Earlier quoted context omitted.
The implication from their last couple of published articles[1][2] is that they think they’ve achieved “recursive self improvement”. [1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/
Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.
On the Navier–Stokes Millennium Prize Problem
921–930 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#922Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.
Re: On the Navier–Stokes Millennium Prize Problem
#923Earlier quoted context omitted.
The point of lean proofs (as it stands) is simply one bit of information: that a given mathematical statement is indeed true. It's a way to be absolutely certain (modulo bugs in the lean kernel) that a proof you came up for a statement is indeed correct. It is really not meant to be analyzed, much less now that they are fully llm written.
Well, how do we know there aren't errors in their construction within the lean code? Does it just "not compile" or something, or is it deeper / more fundemental than that.
Re: On the Navier–Stokes Millennium Prize Problem
#924Earlier quoted context omitted.
Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.
How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.
Re: On the Navier–Stokes Millennium Prize Problem
#925At a conservative estimate of GPT 6 Astra pricing, this would have cost upwards of 15 Million dollars for anyone using the OpenAI API!
To me this is the one silver lining. Yes, they can solve millennium prize problems, but it still costs a fortune.
Re: On the Navier–Stokes Millennium Prize Problem
#926"we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?
Re: On the Navier–Stokes Millennium Prize Problem
#927This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow. Millennium Prize Problems were used as examples of something the current approach to AI just wasn't capable of, discussions that would result in "we'll need a totally new architecture".
> This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow. Wrong.
Re: On the Navier–Stokes Millennium Prize Problem
#928Earlier quoted context omitted.
Most experimental physics and other natural sciences are strongly driven by their theoretical siblings, i.e. in particle research nothing gets built without a solid theoretical foundation of what you expect to find (or where you expect existing theories to break down), the same is true in other areas, no one is doing an experiment in quantum physics before they have a solid theoretical understanding of the effects th…
Most of high energy theoretical physics is very non-rigorous or even hand-wavy. I think AI isn’t there yet for such problems.
Re: On the Navier–Stokes Millennium Prize Problem
#929Earlier quoted context omitted.
Why is it unlikely?
Because the models are trained on hundreds of billions of user conversations, across more than a billion different humans. The conversations are anonymized and not easily traceable back to a specific user. It's unknowable and not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes. We also don't know if the authors unintentionally provided data to OpenAI through alterna…
Further, given that this is all in the open now, they can search the training data. No way somebody is using some specific unique cutting edge mathematical approach to solve a fluid dynamic problem 99.9% of people have never heard of and it's not locatable. Considering they spent $15,000,000 already on this, they could afford to grep around to be able to state that their hands are clean.
Re: On the Navier–Stokes Millennium Prize Problem
#930"we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?
I've been saying it for a while now, but no one gives a fuck. Let me repeat it again. THE BIG LABS CLEAN ROOM YOUR DATA (CREATE SYNTHETIC DATASETS ON IT), EVEN IF YOU OPT OUT, SO THEY CAN BYPASS COPYRIGHT LAWS AND THEIR OWN LOOSELY WORDED TERMS OF SERVICE. "TOS: We don't train on your data" -> Correct. They train on the synthetic version of your data. I guess we're just going to ignore this forever though. Who cares…