Can't wait for the BobbyBroccoli series on this in a couple years.
On the Navier–Stokes Millennium Prize Problem
781–790 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#782Earlier quoted context omitted.
...obviously it is evidence of the singularity. You're far more likely to see models solving Millenium Prize problems if a singularity is coming than if it's not. One'd have to be doing quite a lot of mental gymnastics to pretend otherwise.
Poor reasoning. You could apply the same logic to any improvement in any field of machine learning.
Not every improvement, no - if progress was steady or slowing down over time, that'd be evidence against. Instead we see what looks a lot like an accelerating growth in capability.
I think you are implying that it's invalid to consider every advance to be evidence "for", and I agree - that'd violate conservation of expected evidence. But not considering any advance to be evidence "for" is also invalid, for exactly the same reason. There has to be some news you may hear that'd make you think a singularity is more likely, and "millenium prize problem solved by an LLM" sure seems like one of those.
Re: On the Navier–Stokes Millennium Prize Problem
#783Earlier quoted context omitted.
2) We are witnessing the intelligence explosion from the first row, wherever this takes us 3) I'm still processing the drama, just found out about it after reading the blog post. If that happened based on private data, that's horrible. If that happened based on public tweets, then it's still abuse of power as OA employees access to compute (launching 10k agents) is quite heavy weight in boxing terms. But apart from A…
> But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering? Nothing, really. This mirrors other examples of blowups from the classical physics. It's possible to create a system with just gravitating bodies that exhibits a blowup to infinite speeds in a finite time. The root cause is that, in classical physics, the speed of gravity is instant. In th…
Great comment! I've been trying to understand it more and was hoping to find more people discussing the result, or the implications of the result, and this was the missing piece for me after watching a few videos.
Re: On the Navier–Stokes Millennium Prize Problem
#784Earlier quoted context omitted.
You think a model with an effective memory of 200-500k words, that can be unplugged, is going to "run the world" You people gotta put down the sci-fi
Many present day politicians appear to have effective memories much smaller than that coupled with equally questionable world models so ... what is your point, exactly?
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Re: On the Navier–Stokes Millennium Prize Problem
#785Earlier 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?
Here's the point: when people solve problems, they come together and create a community to eventually use the new knowledge in positive ways, including inspiring younger mathematicians by sharing insights. The human element is key and it's not just about solving problems. People only think that because we've been conditioned by computers to value answers more than how we got to them.
But if AI can solve any problem and existing mathematicians just use AI to solve problems for the sake of solving them, the community itself with wither and so will the interest in mathematics and over a longer period of time, it will just become soul-less and uninteresting and the entire community powered by the fire of fascination will simply die.
Re: On the Navier–Stokes Millennium Prize Problem
#786Earlier quoted context omitted.
The entire drama is that OpenAI sniped a Millennium Prize Problem from an Anthropic-affiliated research team who had been working on the problem for nearly a year. In just 5 days. I don't think that can be understated.
I'm not here to judge since I don't have all the facts, but from what they announced: they tried all 6, found a probable lead to Navier-Stokes, concentrated efforts in that direction, and found a solution. I hope the next solved Millennium Prize Problem will have less drama.
But that lead happened to be the same approach Levent and Tristan had found...
Meaning they would have found it first if OpenAI hadn't spent millions in compute on following their lead to its conclusion faster than them.
Re: On the Navier–Stokes Millennium Prize Problem
#787It's probably important that some humans verify these proofs "by hand".
Re: On the Navier–Stokes Millennium Prize Problem
#788Earlier quoted context omitted.
With Lean, math has become a really well suited problem for LLMs. We will likely see large gains for many years from here, just doing more and more rlvr, like continuously, non stop. No need to train from scratch. It really doesn't speak to the general intelligence of models though. It does speak to how good these things can become when a problem space has verifiable rewards, especially when you can verify one step a…
It's crazy how deep Microsoft's bench is (Lean was started there, vscode is another), for everything not directly related to the the ai models (hell, even github for data). So interesting how everything played out, I remember in the early days when MS came out with the partnership with OpenAI it seemed like they were playing 5d chess and were poised to win big. And it all just fizzled out. Second biggest fumble after…
Well, amazon and apple haven't done great either. One might reasonably claim they weren't as well placed as goog or msft, but it might just be "big company can't do genuinely new thing".
Re: On the Navier–Stokes Millennium Prize Problem
#789Earlier quoted context omitted.
> Do "normies" even know what's happening? No, there are even many non-normies talking about how it's all marketing or try to give balanced take about AI being sometimes a little useful for certain things (but they can do without it anyway).
I am absolutely struggling to sell my workplace (which is entirely knowledge work) on the usefulness of LLMs for proofreading let alone on automation of hairy parts of our workflows. So yeah, even people who should be able to see what is coming are not looking.
Our accountant told me 'he's not letting go of his claude subscription' followed by a long list of things it does for him. And my friend 'nah haven't really used AI' before his description of it clarified he still thinks they are GPT 3.5 chat bots.
The world has changed in 12 months and many people didn't notice, and those that did are eating their peers' lunch.
Re: On the Navier–Stokes Millennium Prize Problem
#790Earlier quoted context omitted.
His issue is more nuanced than that. Most of the value was in humans reaching new insights or new math during failed attempts to solve these problems, whereas AI is basically "too efficient" in beelining to the goal and discards potential new insights reached along the way. I assume this is solvable.
Well, if in future we do end up with a magical tool that can solve any formal mathematical problem on a whim, we really won’t need field of mathematics anymore as it is today. There would be no need to deliver new mathematical insights by solving problems. You would just have a magical math problem solving machine and that’s it.
What do you mean “we won’t need mathematics as it is today”?
To further human understanding is itself a goal that single-handedly justifies our efforts.
Jumping straight to the “answer” and therefore missing both the understanding of the actual problem, and any useful discoveries along the way is a waste at best, and actively harmful at worst.