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v64 7 hours ago

This is going around due to rumors and baseless speculation on Twitter [1] right now that Anthropic has solved the Millennium problem related to Navier-Stokes [2]

[1] https://x.com/AndrewCurran_/status/2096062392442724805 for example

[2] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...

cacio-e-pepe 6 hours ago | parent | next [-]

relevant: https://mathstodon.xyz/@tao/117219101339291693

hodgehog11 2 hours ago | parent | prev | next [-]

Why would they send it out for "expert review"? Every time, they have just made the AI generate a Lean proof. In fact, it seems like the most plausible direction to NS is computationally assisted detection of a blowup solution, which has fantastic automatic validation.

lumost an hour ago | parent [-]

How do you know the lean is correct? You don’t bet the two trillion dollar company on “the ai said so”

adrianN 12 minutes ago | parent [-]

You carefully check that the problem is formalized correctly and then trust the Lean machinery to check the proof.

strangescript 2 hours ago | parent | prev | next [-]

This is a step beyond baseless predictions. Tao also had a "weird" "hypothetical" comment about LLMs solving complex proofs with impossible to human verify Lean.

CSMastermind 7 hours ago | parent | prev | next [-]

Lol as far as I know that post was the origin of that claim and it's clearly just a guy predicting something that will happen in the future with no information about it.

krackers 6 hours ago | parent [-]

Elliot Glazer (FrontierMath lead) traces how it snowballed over time

https://x.com/ElliotGlazer/status/2096298696438906934

Arodex 6 hours ago | parent [-]

Not reading any x.com content until xcancel and nitter are back.

sawjet 5 hours ago | parent | next [-]

Dear diary...

perching_aix 5 hours ago | parent | prev [-]

here you go: https://nitter.kareem.one

bee_rider 6 hours ago | parent | prev | next [-]

For a second I thought they were aiming the scary proof machine at us mortals doing PDE stuff. Fortunately the speculation is just that they happen to be aiming it at a nearby mathematician type problem. Phew.

bobmarleybiceps 4 hours ago | parent | prev | next [-]

if there's anything that would convince that LLMS are one of the biggest innovations ever, it would be this :-D

bilsbie 6 hours ago | parent | prev [-]

If it is solved what are the applications of that? What changes?

lumost an hour ago | parent | next [-]

Maximally, a closed form solution would remove the need for Computational Fluid Dynamics. Any property could be derived from a (presumably expensive) analytic function.

Minimally. It could say that no such analytic function can ever exist. Which would be rather boring.

Turbulent fluids look awfully predictable with their spirals….

amluto 15 minutes ago | parent [-]

That would be surprising IMO. We have closed form solutions to Newton’s Laws plus gravity (albeit not very many of them), we have several closed form solutions to Einstein’s equation in GR, and we have a whole lot of closed form solutions to Maxwell’s equations. But we still use numerical methods to solve interesting problems in all of these fields.

margorczynski 6 hours ago | parent | prev | next [-]

None really. It just says if the NS equations are realistic and can really model real physics or there exist some solutions that make it blow up (infinite energy). But even if that would exist (a solution that blows up) it doesn't mean it doesn't work for 99,999999% of the stuff we're interested in.

The question is basically a pure math question about PDEs.

fatcatsbestcats 6 hours ago | parent | prev [-]

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