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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#551

Post by _alternator_ »

dorjoycb wrote: post #13

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

> The significance of this with respect to the way we train students, assign credit, referee, and decide what is worth one human life’s attention cannot be understated.

This. What is worth a human life's attention? As little as a month ago, mathematics was valuable in part because only a small number of people could possibly make progress on the frontier. We are confronting an existential moment for a 4000+ year-old human cultural endeavor. The assumption that "mathematical thinking is hard" has been built-in at a number of important points in how we support mathematics and mathematicians.

We need a different model, and fast. Already, the research community is feeling unable to digest proofs fast enough to keep up with the output of AI models. The paper is 165 pages, and the discovery was finalized two days ago. What this means is that nobody really understands it. Nobody would accept OpenAI's proof in this amount of time, except that they formalized it in lean. The formalization alone would normally be another years-long (or career-long!) effort if the world was the way it was one year ago.

So, again, what efforts are worth a life's attention today? It's a harrowing change.

Re: On the Navier–Stokes Millennium Prize Problem

#552

Post by spruce_tips »

WarmWash wrote: post #209
mewse-hn wrote: post #78

"we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?

Everyone knows that they train on the discounted rate plans data. All the labs are upfront about this too. If you need privacy, then you are going to have to pay full price for those tokens (API). This has been true since day one. Everyone knows it, I guess though this is the first time that it has become "real".

what counts as discounted rate plans? if i pay for a year in advance (and get the yearly discount) and have train on my data set to off.. are you saying that is still being trained on?

Re: On the Navier–Stokes Millennium Prize Problem

#553

Post by stevenhuang »

WarmWash wrote: post #230
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?

Both

Re: On the Navier–Stokes Millennium Prize Problem

#555

Post by irthomasthomas »

igleria wrote: post #325
hkmaxpro wrote: post #304

Earlier quoted context omitted.

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”.

If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.

It can still be academic plagiarism even if they ticked the box to allow training on their prompts.

Re: On the Navier–Stokes Millennium Prize Problem

#556

Post by tzone »

It is so disappointing that we can't have such a monumental moment in history without the controversy. OpenAI leadership clearly doesn't seem to care too much about ethics. Is it a requirement to completely lack integrity to have a ground breaking company?

The reality is clear though. The chances of AI models overtaking majority of mathematics within next 10 years is becoming very high. Especially if it becomes cheaper to run these models.

As math formalizations improve, AI can have faster progress in math, compared to even computer science or software engineering.

It is simultaneously the best and the worst time to be a mathematician right now.

Re: On the Navier–Stokes Millennium Prize Problem

#557

Post by igleria »

linkregister wrote: post #361
igleria wrote: post #325

Earlier quoted context omitted.

If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.

Is there an implication of violation of ZDR here? Not a challenge. Just a request for clarification.

to my knowledge the mathematicians did not have ZDR so it would be incorrect to assume OAI violated such a thing.

I'm suggesting audits, not suing... if that is the implication.

Re: On the Navier–Stokes Millennium Prize Problem

#558

Post by traes »

mswphd wrote: post #94
Legend2440 wrote: post #31

Earlier quoted context omitted.

That other researcher was working on a smaller related problem. He was also using LLMs to do it, so either way most of the credit goes to the LLM here.

both wrong. 1. he was working on the same class of problems. He explicitly mentions they were working to extend their techniques to NS (the same techniques that OpenAI may have scooped somehow), and 2. while he was using LLMs to do it, this was part of fleshing out another mathematician's work in the area. He explicitly writes in his note that this other mathematician (Luis Martinez-Zoroa) deserves a Fields medal for…

He was specifically working on the Euler equations, which are the Navier-Stokes equations with the viscosity term removed. This is definitionally a smaller related problem. I'm not sure how you are calling that claim wrong.

Re: On the Navier–Stokes Millennium Prize Problem

#559

Post by AlexErrant »

recitedropper wrote: post #528
AlexErrant wrote: post #400

Earlier quoted context omitted.

This clarification substantially changes the flavor/nuance of your OP; may I suggest an edit (assuming the locktime hasn't passed)? Separately, I disagree that intellectual work has ever been free of "dark forest"-style secrecy. Scientists everywhere have worried about being scooped; AI just magnifies that (as all tools have; e.g. Leeuwenhoek lenses). And thirdly, if you want to make a stronger case for "I feel even…

I don't comment on HN much, and I don't really expect HN comments to hold to rigorous standards. This forum is more casual than other places on the internet where people expect heavy citations. I also wasn't expecting this to blow up, although it is interesting to see that a lot of people react to this announcement with a negative sentiment. I appreciate your upholding of ideals, and since I respect that, I will hono…

2. Fair, and further I would agree that OpenAI not knowing if prior user prompts were part of training data is concerning and will only lead to more secrecy.

3. ctrl-f "x.com" in this thread only yields https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 https://x.com/OpenAI/status/2097375276384567642

and frankly, I'm unwilling to give Elon any more traffic to dig up drama that ultimately doesn't matter. I'm not seeing anything especially childish, but y'know... I'm not sure I care.

Re: On the Navier–Stokes Millennium Prize Problem

#560

Post by an0malous »

ameliaquining wrote: post #220
magicalist wrote: post #160

Earlier quoted context omitted.

> Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra. Is this buried under the drama or are the major OpenAI twitter accounts from the people involved in the drama desperately attempting to make this the story after everything else obviously got away from them?

I don't know what anyone's been saying on Twitter and I don't care. If it's really true that there's a model out there that's that capable two weeks after the start of training, then that's objectively a much bigger deal than a priority dispute, even if the latter involves juicy allegations of espionage and skulduggery.

The things you don’t care about are highly relevant to that claim
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