Scientific American asks whether OpenAI solved the wrong problem
3 Sep 21 · 2d ago · 2 posts · 2 sources · development 3 of 3
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 SilvestreOpenAI AI companyLuis Silvestre Mathematician, University of ChicagoDiego Córdoba MathematicianLuis Martínez-Zoroa Mathematician8Braid Independent verification team
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What was reported 1 claim about this development
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first by Scientific American, 2d ago
What people said 15 voices · best of 16 · verbatim
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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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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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C'mon @npr.org, keep up. It didn't actually solve it, only an edge case.
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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…
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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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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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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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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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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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> 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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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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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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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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Or a better framing: Clay Institute chose the wrong Navier-Stokes problem for a Millennium Prize.
All 3 developments of Mathematicians Rebut OpenAI's Navier-Stokes Proof as… →
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