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The Navier–Stokes Millennium Prize Problem

simonwillison.net

191–200 of 235 posts

Re: The Navier–Stokes Millennium Prize Problem

#191

> 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.

Put down the pitchfork. It's a toggle in their settings.

Re: The Navier–Stokes Millennium Prize Problem

#192
post #143

Earlier quoted context omitted.

Because it is not finished. Their follow up claim is that OpenAI’s approach looks like another proof they had been working on the side, but hasn’t published yet

1) Because AI models are 1000x better about following a problem to its conclusion than coming up with a genuinely new idea. 2) Because if we accept the facts ChatGPT only came up with its "new" idea after being told exactly what the new idea was by a mathematician (OpenAI doesn't dispute this btw). And OpenAIs story comes down to the usual "We didn't look at it, trust me bro", which is made more hard to believe becau…

I don’t know much about NS problem or Euler problem anyway. Can’t tell how significant it is to go from Tristan approach to OpenAI’s results.

It is 10k agents after all with a model that is 2x-3x more powerful than Astra. So claims some intuition is his alone and the model can’t find it independently is Tristan’s belief not the reality, which I don’t find particularly convincing.

I do think that Levent guy isn’t independent and indeed does have an enormous amount of tokens to spend and also on an internal model from Anthropic.

All things considered, I think OpenAI people are competitive, even aggressive. But I don’t think they steal anything. Ultimately, the model’s capability is the real surprise factor here, the fact they could get a solution after all in 3 days, that is the cause of drama, if it is 3 months, then it is a nothing burger, because by then the original results had already been published.

Re: The Navier–Stokes Millennium Prize Problem

#193
I keep looking for a technical article to appear on HN discussing literally anything about the mathematical result--- Not fluff, not marketing, actual content.

Instead, all I read on HN about N.-S. is human soap opera, told from every possible angle.

In 100 years we won't care about the soap opera. The N.-S. result itself will still matter.

Someone, anyone, please, submit articles on the result itself.

Re: The Navier–Stokes Millennium Prize Problem

#194
post #142

Earlier quoted context omitted.

Or if you're going to trust one of them, maybe it shouldn't be OpenAI

Why would I trust any of them?

It's either that, not use an LLM, or local-host an LLM. If you can local-host one then great, this is a compelling reason to do that too. A lot of people aren't in that position.

Re: The Navier–Stokes Millennium Prize Problem

#195
post #182

Earlier quoted context omitted.

Reminds me of amateur table tennis. There is a strange dynamic where you down regulate your performance unconsciously when the opponent is playing worse and vice versa. Could be described as some physical form of this effect: https://en.wikipedia.org/wiki/Asch_conformity_experiments The term would be conformity / normative social influence.

Surely this has nothing to do with specifically table tennis, nor that it's amateur. A better example would be mixed boys/girls sports classes in school, where the boys deliberately hold back as to not injure/scare the girls. It's a pretty obvious and human thing not to go out and completely destroy a much weaker opponent. We're social animals after all. There also may be an element of energy conservation, there's ob…

I think the difference is that, in the table tennis example, it happens unconsciously and you can't help it. But you're right, it likely happens in most sports.

The mixed boys/girls classes example is, as you said, deliberate. And I too remember holding back on purpose in such situations when I was a kid.

With the arcade, no one was deliberately holding back. I'm sure of it.

Re: The Navier–Stokes Millennium Prize Problem

#196

Earlier quoted context omitted.

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.

The only way it would be able to tell you the ending is if it was somehow given more importance in pretraining, loaded into context, or represented in multiple sets of training samples. I have a blog that I make very LLM friendly and usually load posts up into context when I’m working on something relevant. I’ve also opted to improve models for everyone. Despite this, the model can’t recognize my site or any of my posts when I ask it to recall without internet usage (I also turn memory off btw).

Re: The Navier–Stokes Millennium Prize Problem

#197
post #160

People are focused on the drama but the problem showing is the data. This is the elephant in the room and I am surprised that openai can be that stupid with it. How can openai do this, what is being claimed, at the scale of their entire userbase? If they do this only for particular sessions then how do they sieve through sessions for the good stuff? How are sessions stored, how are they processed, how much storage an…

It seems completely trivial to feed sessions to their own LLM and ask it to look for various things in them, from detecting problematic use cases to finding interesting mathematical work.

let's say that they ask a single question for each session they get. they are immediately doubling the compute they need in processing and then post-processing the same session twice.

nothing trivial about it. not saying they cannot feed "their own LLM" saying it isn't trivial especially at scale.

if you do not trust me try it without the "at scale" part.

Re: The Navier–Stokes Millennium Prize Problem

#198
post #146
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…

I have a similar story, but perhaps even stranger. I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick. The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters. There are always a few competitive guys who spend the entire conference taking tu…

I like to leverage that when brainstorming solutions to hard problems. Instead of contemplating small percentage improvements, try to think about what's in the way of improvements that are orders of magnitude better (e.g., don't take time to run a big task from 100s to 90s, take it to milliseconds). Sometimes it unlocks big ideas.

Re: The Navier–Stokes Millennium Prize Problem

#199
post #32

Earlier quoted context omitted.

It's something that happened before LLMs - multiple discovery. Calculus is a classic example.

Yes but in this case, the allegation is Leibniz literally looked into newtons notebooks

Yep - it's a different case. But the idea that without LLMs, it's unlikely the same idea would be discovered independently is not true - it does happen.

Re: The Navier–Stokes Millennium Prize Problem

#200

Earlier quoted context omitted.

That they do it is just concerning to me in that it says that home-ran models just aren't good enough. Surely researchers like this have the processing power to run them at home, they just don't have the processing power to train models of comparable level. This is something I feared would happen and where open source would be left behind. Maybe they can do something with crowd-sourcing computational power from volun…

> Surely researchers like this have the processing power to run them at home, Nobody has that power. Certainly not mathematicians.

Yes people have to service the use case of a single person. All sorts of models exist that are designed to be ran at home. Yes, you need a relatively beefy graphics card for it but if your machine can handle the latest video games at good graphics it can handle these local models. How well they compare against these things remains to be seen but apparently OpenAI released gpt-oss-20b which is comparable to o3-mini apparently in terms of reasoning power. There's also oss-120b which does require at least a company server to run but this should well be within the budget of a university.
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