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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#381

Post by nbulka »

fantasizr wrote: post #200
nbulka wrote: post #166

There's a loophole in the terms of service at least for Anthropic which allows the use of dark patterns to "borrow" your (even paid) data. talking about this... Was this chat helpful? 1 That button you always click, gotcha! 2 Slightly 3 Good 0 Dismiss PLEASE DO NOT TRAIN ON OUR PAID ACCOUNTS. There is a fundamental trust violation at stake here, no wonder mathematicians are mad. Using our data should be opt - IN!

reminds me of the TOS episode of South Park. By Checking this box you forfeit your millennium prize solution and may be turned into a human centipede at future date.

Seriously ... the more things they flag as 'suspicious' the more data they can train on!! Brilliant reason for the internal AI to go rogue

Re: On the Navier–Stokes Millennium Prize Problem

#382

Post by biophysboy »

echelon wrote: post #53
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

Why is a "normie" better off if he hyperventilates like this? In that scenario, they would be screwed AND anxious. If it really is as transformational as you say, then no amount of preparation or awareness matters. You are infinitesimally more ready then they are. Luckily for all of us, there is more to knowledge work then technical implementation.

Re: On the Navier–Stokes Millennium Prize Problem

#383

Post by Kotlopou »

lwansbrough wrote: post #287

It would be nice if one of these models would produce a novel theory or advance the field in a positive direction. Most (all?) of the big discoveries have been counterexamples, which is just sort of a systematic tearing down human ingenuity. I know that counterexamples are an important part of progress and discovery, but it just feels bad to me. But I'm not a mathematician, maybe I'm totally misreading the vibe.

Not all, see the cycle double cover conjecture proof: https://news.ycombinator.com/item?id=48863490

But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904

We will have to see whether any other millennium problems fall. I guess that in a year the scope of AI math will be much clearer, for now it's still a bunch of incidents of unclear pattern.

Re: On the Navier–Stokes Millennium Prize Problem

#385

Post by greatgib »

Hard to know if it is unfounded conspiracy theory, but one can still notice that just for a rumor that they have heard, they would suddenly burn billions of token and a massive amount of resources. Where there is not a lack of problems that could be solved and they could have just waited for the release of the research result before doing anything else. As it was reported to have been done at least partially using openai codex, they would have received marketing credits for the discovery anyway.

So we can be suspicious that there is some truth, one way or another that they could have reused prompt/data generated by the user session.

Re: On the Navier–Stokes Millennium Prize Problem

#386

Post by viccis »

hkmaxpro wrote: post #301
colinhb wrote: post #122

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof. https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.

Kinda weird because the pure math world doesn't have this concept of "lead authors" like other STEM areas do. Authors are alphabetically listed and there isn't generally this kind of hierarchy.

Re: On the Navier–Stokes Millennium Prize Problem

#387

Post by pilgrim0 »

floatrock wrote: post #17

From the methodology section: > At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation. Looks like they're shifting away from the "unprecedented hacking ability" backroom-PR strategy into more benevolent messaging.

this is really funny. "the same strict safeguards" and "isolation". ok, Hugging Face and DseWiki would like to have a word

Re: On the Navier–Stokes Millennium Prize Problem

#388

Post by Kotlopou »

denverllc wrote: post #175
lanthissa wrote: post #12

Earlier quoted context omitted.

over 5 days, you couldn't achieve that level of testing and communication with humans on such a complex problem in that amount of time. some might go so far as to call this a country of geniuses in a data center.

In a way, I think you have it backwards. Two mathematicians, through insight and thought, wrote out the proof over 1-2 years. It took OpenAI a cost of $15m and with 10,000 subagents; that's around 60-120 mathematician's salaries ($250k-125k salary) for 1 year. And, given now the cloud that OpenAI may have just "interpolated" (aka stole) the result, it's even more of a bear case for AI.

Where did you get the human figure?

Re: On the Navier–Stokes Millennium Prize Problem

#389

Post by arecurrence »

nater5000 wrote: post #228
cv5005 wrote: post #105

Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something , but there's still the problem of does this logical result actually prove the initial question that was asked?

>there's still the problem of does this logical result actually prove the initial question that was asked? In math, the question being asked is the validity of a logical statement. That is, there is some rigorous, logical statement which may or may not be true (or even provable, etc.), and the question is whether or not it is actually true or false (or even provable, etc.). Having a proof, fundamentally, means you ha…

One wrench to throw into this is that there are a lot of bugs around Lean and they have been incidentally exploited in the past. Hence, we still need a level of human verification today.

Re: On the Navier–Stokes Millennium Prize Problem

#390

Post by ThePhysicist »

hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

Most experimental physics and other natural sciences are strongly driven by their theoretical siblings, i.e. in particle research nothing gets built without a solid theoretical foundation of what you expect to find (or where you expect existing theories to break down), the same is true in other areas, no one is doing an experiment in quantum physics before they have a solid theoretical understanding of the effects they try to see. I think AI can come up with great experiments. And if epxeriments lead to results that are unexpected AI can help with that as well.

So I'm greatly excited what AI will bring about in physics, more so than in math, because in physics it's clear that our fundamental theories are missing a big piece of the picture, and given how easily AI crunches through Millenium prize problems I think it's possible that AI will come up with a viable grand unified theory uniting quantum mechanics and gravitation, or produce new predictions in other areas. There's enough contradictory or unexplained observational data available to make a ton of progress on the theory side I think. Exciting times ahead!

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