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The Navier–Stokes Millennium Prize Problem

simonwillison.net

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Re: The Navier–Stokes Millennium Prize Problem

#201

Post by paxys »

civvv wrote: post #15

LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence»,…

The kind of humans who invent entire fields of science on their own come by a few times a generation. It’s fine to say AI isn’t anywhere as close to them in intelligence, but instead is comparable to the “average” mathematician who is building on the work done by others and taking it a bit further.

Re: The Navier–Stokes Millennium Prize Problem

#202

Post by g-b-r »

sodic wrote: post #146
bob1029 wrote: 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…

Achieving a high score requires focus and effort.

There's little reason to aim for a score a lot higher than the current best; and when getting close to the score you're aiming for, it's easy to get agitated and make a mistake.

And if you do beat the high score, you're likely to loosen your attention right after that, and it's even annoying to keep going for much more.

Re: The Navier–Stokes Millennium Prize Problem

#203

Post by paxys »

tu26muwu wrote: post #79

> The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster [...] I think you should not say that. Buckmaster did only state his version of events and was very clear on that he did not make any accusations at all. To quote from his statement pdf: > I am not accusing anyone of anything.

Oh please. This whole “I’m not accusing them of anything, but this sure seems suspicious” doesn’t work past the 6th grade. He knew exactly what he was doing.

Re: The Navier–Stokes Millennium Prize Problem

#204

Post by HEX4AGON »

zshn wrote: post #130

I really should get up to speed with LEAN, I know AI can probably write it better than me but I'd like to grasp it better still...

If you’ve done functional programming and is familiar with mathematical proofs it should be quite intuitive to read the language

Re: The Navier–Stokes Millennium Prize Problem

#205

Post by paxys »

l5870uoo9y wrote: post #28

I run a small SaaS[1], like so many others, that uses AI to generate and optimize SQL. Getting this to perform optimally has been a lot of work and now I wonder if OpenAI is outright stealing this knowledge, which without a doubt is highly valuable to them. [1]: https://www.sqlai.ai

No one wants to “steal” your vibe coded crap. Your prompts aren’t as unique or valuable as you think.

Re: The Navier–Stokes Millennium Prize Problem

#206

Post by paxys »

RhysU wrote: post #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.

If you want a level headed technical discussion instead of pitchforks and drama you have come to the wrong forum.

Re: The Navier–Stokes Millennium Prize Problem

#207

Post by krapp »

biorach wrote: post #75
l5870uoo9y wrote: post #28

I run a small SaaS[1], like so many others, that uses AI to generate and optimize SQL. Getting this to perform optimally has been a lot of work and now I wonder if OpenAI is outright stealing this knowledge, which without a doubt is highly valuable to them. [1]: https://www.sqlai.ai

It's extremely unlikely that there is anything interesting or novel in the optimisation of a small SaaS SQL

But what if they added "be interesting and novel" to their prompt? Did you consider that?

Re: The Navier–Stokes Millennium Prize Problem

#208

Post by vb-8448 »

unified101 wrote: post #191
vb-8448 wrote: post #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.

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

If you trust a "toggle" I have a bridge to sell.

Users data is just too precious to ignore.

Re: The Navier–Stokes Millennium Prize Problem

#210

Post by civvv »

paxys wrote: post #201
civvv wrote: post #15

LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence»,…

The kind of humans who invent entire fields of science on their own come by a few times a generation. It’s fine to say AI isn’t anywhere as close to them in intelligence, but instead is comparable to the “average” mathematician who is building on the work done by others and taking it a bit further.

Yeah, thats likely true to some extent. But my point is perhaps a "counter-thought" to the idea that this is ASI level intelligence and that math is now a computer task and not a human one. If it is incapable of moving maths forwards into the "unknown" it simply can not replace humans, and this might be a hard structural block for LLM's.
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