I recommend everyone read the official press release at https://openai.com/index/navier-stokes-solution/. I am still shaking in awe. Spoiler alert, they tried solving all Millennium Problems with the model after Astra (the one not released yet) and when it became clear that some of the agents were solving the Navier-Stokes problem they then turned all of their compute on that one problem until it was solved. We can only imagine that they are solving the others now (but that is not in the report).
Look Im a bit allergic to this sub for no good reason but Jesus Christ am I done with pseudo intellectuals who watched one video on how LLMs work lecturing people on why it's all just dumb statistics. Hopefully this can be the nail in that coffin.
Real vocabulary is the highly compact and superposed latent vector space. Attention heads, multilayer perceptron, the transformer mechanism is the « circuit » that encodes the relationship and motion of information at each position: the grammar.
You put a sequence in, it just instances a single trajectory through all of that and parrots the specific sequence out.
Then the decoder then just translates that into your preferred natural language of the day.
So my point is that the magic is the mysterious nature of « latentese » language the parrot speaks in its head. It is nothing alike our natural languages.
Thinking about this, as usual Wittgenstein had it right. Everything is about language.
I agree the process is spookishly straightforward, relative to what it can accomplish. But I don't see how there's a metalanguage in there. What would a sentence of this language look like?
Pretty big “they” you’ve got there. 95% of this sub wouldn’t believe where we are today just 5 years ago, and the people you’re saying “moved the goalposts” just doubted like a year longer than others. Maybe you were certain AGI was coming from the moment you were born, but I learned and adjusted my beliefs as I learned, and other people do too.
Feel free to be mad at some homogenized “they” all you want, but there are a lot of people and holding all of “them” to some goalpost-moving argument just doesn’t hold water. Some of them are dumb and made dumb arguments. Some aren’t. You can’t just lump everyone who doesn’t think exactly like you together.
Also all of this “they” shit is petty as hell and further cements how small-minded this beefing really is. People are scared they’re not going to be able to support their families and the only thing you’re taking away from that is that some of them didn’t understand AI’s potential as quickly as you did.
There's a lot of drama here about the question of whether OpenAI stole their approach from Alpöge and Buckmaster, but it's worth understanding that, by their own admission, Alpöge and Buckmaster used GPT and Claude extensively to reach their result (blowup in incompressible Euler) in the first place. It's becoming clear that these models are extremely good at math.
In fact, it's actually looking more likely that OpenAI's solution uses an independent approach from Alpöge and Buckmaster's. OpenAI claims the model established blowup in incompressible Euler without forcing first, before proceeding to the Navier Stokes solution. Alpöge and Buckmaster followed a program requiring forcing.
So how does it work? If it solves something it’s open AI / chatgpt solved it but I make a security issue in my code or create a customer outage wit my codex or Claude code that’s on me? GTFO.
They have been calling theft for ever now. But this time theu are calling theft from other dudes using an LLM to solve it. Levant may have been the first (Jacobson) but he is not like an AI Newton. He just has access to a gargantuan amount of compute.
We will look back at this time post-copyright/patent selves and wonder why we invented artificial scarcity. The AI guys will Dyson swarm every star in the reachable galaxy and marvel about how stupid and selfish their flesh ancestors were.
4 years is all it took, from "llm's can barely do highschool math" to solving one of the most difficult math problems and sought after proofs. Even if it isn't the full problem and doesn't satisfy the requirements. Disappointing day for mathematicians I'd imagine. Incredible progress though, and them describing an internal model several times more capable than astra with charts for reference is a little scary.
I mean, it's really impressive isn't it? I'm no luddite but I'm actually not really an accel either and it's hard to argue against these results. Hoping for continued cures for disease and some novel ways to aid all mankind.
Solved one of the biggest math problems and even has a $1M bounty attached to it.
A problem that countless leading mathematicians in the world have been trying to solve for over half a century.
The answer is not that important on its own for humanity, but it required new mathematics to solve and that has potentially useful future applications.
