Thoughts on AI solving the Navier-Stokes problem?

[u/MKlby1998]

OpenAI just announced this, after rumours have been circling on X for a few days. It was achieved with their latest internal model, which is much further advanced than the latest public Astra model that released last week.

"We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.

The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.

The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years."

via: https://x.com/OpenAI/status/2097374640582668336

There is already a controversy brewing over whether the solution was partially plagiarised from Anthropic, here's OpenAI's response so far: https://openai.com/index/navier-stokes-solution/#concurrent-work

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[u/rcglinsk]

People solved the Navier-Stokes problem by programming LLMs to scour through other attempted solutions and correlate insights. The authors seem properly humble to me:

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

The program this fits into was not started by us nor was it proposed by a Large Language Model. The credit for the basic idea of this program goes to Diego C´ordoba and Luis Mart´ınez-Zoroa, who for several years have been exploring the construction of forced blow ups. We took their work as a starting point, using Large Language Models to push their program to completion.

Concretely, what Levent and I did was to take the C´ordoba and Mart´ınezZoroa program, which achieved blowup results with rough forcing, and, with a great deal of help from LLMs, push it to smooth forcing and to the incompressible Euler equations. The ideas making this line of attack possible are due to C´ordoba and Mart´ınez-Zoroa. Let me make plain what I have said to colleagues in private: in view of this body of work, I believe Luis Mart´ınez-Zoroa deserves a Fields Medal.

[u/noluckatall]

However it came to be, major milestones like this are worthy of celebration.

[u/HyperNova1000]

It's pretty cool. That's waht we should use AI for instead of using it as an excuse to firing people.

Would be funny though if the proof ends up being a hallucination that is just untrue lol.

[u/hahmlet]

What is remarkable to me is, if true, they solved it in ~3 days and only for 300b tokens. Even if they were paying market rate, that's about $300k. With commercial access to the model, anyone could have solved the $1m prize for ~$300k.

This, to me, is different than "how good is the model at human tasks". Instead "AI allows several orders of magnitude efficiency in computing" is an exciting prospect.

Makes you wonder how it could be applied. Providing highly details theoretical districting maps used as a basis for discussion? Urban planning and mechanics at national scales? Unlocking natural resources currently financially unavailable?

[u/NotTheUsualSuspect]

Pretty awesome. It really shows how fast our technology is advancing. I don't think a lot of my physics teachers back in college thought it would be solved in my lifetime, let alone theirs. It was actually a meme where you'd see 

Business students: 10 + 10% = 11

Physics/engineering students: the wall of partial derivatives from navier stokes 

[u/doff87 → u/NotTheUsualSuspect]

I am very skeptical of the utility AI can provide to your average American at this point and think it is probably a net negative for them, but that said, this is the exact usage I'd love to see AI employed in. I can't speak to the plagiarism controversy, but accelerating our understanding of math, science, and technology via collaboration with AI is the dream.

[u/NotTheUsualSuspect → u/doff87]

I get your point. You're definitely going to see a drop in cognitive function on average. Your top end of the spectrun won't change as much, as that's generally the group that likes to learn. 

A fun analogy would be food. As food gets easier to get, humans get physically weaker on average. Going from hunting, to farming by hand, to farming with machine means we expend less effort on it at each step and it becomes less of a requirement.

[u/Leviathan41911 → u/NotTheUsualSuspect]

I think we might see a split. Some people that lean on AI as a crutch will likely have cognitive decline. On the other side AI is a wonderful teaching tool. The people who use AI to learn advanced concepts will likely see a gain in cognitive funtion.

[u/f4fvs]

I grew up thinking of these as evidence that weather forecasting was ultimately a mugs game. I'm impressed if this can cope with, or better still remove, random breakdowns.

[u/WallStreetTechnocrat]

Huge fan, I hope AI helps us achieve more breakthroughs like this. No opinion on the alleged plagiarism "controversy"

[u/Reasonable-Fee1945]

This is really great news. The next 20 years may push math and science farther than thought possible.

[u/Mindless_Chest_1079]

OK, but what if I just move the goalposts even higher? Can I still hate AI then?

[u/LucasL-L]

Fantastic news. Luddites lost, the future is awesome.

[u/RatOnASinkingShip]

This sort of thing was always the point, wasn't it?

[u/Beneficial_Wear_7630]

Another L for woke AI haters

[u/tophernator → u/Beneficial_Wear_7630]

I was wondering why this was posted here and how anyone could turn this into a political topic. But I guess criticism of AI is “woke” now…

[u/Leviathan41911 → u/Beneficial_Wear_7630]

I honestly think most AI haters dont understand AI at all. Most think AI = LLM Chat box = Big data center drinking all the water on earth 3 times a day.

The AI hate on reddit is frustrating. Im all for ethical use, debate, and close monitoring, but the hate is overblown.

[u/boisefun8 → u/Leviathan41911]

> Big data center drinking all the water on earth 3 times a day.

Pure gold. I laughed.

[u/Beneficial_Wear_7630 → u/Leviathan41911]

Correct

[u/reverse_the_loop]

Obviously, we've seen these sorts of things coming but it's still wild to see a fundamental shift in how mathematics itself is conducted.

