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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#841
post #312

Earlier quoted context omitted.

>- Do "normies" even know what's happening? Absolutely not. Even to a lot of techy/nerdy people it's still just a chatbot that they sometimes use to help them at work. Even on here people will do whatever they can to downplay. The lack of fucks given is staggering.

How many fucks should be given, in your estimation?

∀ε>0, ∀x: ‖s−x‖ 1/ε

Re: On the Navier–Stokes Millennium Prize Problem

#842
post #544

Earlier quoted context omitted.

Which seems to be entirely true by their own admission! [0] Both the comments about him risking his career and about Levent's authorship seem to have indeed occurred. > 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed…

Hm. Looks like its possible everyone behaved terribly here unfortunately. :/ I remained impressed by ChatGPT however!

Everyone?? No, most definitely OpenAI.

But they have learnt their lesson, next time they won't reach out to who they stole it from, they will publish first.

Re: On the Navier–Stokes Millennium Prize Problem

#843
post #830

Earlier quoted context omitted.

How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.

You have to look at the incentives

Incentives are one thing, even adjusting for them it's huge, and I don't understand this incentive play for only openai, academics have perverse incentives too, to overreport, overclaim, publication bias etc why are we scrutinizing AI industry to such high degree when they have demonstrated capability and often times are off by a model release at worst.

Re: On the Navier–Stokes Millennium Prize Problem

#844
post #183

Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.

Not only that, but it used 10k agents coherently over 88 hours to come up with the proof. This is a significant advance.

What makes you think they were coherent?

Re: On the Navier–Stokes Millennium Prize Problem

#845
post #737

Earlier quoted context omitted.

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…

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#847

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

> https://cims.nyu.edu/~tristanb/statement.pdf

This really need to be a top-level story on HN..

I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.

This whole episode is more horrific than "AI is eating math". We now have a clear and economically damaging (or at least career damaging) example of the "training on customer tokens" problem.

We can't ignore this problem any longer.

Re: On the Navier–Stokes Millennium Prize Problem

#848
post #830

Earlier quoted context omitted.

How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.

You have to look at the incentives

I swear to god, people would look at the successes of Xerox palo alto and just shrug and say - "yeah, but I mean, this is all marketing"

Re: On the Navier–Stokes Millennium Prize Problem

#850

Earlier quoted context omitted.

Hm. Looks like its possible everyone behaved terribly here unfortunately. :/ I remained impressed by ChatGPT however!

Everyone?? No, most definitely OpenAI. But they have learnt their lesson, next time they won't reach out to who they stole it from, they will publish first.

Seems like OpenAI did a boring normal corporate thing (find out your competitor made a breakthrough, try to replicate it) and then when the other mathematicians found out OpenAI had beat them to Navier-Stokes, they decided to lie about what happened because they were upset they didn't get to make the big breakthrough themselves.
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