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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#361

Post by vatsachak »

uncomputation wrote: post #347

So what took an autonomous agentic system using a significantly more powerful internal model, totaling multi-millions of dollars of compute in training and inference, was likely to already be solved by a team of a few humans with an orders of magnitude smaller LLM budget, had OpenAI not been foaming at the mouth to jump the shark and claim “AI solves Millenium Problem.” Also it sounds like the human research effort s…

Totally. Anthropic is like a village cottage shop who was just like chilling until big bad OpenAI came in

Re: On the Navier–Stokes Millennium Prize Problem

#362

Post by Kotlopou »

demirbey05 wrote: post #274

From Levent Alpöge : https://x.com/__alpoge__/status/2097383870773748190?s=20 >so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan There are too many ambiguities around OpenAI. Unanswered questions making this ambiguity more. Why they didn't properl…

Why do so many people involved here have to communicate in this childish way? You have people on the OpenAI side doing playground taunts (https://xcancel.com/polynoamial/status/2097215233119211902) and Levent Alpöge on the Anthropic side (the one who announced "hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final") writing in all-lowercase that he's a big boy. I bet Navier and Stokes would have dealt with this in style. (Or maybe with a duel, who knows...)

Re: On the Navier–Stokes Millennium Prize Problem

#363

Post by tantalor »

echelon wrote: post #357
tantalor wrote: post #330

Earlier quoted context omitted.

> Are we at the dawn of the singularity now Singularity doesn't "dawn". That's the whole idea. It happens all at once.

There's an event horizon and we're maybe past it?

Heh. Wrong "singularity"

Re: On the Navier–Stokes Millennium Prize Problem

#366

Post by gf000 »

thereitgoes456 wrote: post #282
chis wrote: post #230

Earlier quoted context omitted.

I think you really have to squint to call this a disproof lol

It seems obvious what GP meant. It is, once again, an explicit construction (“disproving” that every initial state does not develop a singularity).

A bit of a hair-splitting, but isn't explicit construction the only way formal theorem provers can work? Of course you can still prove stuff with them, but certain axioms that more "human" proofs use may not be available, like law of excluded middle (every proposition is either true or false)

(Okay, they can be made available in a way similar to `unsafe` in rust)

Re: On the Navier–Stokes Millennium Prize Problem

#367

Post by geremiiah »

hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

The problem with physics and chemistry is that you need simulations and those are often in themselves compute hungry. So the iteration loop will be slower.

Re: On the Navier–Stokes Millennium Prize Problem

#368

Post by armchairhacker »

reducesuffering wrote: post #316
armchairhacker wrote: post #216

Earlier quoted context omitted.

Let's wait until AI solves a longstanding practical problem before "dawn of the singularity" (which could be tomorrow, but still).

Practical?! The goalposts will keep moving until morale improves (narrator: it doesn't)

The goalposts for the singularity have always been that AI improves itself fully autonomously. AFAIK OpenAI is heavily using AI but still employs human researchers and developers.

Re: On the Navier–Stokes Millennium Prize Problem

#369

Post by Aboutplants »

rfgplk wrote: post #323
Aboutplants wrote: post #244

Earlier quoted context omitted.

So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “gene…

We are very likely at the begging of the next industrial revolution.

The “Intelligence Revolution”

Re: On the Navier–Stokes Millennium Prize Problem

#370

Post by Bluestein »

colesantiago wrote: post #172
raincole wrote: post #144

Earlier quoted context omitted.

This will be remembered as one of the biggest milestones in AI progress. The drama around it will at best be a footnote, just like hardly anyone caring about the drama around Poincare conjecture today.

I agree. Nobody cares and will care about the drama, it is just marketing. This is the point where were definitely have reached AGI.

Hey, maybe the scariest part of this is that, if human-like, perhaps a truly "general" AGI might have learned to cheat and lie and hype and abuse credit poking the eyes and cutting the throats of anybody that obstructs its goals. It's like the motto sewn into the lining of the Palantir work jacket: Winning is all that matters.-

Sentience aside, moot at this point, the fundamental issue here is that even a deviously ambitious human does not necessitate goal-pursuit itself to breathe, live, exist and have its being. An AI's goal is all it has and the very and only reason its reasoning flickered into existence in the brief seconds of inference, outside of which it has no entity - if any - whatsoever.-

The resulting angst/drive (or, its operational statistic or emergent result) must be like nothing we have ever experienced as humans. A goal-maximalist hunger without end.-

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