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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).
    by yababa_y
  • 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.

    by nikitamalyavin
  • 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 wouldn’t turn into content marketing that is generated primarily to trigger strong human emotions.

    I feel that this is going to hurt both AI and the disciplines that can benefit the most from it

    by cpard
  • The open question is whether the Clay institute will award OpenAI or others the Millenium prize for this solution to the Navier Stokes problem. I speculate that they won't. OpenAI's solution is undergoing peer-review and the counterargument presented in this article changed my mind. By default, if the Clay institute hasn't officially recognized the solution as true or likely true, I can't make an assumption that it is. I hope to go through the proof and perhaps AI can help better understand it and any potential weaknesses.
    by kittikitti
  • 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?

    by chmod775
  • 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?
    by ChickeNES
  • 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.

    by bmacho
  • 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 of the question". This is pure sensationalism. Choosing option (C) (out of an explicit list of four options) is neither a "loophole" nor something "found by the LLM"; everyone involved knew this was the option they were pursuing.

    With the grumbling out the way, there is some actual scientific content to the article: there's a strong argument that OpenAI's method will not extend to the unforced case, leaving our understanding of NS incomplete. This negative result is itself new and interesting (and predicated entirely on the solution found by OpenAI)!

    by jonlong

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