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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#831

Post by cman1444 »

sensanaty wrote: post #525
tedsanders wrote: post #360

Earlier quoted context omitted.

Also possible: we're 99.999% sure, but a lawyer said to be safe and strictly accurate, we should stick in a sentence in saying we can't be perfectly sure, since it's infeasible for us to prove it. I promise you that if we took their work from ChatGPT and stuck in a bunch of weasel words to give the opposite impression while remaining technically true, I would quit on the spot. (I work at OpenAI.)

Nice damage control bud, too bad the veil's lifting and everyone's seeing what you sociopaths at OpenAI are really like

Where did the veil lift? This feels like a witch-hunt to me.

Re: On the Navier–Stokes Millennium Prize Problem

#832

Post by [deleted] »

hansvm wrote: post #737
intenex wrote: post #440

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Not a counterpoint per se, but I burned $50k recently on a much more modest math problem (result already known, just thought I had a sketch of a more interesting proof), and the LLM thought it had proved it within those bounds but had instead subtly fucked up the Lean definition. Take from that what you will. Not to mention, it's still very much up in the air whether the model derived the answer of its own accord or…

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#833

Post by mickael-kerjean »

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…

There is this infamous xkcd (https://xkcd.com/435/) going like this: sociology is applied psychology -> physchology is applied biology -> biology is applied chemistry -> chemistry is applied physics -> physics is applied math -> math is way up there looking down on other fields

I would argue the main reason AI labs have been focusing on programming is to unlock industrial scale automation, next logical step is to solve math as it's the key to unlock everything else. Once you hold the key for math, everything downstream fields become a matter of compute

Re: On the Navier–Stokes Millennium Prize Problem

#834

Post by karmasimida »

biophysboy wrote: post #109
floatrock wrote: post #43

Earlier quoted context omitted.

OpenAI's position: > 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 p…

Why is it unlikely?

Their base model must have been trained with hundreds of trillions of tokens several months ahead, at this point of time, it is impossible to rule out the possibility the model had seen that session at one point of time, and it probably did, without any OpenAI personnels actually know about it.

Re: On the Navier–Stokes Millennium Prize Problem

#835

Post by hollowcelery »

hansvm wrote: post #737
intenex wrote: post #440

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Not a counterpoint per se, but I burned $50k recently on a much more modest math problem (result already known, just thought I had a sketch of a more interesting proof), and the LLM thought it had proved it within those bounds but had instead subtly fucked up the Lean definition. Take from that what you will. Not to mention, it's still very much up in the air whether the model derived the answer of its own accord or…

But the researchers also did their research using essentially the same models, so that isn’t a counterpoint to AI models being at the far frontier…

Re: On the Navier–Stokes Millennium Prize Problem

#837

Post by aeve890 »

masterspy7 wrote: post #759
aeve890 wrote: post #697

Earlier quoted context omitted.

Parent comment is claiming creativity and genius beyond human experts, so why not ask for a fully unassisted AI novel result? Having access to the entire corpus of human knowledge, what else such amazing entity would require to solve a hard problem by its own? Any result of such kind from an AI alone would be enough to refute my argument, yet you don't present any. >Also there are proofs where the only human steering…

https://www.anthropic.com/research/riemann-zeta >Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.

Do you even know what a proof entails? This shit is not a proof, come on.

Re: On the Navier–Stokes Millennium Prize Problem

#838

Post by Jblx2 »

professoretc wrote: post #537
rfgplk wrote: post #138

Earlier quoted context omitted.

Skill issue. Also lean is meant to be executed, not read.

A proof is not like a program. The goal of a program is to "do the thing", thus you can make the argument that it doesn't matter what the code looks like as long as its works right. But the goal of a proof isn't to "do the thing" (where "the thing" is just to print Yes or No), it's to communicate . An unintelligible proof is really just a first draft.

>A proof is not like a program.

https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...

Re: On the Navier–Stokes Millennium Prize Problem

#839

Post by frabcus »

derangedHorse wrote: post #765
pred_ wrote: post #151

Earlier quoted context omitted.

> we did not read any private chats Your post says “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .” We can discuss what it means to “read” things but obviously the issue here isn't whether you did it manually or automatically. But more importantly, what on earth are you doing threatening real scientists to remove their coauthors, then ma…

Except that’s not what happened. OpenAI offered to collaborate and put conditions on their offer. They aren’t threatening the removal of a coauthor for an independent work.

The condition was ludicrous, and for political reasons, because one of the authors was also an Anthropic employee.

It's completely childish, and not befitting of the weight of the times we're living in.

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