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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 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

#512

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

#513

Post by tensor »

curt15 wrote: post #456
charm137 wrote: post #300

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

#514

Post by Fordec »

monster_truck wrote: post #503
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

#515

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

#516

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

#517

Post by baq »

SJMG wrote: post #361
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

#518

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

#519

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.

Re: On the Navier–Stokes Millennium Prize Problem

#520

Post by kzrdude »

famouswaffles wrote: post #354
kzrdude wrote: post #295

Earlier quoted context omitted.

I don't see how it would be negative PR. If anything, the love these breakthroughs and use it in their PR campaigns.

They don't need to collect the monetary prize to announce the result and use it for marketing. On the other hand, trying to collect the prize would probably not go uncontested.

Let's see what happens. In contrast to this whirlwind of math that's going on right now, the millennium prize rules require publishing in a reputable journal and 2 years of waiting time to establish that the proof has been accepted by the community. So nothing happens in the short term.
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