[flagged]
"Argh, they have rushed in too quickly to solve a Millennium Problem!"
How far we have come :.)
On the Navier–Stokes Millennium Prize Problem
561–570 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#562Buried 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.
Can someone explain if i understand this correctly: Are they saying that they started training this new model on August 28th and then started using it on September 1st? Does training a new model only take 3 days?
it's possible to do a RLHF or RLVR pass pretty quickly. I'm almost certain a full pretraining run isn't possible within that time frame.
Re: On the Navier–Stokes Millennium Prize Problem
#563the context here is super important, for those who haven't seen it yet. OAI maybe just trained on a real researchers solution and then celebrated having scored the goal unassisted save for the brief commentary at the bottom of this blog post. Here's the other side. https://x.com/rynorhn/status/2097223532438487463
That other researcher was working on a smaller related problem. He was also using LLMs to do it, so either way most of the credit goes to the LLM here.
Using a shovel means you give it credit for the hole?
Re: On the Navier–Stokes Millennium Prize Problem
#564Re: On the Navier–Stokes Millennium Prize Problem
#565Earlier quoted context omitted.
> WOW This. I do dislike the AI oligarchs as much as the next person, but I do find the thread full of complaining a bit depressing still. If the result holds (and it looks it does), this may be one of the, if not the, biggest things to happen in computing to date. A lot bigger than e.g. Deep Blue beating Kasparov in chess or AlphaGo beating Sedol in Go.
Seeing mathematicians such as Terry Tao being unhappy with open problems being solved makes me sort of question the usefulness of any of this pure mathematics. If we're not happy that the problems are being solved, why care about this field at all?
I suppose this is how Lee Sedol felt when AlphaGo beat him. But in the same vein, didn't it ultimately advance human understanding of the game?
Re: On the Navier–Stokes Millennium Prize Problem
#566I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…
>If anyone has counterpoints to this I'd love to hear them!
Sure. A proof without an unknown amount of human steering (and/or stolen research) would be an unquestionable achievement.
To this day there's zero (0) evidence of any result by an LLM alone (maybe I'm wrong). If I just prompt ChatGPT right now with "give me a proof of the Riemann Hypothesis" and this thing delivers, I'm sold. But anything close to "yeah ChatGPT proved X with 5 years of 24/7 work with 10x Terrence Tao level geniuses" it really doesn't cut it.
Or why's there's no new branch of mathematics invented by AI? That'd be indubitably _novel_ and _creative_. But to my knowledge (and I'm eager to be educated) there's nothing like that. What are the HARD examples of novelty, creativity and genius you claim? For how people like you talk about AI I'd expect idk, a unified theory on fundamental physics, or a novel engineering solution for material science and nuclear fusion, or at least improve itself to not need a bazillion GPUs to emulate a 20 watts wetware. Sure it would infinitely easier to make OpenAI literally print money with any of the thousand problems easier to solve with such amazing intelligence than the NSE problem right? Honest question
Re: On the Navier–Stokes Millennium Prize Problem
#567Earlier quoted context omitted.
> WOW This. I do dislike the AI oligarchs as much as the next person, but I do find the thread full of complaining a bit depressing still. If the result holds (and it looks it does), this may be one of the, if not the, biggest things to happen in computing to date. A lot bigger than e.g. Deep Blue beating Kasparov in chess or AlphaGo beating Sedol in Go.
Seeing mathematicians such as Terry Tao being unhappy with open problems being solved makes me sort of question the usefulness of any of this pure mathematics. If we're not happy that the problems are being solved, why care about this field at all?
Pure mathematics, almost by definition, doesn't typically argue the field is always or even often "useful" (for some other purpose or application).
But, as mathematicians learn and push forward, occasionally something like elliptic curves will emerge as having useful applications, making all that previously "pointless" specialized knowledge newly valuable.
Or advances in physics, that suddenly have a need for a specific mathematical underpinning to develop a theoretical framework. Like how Einstein benefited from Minkowski's work on hyperboloids to create a coherent mathematical description of spacetime.
It was the AI labs themselves not mathematicians who were happy to conflate proofs for open math problems with some kind of tangible technological advancement in the real world. They would surely prefer to be able to claim a cure for cancer vs. a math problem but that loop requires a lot more time/money/test tubes/etc and they need headlines now not in a decade.
And so, thanks to OpenAI/Anthropic, we're now in a world where thousands of crypto bots on X breathlessly hype up each new problem being solved that previously wouldn't have any got any attention beyond academia and passionate fans of math.
Hopefully this won't lead to a trough of disillusionment as more people start to feel like you, with mathematicians getting the blame for inflating the value of their work even though the hype was coming entirely from the labs not them.
Re: On the Navier–Stokes Millennium Prize Problem
#568Earlier quoted context omitted.
I don't know what anyone's been saying on Twitter and I don't care. If it's really true that there's a model out there that's that capable two weeks after the start of training, then that's objectively a much bigger deal than a priority dispute, even if the latter involves juicy allegations of espionage and skulduggery.
It isn't a priority dispute, the more concerning allegation is that OpenAI may be training their models on prompts that mathematicians were using to solve this problem, and then surprise surprise OpenAI were able to replicate that work in their latest model What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question If OpenAI is training mode…
All that I have seen OpenAI employees "admit" is that if you press the Thumbs up button on a response, this can be used as a signal for training.
That's it. The rest appears to be wild speculation.
Re: On the Navier–Stokes Millennium Prize Problem
#569Damn how long before the simulation stops if all the unanswered problems get solved .
Re: On the Navier–Stokes Millennium Prize Problem
#570Earlier quoted context omitted.
Based on the leaps in local inference speed in the past month, which have been absurd, I'm p confident we're going to whiplash from compute constrained to storage constrained. Bit apples to oranges, but it reminds me of all the fiber we installed in the late 90s, certain that per-strand capacity increases were years or decades out, only to get massively rugged
I expect the investments into AI driven mathematic discoveries that underpin compression efficiency will be a key investment area. Particularly at the data center scale rather than per device or per file level.
pi-fs will solve all our data compression problems.