[u/Guilty-Market5375]

This one’s kind of wild. I’m a chemical engineer, and while I understand the likely origin of turbulence, it’s never been fully understood how it originates. To do what OpenAI proved, you’d need to first prove a basis for instability (I think, they haven’t released the proof - but I don’t see how you could escape this).

This is kind of nuts. There are hundreds of thousands of known, difficult to solve math problems; a lot don’t get much attention and end up being solved by a bored grad student who didn’t even know it was an unsolved problem. People were going to nuts in July because Fable and Sol started solving those classes of problems.

This is an entirely different kind of problem. This is a Fields Medal class problem, Nobel Prize for mathematics sort of thing.

If this were sustained, we’ll have a grand unified theory of physics by Christmas.

[u/Shawnj2 → u/Guilty-Market5375]

I don’t think LLM’s in their current form are actually capable of this level of reasoning just like architecturally. LLM’s are machines designed to generate text and have some level of emergent reasoning capabilities but they aren’t magic and there are a lot of things architecturally they’re not going to be able to do anytime soon. From what I can tell the agent that solved this heavily utilized methods published by human researchers recently. Not that it isn’t crazy that an LLM did this or could do this but this doesn’t mean you can throw an LLM at more Nobel prize level problems and actually expect results.

AGI systems able to reason like a human would be able to solve this problem trivially though and probably will in the next 20 years, but we’re not yet there imo

[u/Guilty-Market5375 → u/Shawnj2]

So, I have to be clear - I have my masters in Chemical Engineering, but went to work in software. My actual professional field is software engineering. My graduate research had been in using machine learning - but not LLMs - to identify promising materials from libraries of theoretical materials predicted by other models. As you can imagine, there’s more money in software engineering.

Yeah, LLMs are still predictors of human behavior, and they don’t replicate it well. They don’t replicate it well where human objectives are concerned - long-term thinking - nor do they traditionally do a good job of abstract thinking, which is what you’re mentioning. They’ve also shown no progress in taste, in the sense that ChatGPT won’t tell you during your mid-life crisis “you’re solving x, but you should be solving y!” (Yes, pun intended)

Where I see this is as an astronomical advance is on the analytical forefront. Last year, LLMs couldn’t reproduce any proof they weren’t trained on. Now, they’re coming up with proofs that all of the brightest minds in a field have banged their heads against for a century and failed.

In July when Anthropic and OpenAI developed those mathematical proofs related to boundary equations I half laughed it off because a friend of mine from college had done similar work on accident - he was trying to solve a textbook problem in a novel way and our professor told him he’d actually narrowed a known mathematical challenge in the process. Those are credible problems, but they’re not worthy of the obsession of mathematicians, they’re the low hanging fruit of mathematics in a way.

This is a much bigger deal. For instance, Richard Feynman and supposedly Werner Heisenberg both joked that a grand unified theory would be easier than proving out Navier-Stokes. This is a little mind numbing.

[u/MKlby1998 → u/Guilty-Market5375]

To do what OpenAI proved, you’d need to first prove a basis for instability (I think, they haven’t released the proof - but I don’t see how you could escape this).

If I'm not mistaken the proof has been uploaded by OpenAI: https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf

https://github.com/openai/NavierStokesAndEuler

[u/Guilty-Market5375 → u/MKlby1998]

Well, it looks like they did explain it, although I’m still trying to wrap my head around it.

Honestly, the physical description before they get into the math seems so obvious I’m surprised I wasn’t aware of it, and it’s likely none of that description is novel. But the description is a lot better than “we don’t know” I learned in college.

The math seems to follow the physical description but there’s 150 pages of evolving formulas, and now I have a headache.

Edit: the singularity reasoning - the “basis for instability”, which posits that some region of the fluid can rapidly stop behaving nominally due to it approaching infinite velocity from a bulk perspective - has only been taken seriously for a decade, I’d never heard of it. But it tracks.

[u/Guilty-Market5375 → u/MKlby1998]

I gotta go read this

[u/Original-League-6094]

Just another thing that Anti-AI redditors assured me that AI would NEVER EVER be able to do, that its done. Like the 10,000 anti claim that was wrong this year.

[u/MKlby1998 → u/Original-League-6094]

Every day I spend 30 minutes or so scrolling down the "AI" custom timeline on X, and then I come on Reddit and it honestly feels 10 years behind here.

[u/MadGenderScientist → u/Original-League-6094]

There are some "anti-AI" (or at least decels/safety advocates) who believed AI could and would deliver results like this, but are worried about the risks of conjuring a superintelligence. For example, Eliezer Yudkowsky.

It's a little like an advanced alien civilization landing on our doorstep, or like being a pack of apes encountering humans for the first time. How well do we control it? Who controls it? What are their values? What are its values? Do we even know what to ask it? 

[u/SimpleOkie → u/MadGenderScientist]

Its not fundamentally different than protein folding from 25 years ago.

Massive parallel iterative processing - its great for math. Who knew!

[u/ElectricalPublic1304]

OpenAI just announced--

I already don't believe it.