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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#591

Post by machina_ex_deus »

sobellian wrote: post #548
HarHarVeryFunny wrote: post #533

[flagged]

Even under your interpretation, OAI pushed a button and solved NS. Yes, that is very impressive. Are you kidding me? Imagine building an automated system that can solve NS.

Possibly after being given the significant part of the solution from actual human researchers. Which they then bullied. And they beat them to the finish line only because they heard rumor and threw everything at the problem. It doesn't look good for openAI in any way. I see more reasons to avoid using them rather than use them from this story.

Re: On the Navier–Stokes Millennium Prize Problem

#592

Post by sobellian »

HarHarVeryFunny wrote: post #580
sobellian wrote: post #548

Earlier quoted context omitted.

Even under your interpretation, OAI pushed a button and solved NS. Yes, that is very impressive. Are you kidding me? Imagine building an automated system that can solve NS.

That's not my interpretation - that is literally what OpenAI say in that press release.

The "steal their thunder" is interpretation. What I'm saying is that you believe they solved NS on a lark to bully some other researchers, and that this is not impressive?

Re: On the Navier–Stokes Millennium Prize Problem

#593

Post by redox99 »

adverbly wrote: post #502
intenex wrote: post #439

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…

> will soon far surpass that of humans To be fair, I think it's still an open question about how far it might surpass human capabilities. I think it's clear that its speed of development will be significantly faster, but it's technically not proven that the frontier and problems don't themselves become increasingly difficult faster than any acceleration in intelligence past the point of human training, data and exist…

Fields that allow verification, like math, will far surpass human level because they don't need human data for training. It's exactly the same as with Chess

Re: On the Navier–Stokes Millennium Prize Problem

#594

Post by HarHarVeryFunny »

rybthrow2 wrote: post #560
HarHarVeryFunny wrote: post #533

[flagged]

"Argh, they have rushed in too quickly to solve a Millennium Problem!" How far we have come :.)

There are bound to be a bunch more results like this, in math, physics, chemistry, and now that we essentially have a DeepBlue for math, a DeepBlue for physics, etc, these results are going to come.

SOME of the problems that have eluded humans are going to turn out to be low hanging fruit that are susceptible to this type of brute force (10,000 agents on a supercomputer running for 7*24 hours straight) AI search.

I'd be more impressed if OpenAI found their own problems to solve, rather than rushing in to re-solve one once they heard it was already solved (and therefore not so hard).

Re: On the Navier–Stokes Millennium Prize Problem

#595

Post by siva7 »

WarmWash wrote: post #229
simianwords wrote: post #136

Earlier quoted context omitted.

> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon https://news.ycombinator.com/item?id=38433655 > Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief t…

Will history look back at comments like these as people being dumb, or people trying to cope?

It's denial and coping. Most people i see show this tendency around AI which is also why it 's easy to be far ahead of most population nowadays

Re: On the Navier–Stokes Millennium Prize Problem

#596

Post by JPC21 »

DudleyBluffles wrote: post #436

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?

Just don't. If you read the story here carefully, you see that AI was used to work from theory built by others which showed that the Euler equations possesed finite-time blow-ups. But to make that step, actual good understanding for mathematics was needed. My experience with software has been the exact same.

Re: On the Navier–Stokes Millennium Prize Problem

#597

Post by redox99 »

aeve890 wrote: post #565
intenex wrote: post #439

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…

>If anyone has counterpoints to this I'd love to hear them! Sure. A proof without an unknown amount of human steering (and/or stolen research) would be an unquestionable achievement. To this day there's zero (0) evidence of any result by an LLM alone (maybe I'm wrong). If I just prompt ChatGPT right now with "give me a proof of the Riemann Hypothesis" and this thing delivers, I'm sold. But anything close to "yeah Cha…

The amount of goalpost moving is insane. "Yeah it can solve Millenium problems, but can it do it with nothing more than a one sentence prompt?"

Also there are proofs where the only human steering was "keep going".

Re: On the Navier–Stokes Millennium Prize Problem

#598

Post by daveguy »

tedsanders wrote: post #181
lambda wrote: post #130

Earlier 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…

If the model has access to the "anonymized" data from chats, and the model is capable of building its own context from data that it can search through, including this data. Then it looks pretty damning. An independent review of the data traces from CoT and tool use involved in producing the result should make it clear one way or the other. Seems like discovery in a civil lawsuit could be very productive.

Re: On the Navier–Stokes Millennium Prize Problem

#599

Post by HarHarVeryFunny »

user19282 wrote: post #576
HarHarVeryFunny wrote: post #533

[flagged]

There's no evidence that Anthropic did it first.

Yes there is - that OpenAI PR says that it was Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU.

Re: On the Navier–Stokes Millennium Prize Problem

#600

Post by HDThoreaun »

20k wrote: post #310
aizk wrote: post #52

People had joked a couple years ago "Well if they solve a Millenium problem it's AGI"... Well here we are.

Yeah well, its easy to do if you steal someone elses work and then try to threaten them into staying quiet about it Edit: OpenAI have now admitted they were training on prompts at the time they made their breakthrough: https://mastodon.social/@tristanbuckmaster/11723647135247030...

All the ai labs are open about training on prompts. The question is if buckmaster had disabled that with the toggle openAI provides.
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