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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#631

Post by enraged_camel »

tedsanders wrote: post #236
contemporary343 wrote: post #132

Earlier quoted context omitted.

"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a num…

All of those statements sound true, based on what I've heard. - "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input - it's all true that a team worked on this, a bunch of compute was burned, and the problem was…

>> I'm not sure how any of this provides evidence that OpenAI took any of their work.

Sorry, but the burden of proof lies in the other direction: OpenAI needs to definitively prove that their agents did not look at the existing work that was about to be published. Otherwise OpenAI simply stole the glory and the spotlight (and I'm being charitable here).

Re: On the Navier–Stokes Millennium Prize Problem

#632

Post by m0rde »

Chinjut wrote: post #605

What is going to become of life for those of us who do not work at AI labs and are unlikely to be hired by AI labs, despite all the years we put into learning math, coding, etc? Those of us who made the mistake of studying anything other than machine learning. How will we make a living? (We don't live in a world that seems likely to distribute gains widely instead of largely to the handful of already mega-rich.)

Do you just go around posting this comment? https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...>

Re: On the Navier–Stokes Millennium Prize Problem

#633

Post by semi-extrinsic »

sobellian wrote: post #516
hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

NS is a question for natural science. Q: can we model these bodies of discrete particles with a continuous approximation? A: if you do, you can get aphysical singularities. "If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics."

This is a wrong interpretation. Physicists have a shit-ton of models that produce "aphysical singularities", they just work around those to get meaningful answers anyway. This is a whole trope and stereotype. Some of the most successfull and accurate predictions in all of physics come out after you discard a bunch of singularities.

See e.g. https://en.wikipedia.org/wiki/Renormalization

Nobody who actually works in fluid dynamics on any sort of application gives a hoot about the N-S millenium problem. Many do not even know what it is. There is no practical effect of this proof on how we do fluid mechanics.

Re: On the Navier–Stokes Millennium Prize Problem

#634

Post by TZubiri »

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".

>They only fuck over the poor ones, I can pay the expensive prices so this is not a problem.

Re: On the Navier–Stokes Millennium Prize Problem

#635

Post by DudleyBluffles »

JPC21 wrote: post #596
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.

I fear this is only temporary and due mostly to the complexity of the problem. Consider the recent counter-example to the Dinitz–Garg–Goemans conjecture:

> https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...

The prompts for the chat above are:

> Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample.

> [gpt works for a while and then gives up]

> Continue the search. Have a clear strategy obtained from deeper understanding of the problem structure.

> [gpt works for a while then gives up]

> it's enough of partial results. let's finish with a complete unconditional counterexample

> [gpt proves the problem]

I could have written these prompts sophmore year of highschool, if not earlier. True, it took more experienced mathematicians to verify it, but I don't fancy a role as a glorified editor. I want to solve problems! Discover new techniques! Not babysit an AI while eating breakfast.

Re: On the Navier–Stokes Millennium Prize Problem

#636

Post by Chinjut »

m0rde wrote: post #632
Chinjut wrote: post #605

What is going to become of life for those of us who do not work at AI labs and are unlikely to be hired by AI labs, despite all the years we put into learning math, coding, etc? Those of us who made the mistake of studying anything other than machine learning. How will we make a living? (We don't live in a world that seems likely to distribute gains widely instead of largely to the handful of already mega-rich.)

Do you just go around posting this comment? https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu... >

Yes, on that occasion and now on this one. As a mathematician, my fears have been amped up yet further by this new development.

Re: On the Navier–Stokes Millennium Prize Problem

#637

Post by keeda »

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?

A 3rd possibility is that they simply have not been exposed to the best models available (which is extremely likely if you only use the free tier chatbots), and/or did not invest the effort needed to truly harness this new very weird new technology, and so had a very skewed perspective of their actual capabilities.

Re: On the Navier–Stokes Millennium Prize Problem

#638

Post by ameliaquining »

an0malous wrote: post #558
ameliaquining wrote: post #220

Earlier quoted context omitted.

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

Elaborate?

Re: On the Navier–Stokes Millennium Prize Problem

#639

Post by HDThoreaun »

Kotlopou wrote: post #385
lwansbrough wrote: post #289

It would be nice if one of these models would produce a novel theory or advance the field in a positive direction. Most (all?) of the big discoveries have been counterexamples, which is just sort of a systematic tearing down human ingenuity. I know that counterexamples are an important part of progress and discovery, but it just feels bad to me. But I'm not a mathematician, maybe I'm totally misreading the vibe.

Not all, see the cycle double cover conjecture proof: https://news.ycombinator.com/item?id=48863490 But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904 We will have to see whether any other millennium problems fall. I guess that in a year th…

Nuts that Tao literally predicted the exact strategy openAI seems to have used not even a week ago

Re: On the Navier–Stokes Millennium Prize Problem

#640

Post by fc417fc802 »

peri-cl wrote: post #284
Maxious wrote: post #205

Earlier quoted context omitted.

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

> "When we learned that they had Euler but not Navier-Stokes, we offered to let them go first, to suggest that they should be the ones to get the prize, and optionally for Tristan to be the lead author on a rewrite of the OpenAI proof. We felt it was challenging to offer the same to Levent (an Anthropic employee), who was not willing to talk or coordinate with us anyway. We were open to other solutions." What an admi…

That isn't what the quoted passage says though? The claim by openai (no idea if true) is that they offered to wait for the other two to claim the prize before publishing their own work. Separately, they also offered to let one of the pair (but not the other) become an author on their own separate work.
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