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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#811

Buried 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.

And... they found this "solution" in 88 hours or so.

It's all gas no brakes now boys and girls. Hold on to your hats!

Re: On the Navier–Stokes Millennium Prize Problem

#812

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.

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

#813
post #253

Earlier quoted context omitted.

>we did not read any private chats The question I am interested in is not "did we read private chats", but "was this new model trained using any of Tristan and Levent's chats, regardless of whether they were marked private". Can you comment on that?

>Can you comment on that? No answer is also an answer. He's a human, like everybody else. Mostly a bunch of hungry animals looking to put bread in our mouths. It's rarely ever something a bit more sophisticated than that.

his choice to defend the indefensible.

Re: On the Navier–Stokes Millennium Prize Problem

#814

Earlier quoted context omitted.

I had a lot of fun during Covid. I loved the working from home. The fact that most outdoor places were sparsely populated, jobs were plentiful and prices were low. Covid was awesome.

Yeah Covid was awesome, say that to the people who died from it, or who committed suicide because of the lockdown depression

Oh, pipe down, I’m talking about that 3 year period, not the disease. You can talk about things that happened during Covid without giving lip service to the people that died during it. If I mention SpaceX‘s first astronaut launch that happened during Covid, am I supposed to talk about the people that died during that period too?

Re: On the Navier–Stokes Millennium Prize Problem

#815
post #761

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

#816

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

#817

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

#818

> 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

#819
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

#820

> 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.

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