Live data from Hacker News

On the Navier–Stokes Millennium Prize Problem

openai.com

461–470 of 1001 posts

Re: On the Navier–Stokes Millennium Prize Problem

#461

Earlier quoted context omitted.

I´m waiting on the other side version, because I know there is no justifiable way to talk to a person like they did. Sociopathic behaviour.

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

In what world a tweet and a screenshot of a private convo are evidence of good faith? Plain sociopathic behavior.

Re: On the Navier–Stokes Millennium Prize Problem

#462
post #130

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

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…

[dead]

Re: On the Navier–Stokes Millennium Prize Problem

#463

Earlier quoted context omitted.

2) We are witnessing the intelligence explosion from the first row, wherever this takes us 3) I'm still processing the drama, just found out about it after reading the blog post. If that happened based on private data, that's horrible. If that happened based on public tweets, then it's still abuse of power as OA employees access to compute (launching 10k agents) is quite heavy weight in boxing terms. But apart from A…

To be quite clear, the solution to the _Navier Stokes problem_ is one in which you get a finite time blow up (i.e. infinite pressure). This is more meant to suggest that Navier Stokes is unphysical in some way which is not necessarily unexpected. There's unlikely to be any engineering applications since even if the solution can be approximated, you still need to set up the initial conditions but at that point you can…

The proof of finite-time singularity may impact both fluid dynamics models (CFD) and AI reasoning models. Under specific conditions, Navier–Stokes equations allow velocity to grow infinitely, causing the continuum fluid assumption to break down. Knowing the exact mathematical breakdown mechanisms helps developers improve adaptive mesh refinement and sub-grid scale models around high-vorticity regions (like vortex stretching and turbulent shear layers). While aerodynamic simulations for vehicles operate far from singularity thresholds, their stability at extreme boundaries could improve?

Proving out the combination of scaling inference-time compute and agent collaboration to solve previously intractable mathematical problems is WOW. By pairing creative candidate generation with automated proof checkers (like Lean) we are leaning into a repeatable framework for AI-driven scientific discovery.

Re: On the Navier–Stokes Millennium Prize Problem

#464

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

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

You’re straddling a weird line here where I am not sure if you are speaking on behalf of OpenAI or not.

Re: On the Navier–Stokes Millennium Prize Problem

#465

> 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?

> WOW This. I do dislike the AI oligarchs as much as the next person, but I do find the thread full of complaining a bit depressing still. If the result holds (and it looks it does), this may be one of the, if not the, biggest things to happen in computing to date. A lot bigger than e.g. Deep Blue beating Kasparov in chess or AlphaGo beating Sedol in Go.

Seeing mathematicians such as Terry Tao being unhappy with open problems being solved makes me sort of question the usefulness of any of this pure mathematics. If we're not happy that the problems are being solved, why care about this field at all?

Re: On the Navier–Stokes Millennium Prize Problem

#466

"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?

What does it matter? They offered concurrent credit to the other team. I thought I saw sole credit elsewhere in the leaked DMs on Reddit too. This is plainly fair.

Re: On the Navier–Stokes Millennium Prize Problem

#467

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”.

Their own claim is that they wanted Buckmaster without Alpöge to lead a rewrite of OpenAI's Navier-Stokes work, not of Alpöge-Buckmaster's Euler work.

No one can know if that's correct without proof but I don't know how you're reading it so differently.

Re: On the Navier–Stokes Millennium Prize Problem

#468

Earlier quoted context omitted.

I thought openai don't use any user data if we opt out of training and via api?

That is correct. It is possible they didn't opt out and given the timeline and anonymization of data unclear whether a particular conversation would have made it into the training set if they hadn't.

Easy to ask for the account used to see if its usage went into training data. Also easy to say "Knowledge cut-off of the used model was date X".

That they don't is telling.

Re: On the Navier–Stokes Millennium Prize Problem

#469

Earlier quoted context omitted.

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.

You think a model with an effective memory of 200-500k words, that can be unplugged, is going to "run the world" You people gotta put down the sci-fi

The scifi pov has a good track record as this point, you people gotta be more open minded

Re: On the Navier–Stokes Millennium Prize Problem

#470
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.

Post reply on HN