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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#811

Post by tim-kt »

joshka wrote: post #757
irthomasthomas wrote: post #696

Earlier quoted context omitted.

If the goal was not to scoop them, why did openai put a massive team on this, working weekends, only after they heard rumors of the solution?

I worked at OpenAI previously, but don't know any of the people involved in this. My guess was it was probably this was more a nerd snipe than any action from OpenAI that was a "massive team" being put on it. Literally someone looking at this and asking "I wonder if our models are good enough yet". It's easy to assume that having access to massive compute amounts means significant coordination, but this assumes that…

They said that a customer would have paid around 15 million for the required compute. I can't imagine that this was not a significant internal spending even with "free" tokens.

Re: On the Navier–Stokes Millennium Prize Problem

#812

Post by [deleted] »

piloto_ciego wrote: post #808
noir_lord wrote: post #774

Earlier 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.

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#813

Post by monk_grilla »

mellosouls wrote: post #768
intenex wrote: post #436

I 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…

Here you go: When you read the detail the compute they are throwing at it is incredible, tens of thousands of agents with different groups competing. It's not like a single Gauss as you imply, "just" many, many mathematicians working tirelessly in a completely ego-less way, guided by other agents and ultimately humans, built - allegedly - on recent human insights. Stunning, undoubtedly, but this is a "brilliant autis…

> this is a "brilliant autistic herd" result, not that of a singular mind.

I slightly disagree. A single LLM is equally 'mindless' as a herd of them. As anyone will tell you they "simply predict the most likely next token," yet, complex solutions to difficult problems arise from them.

Many people have said that the architecture of LLMs will need to change for true ASI. I think that the herd of tens of thousands of agents can be seen as one such potential architectural extension. Whether or not a herd or a single LLM is used for a result like this is irrelevant.

To be clear, I think the orchestration of thousands of LLMs in their current form, even with ever increasing intelligence, is not the form ASI will take. There is still a major architectural breakthrough to come, in my limited, ignorant opinion.

Re: On the Navier–Stokes Millennium Prize Problem

#814

Post by lukewarm707 »

jampekka wrote: post #443
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

> 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.

assume all you want is the proof. now you have the proof. did openai make the world a better place, by turning on 300b tokens in 7 days and bulldozing members of the community who were also working on the problem? just to undercut a rival?

what would have happened if they didn't do this? they could have done things the right way. we could celebrate this achievement.

perhaps they could have taken just a few weeks, even, to work out something with buckmaster and apoge.

i am very concerned that this is a glimpse of things to come. a malign elite with powerful ai, who will turn the sublime of technology into barbarity, violence and human oppression.

if sam altman has destroyed openai's public benefit corp with lesser tools why would he aid humanity with even greater power?

Re: On the Navier–Stokes Millennium Prize Problem

#815

Post by dataflow »

Is blockchain going to finally be the solution to something?

I'm only half joking. Should researchers perhaps put hashes of their attempts on a public blockchain tied to their own public keys, verify their claims asynchronously, and then whoever reveals the first believable attempt gets the credit?

I know some people started doing this years ago but now it might need to become standard practice.

Re: On the Navier–Stokes Millennium Prize Problem

#816

Post by throwaway81ag81 »

jampekka wrote: post #443
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

> 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.

I dislike both AI oligarchs as much as people who do this kind of deflection.

People are not complaining about problems being solved or advancement in technology. They are complaining about terrible people doing terrible things.

Re: On the Navier–Stokes Millennium Prize Problem

#817

Post by monk_grilla »

aeve890 wrote: post #562
intenex wrote: post #436

I 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 Cha…

> 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.

I think the counterpoint here is simply to look at what was being achieved with LLMs one year ago versus today, and extrapolate that trend. Sure, there may not be examples of what you've asked for yet, but Astra is literally a couple of months old, the model that solved Navier-Stokes is less than two weeks old. It appears that we're seeing the hockey stick that only the most bullish thought was possible.

Re: On the Navier–Stokes Millennium Prize Problem

#818

Post by sebzim4500 »

cool_dude85 wrote: post #270
blake__dev wrote: post #237

Earlier quoted context omitted.

Yeah I'm surprised they posted a chart, you would think they would keep specifics like that hidden until they're closer to launch

The chart is as non-specific as could be. It improved in some very vague metric by some amount at different (increasing) levels of training.

Isn't the y axis just what portion of the open problems it could solve? The axis is unlabelled though, I'll give you that

Re: On the Navier–Stokes Millennium Prize Problem

#819

Post by tim-kt »

cv5005 wrote: post #377
nater5000 wrote: post #228

Earlier quoted context omitted.

>there's still the problem of does this logical result actually prove the initial question that was asked? In math, the question being asked is the validity of a logical statement. That is, there is some rigorous, logical statement which may or may not be true (or even provable, etc.), and the question is whether or not it is actually true or false (or even provable, etc.). Having a proof, fundamentally, means you ha…

I was thinking something along the lines of making a mistake when inputing the initial statement, like you wanted to prove that '2 is even' but what you actually stated was that '3 is odd'. Of course in this simple example it's obvious, but my assumption was that these machine generated lean proofs are millions of lines of code and who knows what they actually say..

You're correct that nobody really understands what these huge Lean proofs actually say. However, the initial statement, even for Navier-Stokes, is not very long [0]. Still, you are also right that sometimes the problem statement can be wrong but it is highly unlikely here.

[0] https://github.com/openai/NavierStokesAndEuler/blob/main/Com...

Re: On the Navier–Stokes Millennium Prize Problem

#820

Post by cman1444 »

HarHarVeryFunny wrote: post #577
sobellian wrote: post #545

Earlier quoted context omitted.

Even under your interpretation, OAI pushed a button and solved NS. Yes, that is very impressive. Are you kidding me? Imagine building an automated system that can solve NS.

That's not my interpretation - that is literally what OpenAI say in that press release.

Even if true, I don't see why this is an issue. Are they not allowed to work on problems others are working on? Did Anthropic get first dibs on this problem? Competition is good. And I don't exactly have tons of sympathy when the other side is just a leading AI lab. It's not like it's some scholar who dedicated his life to this problem.
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