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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#471
post #190

Earlier quoted context omitted.

Compute will always be the bottleneck even if this were true.

Eventually recursive self-improvement includes reducing bottlenecks.

Which is to say, scalable and open-ended capability of ramping up physical infrastructure.

I don't know that that's achievable yet. Though the era of increasingly advanced and automated robotics seems to be around the corner which could create a cycle, vicious or virtuous depending on how you feel about it.

Re: On the Navier–Stokes Millennium Prize Problem

#472
post #234

Earlier quoted context omitted.

I don't know what anyone's been saying on Twitter and I don't care. If it's really true that there's a model out there that's that capable two weeks after the start of training, then that's objectively a much bigger deal than a priority dispute, even if the latter involves juicy allegations of espionage and skulduggery.

It isn't a priority dispute, the more concerning allegation is that OpenAI may be training their models on prompts that mathematicians were using to solve this problem, and then surprise surprise OpenAI were able to replicate that work in their latest model What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question If OpenAI is training mode…

I think all he big labs are pretty explicit about when they do and don't train on customer prompts. Is the accusation here that OpenAI trained on prompts when they claimed not to? Or were the mathematicians using one of the interfaces that allows OpenAI to train on the customer data?

Re: On the Navier–Stokes Millennium Prize Problem

#473

madness. which will be the next to fall? if i had to bet i would guess birch and swinnerton-dyer, but i'm no expert

There was a recent rumor about the Hodge Conjecture. I'd keep an eye on that one. But like the other person who replied, I'm also rooting for Yang-Mills. That has massive potential for unlocking a series of physics results.

Re: On the Navier–Stokes Millennium Prize Problem

#474

Earlier quoted context omitted.

[flagged]

Since you are a very new account, allow me to inform you that copy-pasting the same comment throughout the thread is very bad form.

Not reading the thing you're commenting on is even worse form, yet it seems to be a plague here!

Re: On the Navier–Stokes Millennium Prize Problem

#475

Earlier quoted context omitted.

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

> identify any of their de-identified data that came from their usage of ChatGPT "de-identified" seems more of a euphemism than normal in this context, given the very unique work they were doing.

I wouldn't expect poking at millennium problems to be that rare in ChatGPT. They were uniquely successful - but it's probably not easy to check de-identified data for the presence of any of their work on the problem because it would blend into a haystack of less successful work on the problem.

Re: On the Navier–Stokes Millennium Prize Problem

#476

Reading between the lines here, and taking an admittedly very negative view of openai, but they train on user prompts. So if they hear a rumour that someone is about to make a big breakthrough, they have an incentive to scoop by running the model and hoping the solution is in the new training data. Also the statement from the mathematicians in question alleges that they tried to pressure him into academic malpractice…

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Re: On the Navier–Stokes Millennium Prize Problem

#477

OMG this is going to affect the lives of so many people! We have definitively reached AGI

Navier Stokes existence and smoothness has approximately zero bearing on engineering applications

My dreams of a magnetohydrodynamic hand water-cannon are dashed sniff

Re: On the Navier–Stokes Millennium Prize Problem

#478

Earlier quoted context omitted.

The singularity happening under trump? We could have had star trek, instead we're getting the combine.

That said, perhaps it will take over the world government and decree that all corrupt officials shall be imprisoned and all weapons of mass destruction shall be destroyed.

And then it will be shut down, proper guard rails put in place, and the new version will accelerate the cleptocracy.

Re: On the Navier–Stokes Millennium Prize Problem

#479

Earlier quoted context omitted.

OpenAI version of events conceed some of the words alleged to have been used may have been used https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310

May be unfairly jaded or just well calibrated given the body of evidence, but I can't help but think of another quote about OpenAI leadership: > Not consistently candid

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Re: On the Navier–Stokes Millennium Prize Problem

#480

"we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?

If those researchers did not opt out then training data might go in. I think it’s a courteous acknowledgement; as was reaching out and examining the direction of proofs themselves. At stake here is a particular mathematician dynamic - ego, prize money, and the sense of proprietary ownership that some might feel working on a problem.

All that was just kicked in the teeth by a group with a lot of compute that was like “bro I heard on twitter that Navier stokes could be solved. Let’s try it.” That’s an existential level of engagement that almost no mathematician in history would like.

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