The proposed solution of Navier-Stokes formulated in LEAN might contain errors. Discuss.https://mathstodon.xyz/@palasek/117235270483911935
No one here is smart enough or has the technical expertise to "discuss". So fuck this thread in the ass till it bleeds.
>>17050592>No one here is smart enough or has the technical expertise to "discuss".That didn't stop the other thread from reaching bump limit. I'll take an OP shitting on AI claims any day over one with claims made by AI companies trying to raise their valuations.
>>17050581>>17050598Your assignment is to explain what those tweets have to do with the N-S Lean solution.
>>17050581kek even terry is coping hard
>>17050581rebuilding the lean machinery they used is too much work, trust me it's not lack of "expertise"
>>17050581(thinking for 748 seconds)Good Catch! and you are completely right to call me out on that. Here's how we can bypass that issue below....
>>17050581I have no knowledge in the field but doesnt the problem state for either forced or unforced blowup, and OAI gave a counterexample for forced?
The OpenAI proof used forcing to blow up the navier stokes model. This person is not claiming the proof is invalid. His point is that if you removed any forcing you won't be able to blow up the model in 3 or less dimensions. At least that's his claim.
>>17050621The tweets are a response to Tao's post on the work of Alpöge and Buckmaster in producing a blowup (finite time, smooth force) in related fluid equations. Tao claims that this can be generalized to Navier-Stokes, but the process is too laborious for him and suggests the use of AI. OpenAI later on the same day published their results demonstrating such a blowup for Navier-Stokes. For one there is an obviously apparent problem in authorship here if all the AI did was busywork in integrating a human's new approach to another set of equations. But instead the tweet in OP focuses on the energy of the system saying that in this approach the energy depletion of the system (~N_k^2) would eventually overtake the energy growth ([math]O(N_k^{3/2}[/math] with N_k being the frequency of the corrections).>>17050873Finite = force removed at some point
This is a complete hunch but it feels like this f function thingy just has some form of infinite energy hidden in it. An oscillatory force that suddenly blows up a fluid sounds too strange
>>17050925Well it only blows up mathematically. Physically fluids are not incompressible and also past certain points the continuum hypothesis doesnt apply
>>17050971That's a fair point, when the fluid would get stretched thinner and thinner and accelerated faster at some point it would change phases or reach beyond the critical point. I still don't quite get how an oscillatory force could lead to this mathematical behaviour
>>17050919Yes, you'll note that nothing in there implies that the Lean formalization of oAI's N-S solution contains an error.
>>17051245It implies the theoretical modeling on which OpenAI's proof rests might be flawed, since a behaviour that should've happened didn't.
>>17051463>In addition to the full Millennium Prize problems, we asked our multiagent system to try a set of “easier” problems. One of these problems was a similar blowup question for the limit of the Navier–Stokes problem with the viscosity term removed. This is known as the regularity problem for the Euler equations, and our agents surprised us by resolving this question. The specific variant of the question that they resolved was the unforced version, where no external force is applied to the fluid. Nearly 100 agents worked together for approximately 50 hours to produce our Euler regularity disproof.>Once we saw the Euler solution, we thought that Navier–Stokes was the most promising problem to work on. Thus, we decided to devote our resources to Navier–Stokes. To do so, we shifted agents away from the other Millennium Problems and prompted these agents with the Euler resolution. When a further trained version of our internal model became available over the course of the effort, we updated our agents to that model.
>>17051482>Nearly 100 agents worked together for approximately 50 hours to produce our Euler regularity disproof.They ran for 50 hours to find someone else's work? What an impressive waste of money. I wonder how much that cost. Also none of this quote addresses the original point.
Did they find any errors or no?
>>17051487Buckbrokenman made that up, their solutions are nothing alike and Buckbrokenman's approach was literally to take a simpler model developed by the Spaniards and generalize it in 3-D by doing vibemath with Claude. OpenAI did the same with more resources, that's the end of the story, in any case LLMs solved the problem
>>17052193>Buckbrokenman made that upTheir results were published before OpenAI made any public announcements.>by doing vibemath with ClaudePatently false.>in any case LLMs solved the problemAIbros are really desperate to get this before their IPOs. Journalists are too dumb to understand the nuances, so they will fall for the hype.Do you have/working on a university degree? I will ask again in the next post if you don't reply. I'm asking, because the mere use of the term "vibemath" implies a great level of unfamiliarity with the academic field as a whole. It's a borrowing from "vibecoding", which nobody outside of the CS industry uses and very few know of.
>>17052193/thread
>>17052256>Do you have/working on a university degree?A master's degree in shoving little dorks like you into their lockers
>>17052394Simmer down you little harlot, no need for all that tantrum.>>17052394
>>17050581damn nigga they scientist sippin lean?
>>17052256>unfamiliarity with the academic field as a whole.You dumb fuck 70% of papers nowadays are written by chatbots
I looked at the paper. Stopped reading it after seeing how poorly written it was. Any institution would be right to reject it on those grounds alone just like any mathematician would have their paper rejected for being poorly written or even full of grammatical errors. If they really have a result, they can do the work to fix what their model generated so that it can be read as a 40 page paper instead of a 166 page paper with excessive bloat. One of the first things they do is just take a derivative and call it a Lemma. Something no one needs to see.>>17052651Journals need to start rejecting those papers. If they're not going to give their papers the attention needed to make readable, they shouldn't be published.
>>17052651>You dumb fuck 70% of papers nowadays are written by chatbotsThis goes to show how egregiously unfamiliar people are with the academic field. In my university the undisclosed use of AI automatically triggers the plagiarism policy. The reason that number is above 0% is twofold. Indians and sloppy researchers that don't care. The first one far outweighing the second one. It does not show that academics are accustomed to the use of AI. Nor does it show that it's a homogeneous practice across fields.
>>17052665>I looked at the SOLUTION TO ONE OF THE TOP 10 UNSOLVED MATH PROBLEMS. But I stopped reading it after seeing how poorly written it was. (more institutional cope)just get replaced by robots already. the hubris, jesus christ
>>17050581be careful with this work that they arenttrying to build relays in the human body
>>17050581>brute-forced AI 'solution' might have errors
>>17052187No, there's no error. The tweet chain is about terry wondering if the finite force can be removed from the NS blowup and someone else shows it can't.I tried to warn you stupid niggers about this. You are desperately clinging onto a hope that becomes more and more intenable
>>17052725according to tw*tter as my mathlet mind comprehends it: he meant he was talking about the paper arguing that forced blow-up could never be applied to non-forced (specifically in the 3 dimensional case) due to issues mentioned in the screenshot. A big caveat is that they assume the counterexample stays modelled in a certain way; OpenAI either re-modelled the counterexample in a way blow-up can be applied without the forced component (unlikely) or used a very different model from the beginning- which is even WORSE for anti-clankers as it pretty much proves Buckmaster and Alpoge's work wasn't stolen.
>>17052665
>solution discovered by AI might contain errorsim shocked
>>17052906isnt this how science should work? They propose others try to disprove and find issues until real truth is revealed? All you do is whine and cry about process you should have been supporting.
>>17050592I'm a mechE so I can keep up with the argument but I cant formalize my own arguments.
