It's probably important that some humans verify these proofs "by hand".
On the Navier–Stokes Millennium Prize Problem
791–800 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#792Earlier 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
#793Earlier 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
#794Earlier 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.
Re: On the Navier–Stokes Millennium Prize Problem
#795Earlier 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.
Yeah Covid was awesome, say that to the people who died from it, or who committed suicide because of the lockdown depression
Re: On the Navier–Stokes Millennium Prize Problem
#796Earlier 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.
Building on them without fundamentally understanding is akin to putting on robes, calling yourself a Tech-Priest, worshipping a machine god and doing your best Warhammer 40k impression.
Re: On the Navier–Stokes Millennium Prize Problem
#797Earlier 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.
Here's the paper about the blowup for the gravitating bodies: https://www.jstor.org/stable/2946572?origin=crossref
There's a Wiki article about it: https://en.wikipedia.org/wiki/Painlev%C3%A9_conjecture
Re: On the Navier–Stokes Millennium Prize Problem
#7985 million messages, 300b output tokens, done in 5 days, and achieving something humans couldn't. the first "Country of geniuses in a datacenter" moment.
That is how the PR reads, but is not at all what happened.
A team of highly trained and skilled people used an AI tool, through many many instructions (prompts), to produce a specific mathematical theorem. The tool is impressive, the result (possibly/probably) interesting, but the PR skips the vital role of the humans (for the usual PR reasons).
Re: On the Navier–Stokes Millennium Prize Problem
#799Earlier 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
[dead]
Re: On the Navier–Stokes Millennium Prize Problem
#800Earlier quoted context omitted.
Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…
To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…
[deleted]