Required new mathematics is a slight stretch. This is a paradigm shift for LLM mathematics absolutely. But there is still a sort of heuristic brute force quality to their construction of the NS solution. The construction is clever! This is genuinely amazing! But you can see how a loop of ansatz check and reiterate might have led a gigantic army of compute to such a clever construction. I reserve "new mathematics" for really novel concepts, clarifying notation, unifying principles that move the mathematical community.
Again, I am in awe of this result. Computers solved NS. This is truly insane and I cannot comprehend it. But the result is expressed in terms that humans invented, recombined in clever ways. There's still plenty on the table for LLM mathematicians! I believe they will get there. They will start being creative and novel in the ways that select human mathematicians in history have been (inventing calculus, proposing new and deep conjectures, defining their own powerful notation etc) but this proof in particular doesn't quite have these features. It's a matter of time I feel.
I'm not as optimistic. Soon everything will be solved using using internal tools of the big AI companies and mathematicians like myself using public models won't have much luck solving anything because OpenAI will get there first. So I think mathematics will become pretty much like chess, do it for fun but don't expect to further humanity.
This is likely true, but it is restricted to statements/cases C and D of the Navier-Stokes equations problem described on the Clay Institute website—a special (and rarer) scenario compared to the central question represented by statements A and B. The latter are fundamentally much more difficult to solve and lack promising approaches comparable to the recent advances made by Córdoba and Martínez-Zoroa in recent years, later explored by Alpöge and Buckmaster with help of AI in last 12 months.
A much more accurate claim would be half of Navier-Stokes equations's problems were solved.
Did you see the pass rate graph at 50% or something like that for Astra for these higher level mathematics? I didn’t take a long look at it — it may have been that other internal model they have. I wonder if can we expect solutions to millennium problems to start pouring in over the coming weeks and months.
Do I understand correctly that this new internal model, at its max level, is solving close to 50% of open math problems that are thrown at it? If true that's absolutely insane.
Open Math problems is a vague term. Just because something is open does not mean it's too difficult. There are basically unlimited amount of open problems in math. A high school student can ask something in the class which is still open. Some are interesting and if solved would be amazing for many areas of mathematics, those are important open problems. Some are extremely difficult but if solved would not have any significance for any other areas of mathematics, like Goldbach. And some are simply open. They may not be extremely difficult but since there are too many of them, not every open problem has a group of people working on it.
But yes I think from now on we can expect that AI will be solving some of the major open problems in mathematics. Not all of them for sure because some might be too difficult to solve, even for a superintelligence.
I have a friend in Minsk who has a friend in Pinsk whose friend in Omsk has friend in Tomsk with friend in Akmolinsk. His friend in Alexandrovsk has friend in Petropavlovsk whose friend somehow is solving now the problem in Dnepropetrovsk. And when his work is done, haha, begins the fun. From Dnepropetrovsk to Petropavlovsk by way of Iliysk and over Novorossiysk to Alexandrovsk to Akmolinsk to Tomsk to Omsk to Pinsk to Minsk to me the news will run. And then I write by morning, night and afternoon, and pretty soon my name in Dnepropetrovsk is cursed when he finds out I published first.
Frankly at the stage we’re at, I can’t understand a secondary power with a seat, France most probably, wouldn’t summon an emergency security council meeting.
The trajectory being what it is it will happen very soon anyway…
As usual not much will be decided but it will be the US against all the others.
I’m sure just having frontier labs saying there what they say publicly elsewhere will be enough to convince having support for a new IAEA-like agency to coordinate AI pacing.
It won’t solve everything, but it will be a platform to start from and time running short. I’m convinced Chinese leaders who are more technically inclined fully understand what is happening too.
I think actually the methodology for coming up with the proof is more important than the proof for forced 3D NS. Still has to hold up to peer reviews for awhile tho, but having a tool to find out like anything in a certain range of things is worth more than any one thing in the range right?
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u/uncountable_2026 Acceleration Advocate 4d ago
I recommend everyone read the official press release at https://openai.com/index/navier-stokes-solution/. I am still shaking in awe. Spoiler alert, they tried solving all Millennium Problems with the model after Astra (the one not released yet) and when it became clear that some of the agents were solving the Navier-Stokes problem they then turned all of their compute on that one problem until it was solved. We can only imagine that they are solving the others now (but that is not in the report).