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The Navier–Stokes Millennium Prize Problem

simonwillison.net

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Re: The Navier–Stokes Millennium Prize Problem

#111

Post by sdcfgy »

walrus01 wrote: post #90
sdcfgy wrote: post #14

My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no. I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

> as they all seem to be run by assholes. Wait until you learn how many other SaaS and web 2.0 and cloud based things are also run by assholes. You know this metaphor? https://en.wikipedia.org/wiki/Turtles_all_the_way_down But instead of turtles, it's assholes. But more seriously, no, none of what I wrote above is an attempt to excuse or play down the specific role of assholes in large AI companies.

Of course. I work for assholes. The thing is they’re getting out assholed by several orders of magnitude here.

Re: The Navier–Stokes Millennium Prize Problem

#112

Post by 20k »

tyre wrote: post #8
shellfishgene wrote: post #3

What's missing from the story I think is the part about "...then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear...". If only the two of them were working on the problem in secret, how did their breakthrough become a rumor?

People talk. If you have a breakthrough solving one of the most famous problems outstanding, you're going to tell people. You'll say, "Don't tell anyone", which they will ignore because they get a rush and perceived status by sharing it. So then they tell someone, along with "Don't tell anyone", etc. It's a small enough world (both in academic math, one at Anthropic) that you get to OAI in very few hops.

"The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag."

We know that OpenAI trained on their prompts, plagiarism is incredibly likely. The only thing we don't know is whether or not it was deliberate plagiarism yet

Re: The Navier–Stokes Millennium Prize Problem

#113

Post by maciejzj »

I know that this may be somewhat dramatised and even infantile, but my reflection is that in the world run by these reckless AI companies everyone looses. Navier-Stokes is solved but it feels like no one has won anything, controversy prevails, there is no glory in the math breakthrough. There is hardly anything to cherish, and even the guys at the top of it in OA who sit on the (supposedly) superhuman intelligence come across as massive losers and frauds.

Re: The Navier–Stokes Millennium Prize Problem

#114

Post by sdcfgy »

pansa2 wrote: post #109
sdcfgy wrote: post #14

My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no. I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

> one should not use LLM services for confidential or proprietary information That’s obvious, isn’t it? Just like you wouldn’t upload your confidential documents to an online spellchecker, or your proprietary code to an online compiler?

Everyone, including the security services in my country, uses OneDrive and O365.

I don’t get it.

Re: The Navier–Stokes Millennium Prize Problem

#115

Post by teiferer »

caughtinthought wrote: post #55
kzrdude wrote: post #21

Earlier quoted context omitted.

On the contrary, a level-headed summary that gathers information from all the different sources is necessary.

Sounds like a great use case for an LLM

They are busy generating pelicans on bicycles. The summary therefore needs to be written by a human.

(This was a joke. I value Simon's role in the community.)

Re: The Navier–Stokes Millennium Prize Problem

#116

Post by PowerElectronix »

keremk wrote: post #70

Occam's Razor says: "They heard this problem is solved or about to be solved amongst the rest of the other problems. They prioritized this and put substantial compute with their newest model and solved it." I know everyone loves juicy rumors, theories etc. but honestly that is the simplest and most plausible explanation given the state of AI improvement now. Obviously spending 15 million on a problem is not a slam du…

Funny how they did not solve any of the other problems, just the one where there was already solutions to the NS with some restrictions in their chats, and their solution seems to derive from those.

Re: The Navier–Stokes Millennium Prize Problem

#117

Post by pbmonster »

CSMastermind wrote: post #87
burrish wrote: post #43

>While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. What do you mean, as OpenAI employee, you cannot tell that his work has entered the training data ? But also correct me if I'm wrong, if the two mathematician were really close to finish this problem, and their conversation were used by OpenAI, shouldn't the Agent have succeeded way faster/e…

Having the chat logs enter the training data and having them have a meaningful influence on the ultimate result the model produces are very different things. The text for all the Goosebumps books are certainly in the training data and to some small amount influenced the solve. But their contribution was so vanishingly small it would seem absurd to say R L Stein should have recourse for contibuting to the solve.

But this is different, right?

The equivalent would be taking a (fully offline) LLM and asking it about the ending of one specific Goosebumps book, and it revealing the twist. And although that specific book was (probably) only once in the training data, a high parameter LLM can usually "remember" the twist.

Re: The Navier–Stokes Millennium Prize Problem

#118

Post by pietz »

l5870uoo9y wrote: post #91
keremk wrote: post #70

Occam's Razor says: "They heard this problem is solved or about to be solved amongst the rest of the other problems. They prioritized this and put substantial compute with their newest model and solved it." I know everyone loves juicy rumors, theories etc. but honestly that is the simplest and most plausible explanation given the state of AI improvement now. Obviously spending 15 million on a problem is not a slam du…

Given that the solution took a somewhat “unusual” approach, I find it even more unlikely that an AI model would have come up with this on its own.

Isn't that *exactly* the type of solution you'd expect from AI?

Move 37 comes to mind.

Re: The Navier–Stokes Millennium Prize Problem

#119

Post by dotancohen »

walrus01 wrote: post #90
sdcfgy wrote: post #14

My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no. I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

> as they all seem to be run by assholes. Wait until you learn how many other SaaS and web 2.0 and cloud based things are also run by assholes. You know this metaphor? https://en.wikipedia.org/wiki/Turtles_all_the_way_down But instead of turtles, it's assholes. But more seriously, no, none of what I wrote above is an attempt to excuse or play down the specific role of assholes in large AI companies.

  > Wait until you learn how many other SaaS and web 2.0 and cloud based things are also run by assholes.
Though it's not the real acronym, Larry Ellison himself has stated that Oracle stands for One Real Asshole Called Larry Ellison. He famously prides himself on it.

Re: The Navier–Stokes Millennium Prize Problem

#120

Post by _bobm »

awestroke wrote: post #97
_bobm wrote: post #89

Hah, what is the infrastructure which takes user sessions (chats with API keys, directions, navier-stokes math/progress) and regurgitates this into pre-training, RL, fine-tuning data? Or better, in-context data? People talk about the "compute" but what about the "storage"? Is storage exponentially greater, or soon to be, than the compute? Is the storage going to slow down growing to some constant rate, i.e. all peopl…

AI companies use heuristics to filter sessions, then llms to further filter, then use various techniques too anonymize the session, then process it and add it to various datasets for further selection and refinement. they don't need huge storage for this.

what is behind "process" it and "further selection" and "refinement" and how big are these "datasets"? These companies ship the encrypted session to you not because they want to.

I agree that they have pipelines for what you are describing but how effective they are at scale and at focusing is the question.

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