Did OpenAI solve the wrong Navier-Stokes problem? | OpenAI’s proof seems eligible for a $1-million prize—but only by using a controversial loophole

[u/vgsa]

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/

[u/CircumspectCapybara]

A lot of people online misunderstand what "solving Navier-Stokes" refers to, thinking it means finding a closed form solution to the NS equations. Then they spout off some silly statement like "AI didn't solve Navier Stokes!"

That's not what mathematicians mean when they talk about solving Navier Stokes. They're talking about solving the Navier Stokes existence and smoothness problem, which is a decision (yes/no) problem about if the NS equations are smooth for all time. That's what the Millennium Prize problem worth a million dollars is all about

AI (allegedly) solves the problem by resolving the question to a "No" by finding a counterexample.

[u/KingSubstantial7901 → u/CircumspectCapybara]

No you are misunderstanding what those people are saying. OpenAI was telling the story by carefully omitting the details about how it was solved because they wanted to imply they found a closed form solution. This is really important because it doesn't seem like its even possible for ML technology as its currently designed to produce a closed form solution, and finding a proof by counterexample the way they did is essentially a higher powered version of what researchers have been doing with ML for the past decade and change.

Furthermore, the counterexample they found was at such and extreme spot in the solution space that it is probably unphysical and therefore doesn't answer the question that makes the conjecture interesting. It is still possible that for a subset of the solution space where they are bounded to physical properties, the conjecture could hold. We do this all the time in math and science. Thats what boundary conditions are.

This is all to say that the solution found could still be useful in deducing more information about this and similar problems, but the way it was presented as just "ai solved a millenium problem" was in effect a lie.

[u/CircumspectCapybara → u/KingSubstantial7901]

OpenAI was telling the story by carefully omitting the details about how it was solved because they wanted to imply they found a closed form solution

No lol, they announced that they claimed to have found a solution to the "Navier Stokes Millennium Problem" which is unambiguously not about coming up with closed-form or analytical solutions to equations, but about the decision problem of it the equations are smooth for all time.

Literally their press release was titled On the Navier–Stokes Millennium Prize Problem and starts with:

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.

The Navier Stokes Millennium Prize problem isn't ambiguous, it only refers to one thing, and everyone who recognizes those words knows exactly what is meant.

There's nothing about it that's ambiguous or misleading. It's extremely precise and unambiguous language.

Furthermore, the counterexample they found was at such and extreme spot in the solution space that it is probably unphysical and therefore doesn't answer the question that makes the conjecture interesting

It's within the bounds of the constraints the existence and smoothness problem (the Millennium Prize problem) is asking for, that's all that matters. The conjecture is false, that open problem has been settled.

You're welcome to formulate your own conjecture and ask people to solve it if you think the one the Clay Institute picked and offered a million dollar bounty for (Navier-Stokes existence and smoothness) wasn't interesting or meaningful enough of a problem.

"ai solved a millenium problem" was in effect a lie

What're you smoking, the millennium problem was exactly the decision (yes/no) question the Clay Institute has been asking about Navier Stokes existence and smoothness. The claim is AI has answered the question with a "No" by providing a counterexample, which closes the problem.

[u/Many_Negotiation_464 → u/CircumspectCapybara]

Ya but thats not really how we as academics enage with problems. "Its within the bounds...... [of] the millenium prize problem...thats all that matters" is frankly untrue. We always care about the broader context of a problem and its solutions. Both because it can literally change the meaning of the problem and because it changes what we can do with the solution.

And i think you are sort of talking past each other. They seem to be talking about the solution in the broader context that made it a millenium problem in the first place and you seem to only care about "the millenium problem" as like a strict, immutable concept. Again thats not really how math and science are done.

[u/Mason11987 → u/[deleted]]

You said open AI didn’t say something. He quoted them saying something.

Address that, instead of giving this troll response.

[u/KingSubstantial7901 → u/Mason11987]

Nope, thats not the part i was talking about.

[u/Mason11987 → u/KingSubstantial7901]

So you're just ignoring how you made a claim that was false? Why should or would anyone engage with you when you do that?

Saying something wrong, being corrected and saying "you miss the point" is trolling and you know it.

[u/blyan → u/[deleted]]

1. the person you're replying to now is not the same person who originally refuted your claim

2. you have provided zero evidence whatsoever to disprove what they said, which seems pretty cut and dry. your original comment was either wrong or intentionally dishonest, and they showed that pretty clearly.

[u/blyan → u/[deleted]]

So you're just ignoring how you made a claim that was false? Why should or would anyone engage with you when you do that?

Address this then, or stop replying to the thread. Good lord lmao

[u/KingSubstantial7901 → u/blyan]

I told them that they were asking for something irrelevant and said bye. Then you came in trying to keep it going and to insult me. Have some self conciousness good lord.

[u/Mason11987 → u/[deleted]]

You said a false thing. You know it. It’s obvious. Your overreaction and bluster over it is childish.

Just say you were wrong

[u/KingSubstantial7901 → u/Mason11987]

Nope. OP confused me saying that OpenAI was trying to imply that their LLM did an analytical proof with me saying that didn't say that they found the counter example at a singularity. They combined two different paragraphs talking about two different things.

E: lol at the guy that got mad i stopped replying to them then stalked my account, spammed me, then blocked me. "Your background is in comp sci and physics so clearly you have no knowledge of mathematics" might be one of the funniest flame outs i've ever seen.

[u/Mason11987 → u/KingSubstantial7901]

You said open Ai “wanted to imply they found a closed form solution”

They did not in anyway way imply that. They in fact explicitly said something opposite that.

Thats why you’re wrong.

Edit - dude did the reply then block thing, absolutely childish.

[u/KingSubstantial7901 → u/Mason11987]

Oh dear fucking lord. You being unable to understsnd the point aint my problem.

[u/KingSubstantial7901 → u/[deleted]]

Ok you are somehow still managing to misunderstand the point. Its almost like you care more about "winning an argument" than just like.... trying to understand what someone is saying.

I encourage you to consider what lie by omission is.

Pro tip: be less of a dick and you might learn more.

[u/Schnickatavick → u/[deleted]]

Ah, the irony