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The Navier–Stokes Millennium Prize Problem

simonwillison.net

161–170 of 238 posts

Re: The Navier–Stokes Millennium Prize Problem

#161
post #80
post #48

Earlier quoted context omitted.

Depends on your profession? I sometimes work on open source code as part of my professional duties. Nothing that goes on there is necessary to keep private.

Vulnerabilities, responsible disclosure etc?

You can use 'Daybreak Blue' from OpenAI for that, if you want to.

Re: The Navier–Stokes Millennium Prize Problem

#162
post #24

> ... we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors ... I've observed this exact effect last week. I made a discovery regarding a stepwise performance improvement in a codebase. I shared the benchmark results with a peer and within 12 hours they replicated the same. We had both been looking for this for years. I think giving someone hope that an answer exists might as…

That's the other thing. Even if it somehow magically turns out that they didn't plagiarize Buckmaster and Alpöge, that an independent audit goes through all their processes and finds that they could not possibly have stolen anything, and ignoring their outrageous attempts to force a coauthor off the author list, and ignoring that their employees act like small children on social media, this is a company whose culture is “we heard of a breakthrough being possible, let's scoop it”.

Normally, when you tell a coworker that you're wrapping up a result, unless they're some kind of sociopath, their natural inclination would not be to try to steal it from you.

Re: The Navier–Stokes Millennium Prize Problem

#163
IMO the drama surrounding this case somewhat overshadows some more important facts:

A) That we're at the point where SOTA models can, on their own or guided, be used to solve such monumental problems

B) That EVEN if they exist, they're still so cost prohibitive that they are completely out of range for pretty much everyone. Yes, yes, if the costs drop like a stone the hoi polloi can access this power in a year or two - but fundamentally it will divide cutting edge resource into two groups: Those with money, and those without.

That sort of latency, in turn, could lead to some feedback loop where research centers / groups that break barriers get more resources, and those who do not, are starved of resources. This sort of stratification can seriously lead to more centralized research. Do we want a future where only the chosen few get to make progress? For no other reason than that they are the ones with enough resources to spend on the required compute.

Re: The Navier–Stokes Millennium Prize Problem

#164

LLMs can't contribute good code to some of the good OSS math libraries, How is it even solving these problems?

Math problems are often stated in a way that makes it possible to automatically verify if a solution is correct. Which means a loop that speculates an approach (LLM and/or prompts), implements it (LLM), then checks (automated) can work. You still need to have a very good LLM, and probably very good prompts with interesting research directions otherwise you can probably loop forever.

Re: The Navier–Stokes Millennium Prize Problem

#165
post #153
post #148

Earlier quoted context omitted.

Why in the world is that fishy? Isn't that exactly what almost everyone would do given that they wanted to see how capable their model is and the tense competition they have with Anthropic right now? Stealing impressive headlines from your competitor is pure gold.

If they were willing to spend 105 million it, perhaps. But that would be surprising. It’s fishy because they spent something like 15 million on the right one.

Again, that is the point. There is rumours that this one thing would be solvable, so they focus on this, spending 15m on one specific thing, instead of 105m on many. How is that fishy?

Re: The Navier–Stokes Millennium Prize Problem

#166
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models

AKA everything you send to them (and I bet it's the same for any other lab) will be used, no matter what are the TOS, the law or what they publicly say.

Re: The Navier–Stokes Millennium Prize Problem

#168

IMO the drama surrounding this case somewhat overshadows some more important facts: A) That we're at the point where SOTA models can, on their own or guided, be used to solve such monumental problems B) That EVEN if they exist, they're still so cost prohibitive that they are completely out of range for pretty much everyone. Yes, yes, if the costs drop like a stone the hoi polloi can access this power in a year or two…

This has ~never not been the case for any research in any modern sense.

Re: The Navier–Stokes Millennium Prize Problem

#169
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.

Or use Lumo from Proton. Are there any other privacy first companies offering LLMs?

Chutes.ai models are served from a Trusted Execution Environment, so the GPU owners can't see your prompts.

Re: The Navier–Stokes Millennium Prize Problem

#170
Sorry math proof savants, the narcissism dream part of your career is dead

OpenAI even wanted to respect that part but now you’re too focused on them being able to leverage the treasure map at the same time instead of the treasure for humanity being found at all, a completely different treasure where you both have to deal with getting paid by the bounty provider anyway

Goofy

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