’s surging dominance over human minds, # OpenAI recently claimed to solve one of math’s biggest questions: the Navier-Stokes problem. But now three mathematicians have showed OpenAI’s work dodges the question rather than solving it. » https://www. scientificamerican.com/article…
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No, OpenAI did not solve the "wrong" Navier-Stokes problem. OpenAI did not solve the hardest version of the problem (unforced blow-up), but did give a solution to the Clay Millennium Prize Problem as written and understood, choosing the explicitly allowed forced option.SciAm writes "in a sense, the LLM found and exploited a loophole in the framing…
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- 2 days quiet
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Three mathematicians prove OpenAI's method cannot be extended
Three mathematicians posted a proof showing that OpenAI's forced-fluid approach can never be extended to solve the full, unforced Navier-Stokes problem — meaning the loophole OpenAI exploited is a dead end barring an entirely new idea.
- 1 day quiet
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Independent team verifies OpenAI's formal proof checks
Researchers at 8Braid reproduced OpenAI's submitted Lean formal checks, confirmed both the Nanoda and default Lean kernels accepted the proof, and derived an explicit stability bound for one algebraic step, while noting that formal verification does not settle whether the result matches the intended physical problem.
“We reproduced the formal checks, proved an explicit bound for one construction step, and tested how 8DB handles its evidence.”
— 8Braid -
background
OpenAI announces an AI-generated Navier-Stokes blowup proof — Less than a day after the mathematicians' step, OpenAI released a proof of finite-time breakdown for the Navier-Stokes equations, generated by an internal LLM together with a Lean formalization, claiming eligibility for the Clay Mathematics Institute's $1 million Millennium Prize.
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background
Mathematicians produce a forced blowup using Córdoba–Martínez-Zoroa method — Two mathematicians used a program developed by Diego Córdoba and Luis Martínez-Zoroa, aided by AI, to produce a finite-time blowup for a frictionless fluid under a specific external force — a step widely seen as a major advance toward the Navier-Stokes problem.
Also covered reported alongside — the timeline has no entry for these yet
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first by dars.gov.et, 6d ago · also The Conversation
1 more headline
- OpenAI may have solved the Navier-Stokes equation The Conversation · 4d ago
and 1 smaller piece
What people are saying 21 voices from 5 sites · best of 27 · verbatim
- Yesterday
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What will happen if we'll build a real-life test if the proposed counterexample? The exactly same force, as defined, shape of the vortex, etc?We should either see the effect or get to understanding of how to correct the model.Note that the force is finite and doesn't "know" the vortex config. The singularity should be achieved in a finite time.
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Mixed bag. Sure, any scandal attracts unqualified attention (and I count myself there) In terms of interest among people anywhere close to qualified, OpenAI team is almost surely net negative, but availability of LLMs to qualified people in the field is net positive. The reason for net positive is in a sense because this is a «bad problem», amount…
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Ok you are somehow still managing to misunderstand the point. Its almost like you care more about "winning an argument" than just like.... trying to understand what someone is saying. I encourage you to consider what lie by omission is. Pro tip: be less of a dick and you might learn more.
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I wonder if this interest for the field will continue after an IPO
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I mean, to whatever extent it has caused interest in the problem rather than destroyed interest, great but that was not inevitable. there was no particular reason to expect it. there is no call to start making prophecies about how things will definitely turn out; the future is not written.
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> Now fluid dynamicists are grappling with a possibility few had considered before: the idea that the Navier-Stokes equations can blow up but only with an external force. And there we have it, AI does not subtract, it adds. There is renewed and widespread interest in this problem and it is viewed from a different angle now. I think the AI…
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There might be more value in having LLMs systematically hunt for mistakes in existing and widely assumed correct math papers, or hunt for counter-examples to things thought proven. There's likely to be a couple mistakes hiding in the less well scrutinized corners of mathematics.Maybe something interesting will fall over because of that, who knows?
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TL;DR: when modeling fluid flow, you can either choose to allow an external force (gravity, etc) on the fluid or not. The Clay problem as posed requires a proof of either - stability in all cases for no force - existence of *some* force that causes divergence The proof provided by OAI (authorship claims aside) proves the latter, but the proof…
- Sep 22
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When the news spread about the solution of this problem by AI we started wondering what will happen when AI will start generating proofs we can’t comprehend.Today, we are discussing if AI cheated by picking the easy problem to solve which means that we at least still comprehend what’s going on.I wish mathematics and the rest of the human intellect…
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That's not a loophole, it's just the easiest way to get the CMI prize. It's not like every question about Navier-Stokes got answered. It is still a big achievement, the "who did it" is another question.
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> SciAm writes "in a sense, the LLM found and exploited a loophole in the framing of the question".God, it’s embarrassing to read stuff like this. They’re making it seem as if everyone involved was either stupid or dishonest just so they can pretend they have a scoop here.
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As I understand it the "loophole", if you want to call it that, is that OpenAI's custom-designed forcing function was smooth, as the rules said it had to be, but was non-analytic, consisting of some construction of "compactly supported bump functions", meaning a mass of tiny little pushes at precise points of space and time to push a vortex into…
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Totally agree. I wouldn't quite call it clickbait, but the article does this thing I find annoying where it puts the "sensationalist" framing at the beginning (the "loophole" quote you put), but then closer to the end fully admits that it wasn't really a loophole in any case:> It did, however, unambiguously solve the problem according to the Clay…
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I will admit that when I heard they only had forced blowup I went back to sleep (but I've never been more that cursorily interested in analysis).
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So what they are saying is that humans, in this case Charles Fefferman (a math prodigy, going by his history), failed to specify the problem correctly?
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The bulk of the article (assuming there _is_ one) seems to be behind a paywall.
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Alt title: did _they_ actually solve it?
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C'mon @npr.org, keep up. It didn't actually solve it, only an edge case.
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A lot of people online misunderstand what "solving Navier-Stokes" refers to, thinking it means finding a closed form solution to the NS equations. That's not what mathematicians mean when they talk about solving Navier Stokes. They're talking about solving the Navier Stokes existence and smoothness problem, which is a decision (yes/no) problem…
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Article says that there are 2 formulations of the NS problem and both are interesting: one is about fluid behaviour with no external forces, other is about fluid behaviour with external forces.For a counter-example the latter is easier since you can have a tricky external forcefield.
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“Furthermore, last Thursday, three mathematicians posted a proof of their own that showed that OpenAI’s method can never be extended to solve the full problem. In other words, the loophole will never be closed, barring some completely new idea.” # Math # NavierStokes # ai https://www. scientificamerican.com/article…