Earlier 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?
On the Navier–Stokes Millennium Prize Problem
791–800 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#792Earlier 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?
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
#793Earlier 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.
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
#794Re: On the Navier–Stokes Millennium Prize Problem
#795Earlier 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…
Re: On the Navier–Stokes Millennium Prize Problem
#796Earlier 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.
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
#797Earlier 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.
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.
Re: On the Navier–Stokes Millennium Prize Problem
#798Earlier quoted context omitted.
Not sure about the dystopia... Had a similar thought when covid was beginning 'wow pretty exciting, just like in the movies'. Turns out actually living some terrible catastrophe is only fun in the movies.
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.
Re: On the Navier–Stokes Millennium Prize Problem
#799Earlier quoted context omitted.
> This just pushes knowledge work further up the ladder, toward larger and more complex problems. You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes? I envy your self-confidence.
Maybe I should have been clearer. My point is that solving something like Navier–Stokes just pushes knowledge work further ahead, onto a new set of bigger and more complex problems. Navier–Stokes is a Millennium problem today, but once problems like that become solvable, they can open the door to entirely new classes of problems we haven’t even thought of yet.
Re: On the Navier–Stokes Millennium Prize Problem
#800Earlier quoted context omitted.
> 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.
There's a Wiki article about it: https://en.wikipedia.org/wiki/Painlev%C3%A9_conjecture