131–140 of 243 posts
Earlier quoted context omitted.
For any practical application, numerical solvers for Navier-Stokes already exist and do a good job. This proof is just checking the boxes for mathematicians.
you're as sure of what you say as wrong about it.
> For any practical application, numerical solvers for Navier-Stokes already exist and do a good job.
or
> This proof is just checking the boxes for mathematicians.
Earlier quoted context omitted.
> but only if Alpöge’s name was removed This is blatant scientific misconduct.
Any idea why OpenAI cared about this name removed from the paper?
In short: The problem is about whether a solution (of the NS Equations with external driving force) can be found that blows up in finite time. i.e. exhibits infinite velocity at a point even for a viscous flow.
The solution: Take a circular curl ansatz which shrinks in xy-direction and elongates in z-direction and see whether you can find linearized waves so that these waves show a blow up when propagated on the curl. Then prove that the higher orders of the perturbation are regular before the T0 singularity time and you have solved the problem. The external force is just the remainder of the NS-Equation right hand side.
It is a lot of tedious formula juggling of all the higher orders and some singular perturbation expansions. Perfectly suited for algebra systems. OpenAI was using probably python sympy for the formula work and the researchers had to guide the LLM what to do in higher mathematical language.
Here is the paper:
https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...
when you upload it to chatgpt astra can explain what they do and why it works, have fun.
Earlier quoted context omitted.
Yes, that's a strange mistake to make.
Not really. There's a non-pedantic, charitable interpretation widely available. It's below for reference. > Navier-Stokes is one of six [open] “Millennium Problems” on a list compiled by the Clay Mathematics Institute in 2000.
I think it was a pretty questionable thing to do by trying to front-run these researchers even if they didn’t make use of their techniques. The fact that they may have inadvertently “borrowed” their work via training data makes it much worse. OpenAI’s behavior here — even if you only consider [their] side of the story — was (at best) in bad taste.
Earlier quoted context omitted.
For any practical application, numerical solvers for Navier-Stokes already exist and do a good job. This proof is just checking the boxes for mathematicians.
you're as sure of what you say as wrong about it.
Earlier quoted context omitted.
For any practical application, numerical solvers for Navier-Stokes already exist and do a good job. This proof is just checking the boxes for mathematicians.
you're as sure of what you say as wrong about it.
OpenAI (claim to) show the existence of *a* finite time singularity. It could stimulate more research in PDE solving, and maybe physics, but it has zero impact on practical applications, that I can see. The Millenium problems were chosen based on hardness not practical relevance.
Earlier quoted context omitted.
For any practical application, numerical solvers for Navier-Stokes already exist and do a good job. This proof is just checking the boxes for mathematicians.
you're as sure of what you say as wrong about it.
Earlier quoted context omitted.
If you read Buckmasters statement, he specifically notes that they used the paid subscriptions, iirc.
Paying for an account doesn't opt you out by itself, right? Has he stated anywhere that he actually opted out? But if not, then I also don't understand why OpenAI's communications about this have been so vague, they could've just said that he didn't opt out, using those chats in training data follows their ToS and that's it (whether that's "fair" is a separate discussion).
Regardless of what you think of the priority dispute issue discussed on sibling threads, I’m highly skeptical of the closing quote that this Navier Stokes result means that the same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development. Those problems can’t be formally verified with an automated theorem prover. We have a lot of physics bas…