What is the other clay prize that's might be solved now/soon?
On the Navier–Stokes Millennium Prize Problem
371–380 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#372Earlier 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
#373My 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
#374Earlier 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
#375Earlier 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
#376Earlier 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.-
Re: On the Navier–Stokes Millennium Prize Problem
#377Earlier quoted context omitted.
Their own tweets are also pretty eyebrow-raising: > One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Why would you offer another researcher the lead authorship on your g…
And why cannot they have someone associated with Anthropic as co-author? That’s not obvious at all. For sure they would prefer to be the only ones, but it’s pretty standard to have co-authors from different companies, even if they are technically competitors. What is inappropriate about it?
It's inappropriate if you're a sociopath.
Re: On the Navier–Stokes Millennium Prize Problem
#378Earlier 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/
Compute will always be the bottleneck even if this were true.
If humans can figure out to optimize to circumvent bottlenecks, I have no doubt each new bottleneck will also get routed around, just now automated.
Re: On the Navier–Stokes Millennium Prize Problem
#379> How we found the proof Easy, we stole it from Levent and Tristan https://x.com/kyanyang_/status/2097211154669998337
Or everyone is stealing from everyone, including users... maybe why all the ethics people are leaving or getting fired. What a fiasco
Re: On the Navier–Stokes Millennium Prize Problem
#380Why is no one skeptical that the solution is correct? There's not a _single_ comment asking whether this proof is legit or not.
there is a proof in lean4 it's correct by construction