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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#481

Post by empath75 »

Eridrus wrote: post #463
jampekka wrote: post #444

Earlier 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?

He's not unhappy with it being solved, but the solution is less important than the learning you have to do to arrive at the solution. If they're just chucking compute at it and publishing the answer and hiding the path to get there, it sort of negates the whole point of posing such problems to begin with.

Re: On the Navier–Stokes Millennium Prize Problem

#482

Post by nolta »

hkmaxpro wrote: post #301
colinhb wrote: post #122

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof. https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.

> We did not rush to publish even though the other team wasn't communicating with us.

Pretty clear this was rushed: there are no comments from external mathematicians, unlike the Erdős announcement:

https://openai.com/index/model-disproves-discrete-geometry-c...

Re: On the Navier–Stokes Millennium Prize Problem

#483

Post by jijijijij »

DudleyBluffles wrote: post #434

Not a great time to be starting sophmore year in cs & math. Should I just say fuck it, and go hitchhiking across Europe with some friends?

> Should I just say fuck it, and go hitchhiking across Europe with some friends?

Yes. Assuming you are young and haven't had such experience.

The world is changing not just because of AI. Everything is unstable right now. You may regret not enjoying the remainder of stability and economic viability prior generations had. It's not like you can expect to get ahead by powering through education. Either your career perspective will soon change for the better, or worse. In any case, you gain little by sticking with career building at this moment in life. You are however, at risk of losing the chance to experience the still mostly pleasant world as is.

Re: On the Navier–Stokes Millennium Prize Problem

#484

Post by HenrikPontoppid »

Fordec wrote: post #375
10xDev wrote: post #190

Earlier quoted context omitted.

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.

Yes. In other words: the singularity. I'll only believe it when I see it though.

Re: On the Navier–Stokes Millennium Prize Problem

#485

Post by gpm »

intenex wrote: post #437

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Eh... OpenAI spent significantly more than $1 million solving this...

Re: On the Navier–Stokes Millennium Prize Problem

#486

Post by Fordec »

dakolli wrote: post #426
Fordec wrote: post #375

Earlier quoted context omitted.

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.

How do you automate the mines to get the raw materials to make the compute from, and build additional fabs that take a almost a decade to stand up. You're actually delusional.

Hello good sir from the 1700s pre-industrial revolution who doesn't think that mines and factories can be automated.

Re: On the Navier–Stokes Millennium Prize Problem

#487

Post by superxpro12 »

piker wrote: post #443
intenex wrote: post #437

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Sure, even a 20% chance at 1 million payday after 5-6 years of fulltime work on a project with zero practical application doesn't touch the, say, 200k/year guaranteed our best mathematicians would have to forgo to devote their intellect to the problem.

i wonder how many tokens it takes to run 10,000 agents? One could argue this is simply a problem of appropriations. I find myself wondering if a corporation could spend $5M on mathmeticians and arrive at the same end result.

Re: On the Navier–Stokes Millennium Prize Problem

#488

Post by fooker »

munificent wrote: post #217
stefap2 wrote: post #180

Earlier quoted context omitted.

This just pushes knowledge work further up the ladder, toward larger and more complex problems. If there are no knowledge workers, who is going to interpret these results, validate them, decide what matters, and put them into practical use? Rather than eliminating knowledge work, advances like this could create entirely new layers of problems to solve and opportunities to pursue, which will create even more jobs and…

> 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.

Yes, this is how science and engineering has worked for millennia.

For example there are no engineering implications of this solution yet.

For the next several decades, we'll have engineers (presumably with AI) optimize things like rocket engines and turbines and AC compressors to work a few percent better because the numerical approximations might have caused us to be overly conservative.

AI is not going to magically solve all random problems. Pick a career where you are in the driver seat.

Re: On the Navier–Stokes Millennium Prize Problem

#489

Post by jampekka »

piker wrote: post #443
intenex wrote: post #437

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Sure, even a 20% chance at 1 million payday after 5-6 years of fulltime work on a project with zero practical application doesn't touch the, say, 200k/year guaranteed our best mathematicians would have to forgo to devote their intellect to the problem.

Thousands of some of the brightest minds have worked on this problem for over a century. The million bucks is not the big deal here.

Re: On the Navier–Stokes Millennium Prize Problem

#490

Post by xhevahir »

karmakurtisaani wrote: post #480
Eridrus wrote: post #463

Earlier quoted context omitted.

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?

Where was Tao unhappy? I thought he was sort of anticipating this.

Maybe he was dreading it.
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