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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#201

Post by dsdf3 »

anthonypasq wrote: post #192
QuesnayJr wrote: post #158

Earlier quoted context omitted.

Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach. I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)

the goalposts are on Pluto at this point.

I'd put good money on the fact that we will have a lot of distilled intelligence and yet the world won't look much different.

Re: On the Navier–Stokes Millennium Prize Problem

#202

Post by rvz »

simianwords wrote: post #136
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.

> 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…

You can see that your math friends completely wrote off LLMs entirely and were showing signs of coping.

4 years ago it was a "not yet" [0], since ChatGPT at this time was not ready nor it was "AGI". Now with this 'unreleased' AI model, it has reached a point where it has solved an unsolved problem which only one human solved a millennium prize problem (Poincare conjecture).

Now finally "AGI" means something again.

[0] https://news.ycombinator.com/item?id=33905609

Re: On the Navier–Stokes Millennium Prize Problem

#203

Post by BostonFern »

peri-cl wrote: post #58
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

Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…

The famous Oracle of Delphi in Ancient Greece was said to be the center of the universe in its time. Kings, generals, and officials from poleis across and from without Greece would seek the Oracle’s counsel on important decisions.

Stories of Apollo’s favor and hallucinogenic gases abound, but I think the late Yale professor of Ancient Greek history, Donald Kagan, explained it best:

“Now, you can bet when these folks came and consulted the priests and said, ‘could you please put us down on the list, we want to consult the oracle’, the priests said ‘sure, have a beer, let's talk about your hometown, what's going on out there’. What I'm suggesting to you is that this was the best information gathering and storing device that existed in the Mediterranean world. These people knew more than anybody else about these things, and so consulting that oracle was a very rational act indeed.”

Re: On the Navier–Stokes Millennium Prize Problem

#204

Post by Aboutplants »

chinathrow wrote: post #82
arctic-true wrote: post #35

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, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.

Pre-IPO marketing?

Even if it is, Anthropic better have a few things up their sleeve

Re: On the Navier–Stokes Millennium Prize Problem

#205

Post by Maxious »

igleria wrote: post #184
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…

I´m waiting on the other side version, because I know there is no justifiable way to talk to a person like they did. Sociopathic behaviour.

OpenAI version of events conceed some of the words alleged to have been used may have been used https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310

Re: On the Navier–Stokes Millennium Prize Problem

#206

Post by dandanua »

tedsanders wrote: post #41
pavel_lishin wrote: post #8

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

Your coworkers, after they learned about major progress in this problem, asked a model which was trained on the year of private work (the blog post even acknowledges this). No wonder it found the proof in less than a week using significantly higher compute resources. And if Tristan's accusations are true, that was absolutely intentional on the part of OpenAI. You are an evil company with evil people.

Re: On the Navier–Stokes Millennium Prize Problem

#207

Post by SpicyLemonZest »

fooker wrote: post #102
SpicyLemonZest wrote: post #71

Earlier quoted context omitted.

They could have thought about the problem for like 2 minutes and not done this! I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.

> I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first. Pretty much all of math and science history is basically this pattern again and again. I'm sure all of that was rude as well.

Being scooped is not a new phenomenon, but the scooper's story is almost always that they were working on the problem independently or had some independent insight into it. By OpenAI's own account, they were inspired to start working on this by rumors that there might be Millennium Prize solutions to scoop.

Re: On the Navier–Stokes Millennium Prize Problem

#208

Post by gowld »

nradov wrote: post #106
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?

Is it spying? I think this usage is disclosed in their terms of service.

If it happened it's plagiraism. Consent to see data isn't consent to claim priority.

Re: On the Navier–Stokes Millennium Prize Problem

#209

Post by WarmWash »

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".

Re: On the Navier–Stokes Millennium Prize Problem

#210

Post by jrflo »

ChoosesBarbecue wrote: post #150
jrflo wrote: post #88

Earlier quoted context omitted.

I feel like it's far more likely that ordinary corporate espionage or leak led to this rather than OpenAI sifting through piles of user data to find this approach. Buckmaster's collaborator works at Anthropic, and could have been targeted. That would also explain why they aren't forthcoming with the source of the prompt.

I thought one of the issues was that they wanted to remove credit from Levant, the aforementioned Anthropic collaborator? Which doesn't make sense to me if he was leaking information, or defecting to OpenAI, but I might be misunderstanding your point.

I don't think he was defecting or leaking directly, just that it's entirely possible that this information got to OpenAI as a rumor rather than them directly spying on mathematicians chat logs.
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