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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#361

Post by linkregister »

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.

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

Re: On the Navier–Stokes Millennium Prize Problem

#362

Post by SJMG »

gcr wrote: post #4
minimaxir wrote: post #2

> Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!

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.

Re: On the Navier–Stokes Millennium Prize Problem

#363

Post by echelon »

tantalor wrote: post #336
echelon wrote: post #53

Earlier quoted context omitted.

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

> Are we at the dawn of the singularity now Singularity doesn't "dawn". That's the whole idea. It happens all at once.

There's an event horizon and we're maybe past it?

Re: On the Navier–Stokes Millennium Prize Problem

#364

Post by voxl »

Legend2440 wrote: post #42
seizethecheese wrote: post #26

Elsewhere in the thread, others have calculated $15mm at API rates for just the output token. (So I’ll assume this cost about that much, taking input and human researcher time.) I wonder whether a team of 60 mathematicians working solely on this for a year would have cracked this. (Assuming $250k total compensation.)

Probably not. It's a millennium prize problem, a great many mathematicians have been working on it for a very long time.

Probably yes. Only a handful of mathematicians work on this particular problem, and ALL of them do not exclusively work on this problem, while having administrative and teaching duties.

The real issue is we'll never know. The rich are willing to risk it all on charismatic CEO psychopaths but not on humans.

Re: On the Navier–Stokes Millennium Prize Problem

#366

Post by bluebands »

pu_pe wrote: post #119

OpenAI thinks of this as a scoop, and it is, but the possibility that they trained the model on the prompts of the other mathematicians they were competing with will leave a terrible taste on every scientist's mouth. Seems like yet another advantage of using open models right here.

fwiw there is a big "TRAIN ON MY DATA" toggle you can turn off (that they almost certainly did) and Anthropic MTS are posting that they almost certainly did not "steal" their methods

Re: On the Navier–Stokes Millennium Prize Problem

#367

Post by vatsachak »

uncomputation wrote: post #353

So what took an autonomous agentic system using a significantly more powerful internal model, totaling multi-millions of dollars of compute in training and inference, was likely to already be solved by a team of a few humans with an orders of magnitude smaller LLM budget, had OpenAI not been foaming at the mouth to jump the shark and claim “AI solves Millenium Problem.” Also it sounds like the human research effort s…

Totally. Anthropic is like a village cottage shop who was just like chilling until big bad OpenAI came in

Re: On the Navier–Stokes Millennium Prize Problem

#368

Post by Kotlopou »

demirbey05 wrote: post #278

From Levent Alpöge : https://x.com/__alpoge__/status/2097383870773748190?s=20 >so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan There are too many ambiguities around OpenAI. Unanswered questions making this ambiguity more. Why they didn't properl…

Why do so many people involved here have to communicate in this childish way? You have people on the OpenAI side doing playground taunts (https://xcancel.com/polynoamial/status/2097215233119211902) and Levent Alpöge on the Anthropic side (the one who announced "hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final") writing in all-lowercase that he's a big boy. I bet Navier and Stokes would have dealt with this in style. (Or maybe with a duel, who knows...)

Re: On the Navier–Stokes Millennium Prize Problem

#369

Post by tantalor »

echelon wrote: post #363
tantalor wrote: post #336

Earlier quoted context omitted.

> Are we at the dawn of the singularity now Singularity doesn't "dawn". That's the whole idea. It happens all at once.

There's an event horizon and we're maybe past it?

Heh. Wrong "singularity"
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