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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

#511

Post by concinds »

Eridrus wrote: post #466
jampekka wrote: post #447

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?

His issue is more nuanced than that. Most of the value was in humans reaching new insights or new math during failed attempts to solve these problems, whereas AI is basically "too efficient" in beelining to the goal and discards potential new insights reached along the way. I assume this is solvable.

Re: On the Navier–Stokes Millennium Prize Problem

#512

Post by andriy_koval »

slibhb wrote: post #120
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

Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.

> Either way, it seems AI was involved.

I think the important question which AI made breakthrough, Claude or Codex..

Re: On the Navier–Stokes Millennium Prize Problem

#513

Post by paulsutter »

Here they basically admit that they use session data for training, even sessions that are marked "not for training", and they justify this by "de-identifying" the session.

Which means they can learn from whatever you discuss with ChatGPT unless you are going through a clean API (perhaps Bedrock? Anyone know?)

> We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).

Re: On the Navier–Stokes Millennium Prize Problem

#514

Post by tensor »

curt15 wrote: post #457
charm137 wrote: post #301

Earlier quoted context omitted.

It's astounding that the thought to dissociate one of the mathematicians from the proposed publication was driven by their corporate institutional affiliation - and that that exclusion was suggested by a scientist themselves! This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that! Progress in humanity's knowledge now has to…

The scientist allegedly making that request comes from a machine learning background. Perhaps he's not familiar with the culture in mathematics regarding authorship. That sort of squabbling over author priority would be unconscionable to mathematicians.

No, it's common to list authors alphabetically in a lot of computer science journals too.

Re: On the Navier–Stokes Millennium Prize Problem

#515

Post by Fordec »

monster_truck wrote: post #504
10xDev wrote: post #190

Earlier quoted context omitted.

Compute will always be the bottleneck even if this were true.

Based on the leaps in local inference speed in the past month, which have been absurd, I'm p confident we're going to whiplash from compute constrained to storage constrained. Bit apples to oranges, but it reminds me of all the fiber we installed in the late 90s, certain that per-strand capacity increases were years or decades out, only to get massively rugged

I expect the investments into AI driven mathematic discoveries that underpin compression efficiency will be a key investment area. Particularly at the data center scale rather than per device or per file level.

Re: On the Navier–Stokes Millennium Prize Problem

#516

Post by baq »

denverllc wrote: post #175
lanthissa wrote: post #12

Earlier quoted context omitted.

over 5 days, you couldn't achieve that level of testing and communication with humans on such a complex problem in that amount of time. some might go so far as to call this a country of geniuses in a data center.

In a way, I think you have it backwards. Two mathematicians, through insight and thought, wrote out the proof over 1-2 years. It took OpenAI a cost of $15m and with 10,000 subagents; that's around 60-120 mathematician's salaries ($250k-125k salary) for 1 year. And, given now the cloud that OpenAI may have just "interpolated" (aka stole) the result, it's even more of a bear case for AI.

Bear case? I’m sorry?

70x uplift is a bear case?

Re: On the Navier–Stokes Millennium Prize Problem

#517

Post by sobellian »

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."

Re: On the Navier–Stokes Millennium Prize Problem

#518

Post by baq »

SJMG wrote: post #362
gcr wrote: post #4

Earlier quoted context omitted.

300e9 output tokens at the current Astra per-token API pricing ($50 per 1e6 output tokens) would be roughly $15,000,000 ignoring input tokens.

They pay at cost though, not the public API pricing.

Doesn’t matter for us.

Re: On the Navier–Stokes Millennium Prize Problem

#519

Post by dyauspitr »

alasano wrote: post #21

I don't know about you guys, but I'm hyped about the future. Cure all illnesses Utopia or Robot Wars Dystopia, both are pretty exciting.

Right there with you. Fuck my job, I’m excited to see the future unfold as a homeless bum on the street. I’m not even being sarcastic.

Re: On the Navier–Stokes Millennium Prize Problem

#520

Post by PhunkyPhil »

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…

(a) identify any of their de-identified data that came from their usage of ChatGPT.

You don't need his login information, you just need to identify if anyone was approaching the NS problem using his method. Nobody else on earth (presumably) besides him, his team, and at best OpenAI were approaching the problem this way.

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