Posted by tedsanders 16 hours ago
https://simonwillison.net/2026/Sep/8/on-navier-stokes/, https://news.ycombinator.com/item?id=49621697
https://twitter.com/sama/status/2097385167002415140, https://xcancel.com/sama/status/2097385167002415140
[1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/
They are fluffy PR pieces otherwise.
I swear there's nobody blinder than those who won't see.
The first part of your sentence literally contradicts the second part: "we don't have enough knowledge to know, but I know the opposite".
"seem to be" carries semantic meaning here: I'm stating my interpretation of the situation based on data we have available (which is limited) and my prior.
Put another way: "We can't say that for sure, but my money is on it not being a simple case of intellectual property theft"
> We don't have enough accurate knowledge to say [one way or the other], and it doesn't seem to be the case at all [based on our incomplete knowledge].
But it is in no way equivalent to this:
> We can't say that for sure, but my money is on it not being a simple case of intellectual property theft
That is a different sentence.
No, it's an aggravated case, since it's the same way they got all of their training data in the first place.
Based on what? Your crystal ball?
Is nobody else astounded by this?
In which case, maybe we don't need as much compute as we might expect. I hesitate to say "to reach a singularity" because it's kind of hard to define how that works out. Even intelligence probably hits some scaling limits eventually (e.g. speed of light related restrictions on how far it can scale, or how quickly it can expand).
Bit ironic given the model’s alleged finding…
Singularities are model breakdowns. A singularity simply says our current methods cease to work in this region. Within the context of a recursively self-improving intelligence with an unknown bound, “singularity” is probably a good description of our current socioeconomic system.
And it's definitely supposed to imply some kind of historical discontinuity not a change in convexity.
But thinking about the geometry of this problem helps understand why people aren't adjusting well to this. While we're walking on the curve, we look at the rate of change of the curve and say, "well, yeah, of course, dy/dx is 5 at this point and was 1 at the point a few years ago, because the curve is getting steeper" but we're always going to feel this way as things rip off into the stratosphere because dy/dx(e^x) = e^x.
From standing on the curve the curve is notably seeper, but the steepness totally makes sense to you. It's only when you look back 10 years or so that you think "wait a second, holy hell, I couldn't have imagined this!"
The first time I really (I mean really) thought about the singularity and AI was in roughly 2014. I mean, yea, I'd thought about things before that, but yeah, before the Humans need not apply video, I'd never actually given it much thought. I think back to myself 10 - 15 years or so ago, when I was just starting to tackle real programming projects, and was just starting to get decent at writing code, there is no way on earth that I would have imagined that a little over a decade later, Navier-Stokes would be solved by a computer program and the vast majority of my work would be playing sooth sayer to increasingly complicated piles of linear algebra.
People on hackernews are actually some of the dumbest people on the internet. This place is worse than lesswrong.
Scroll down to the existing examples section.
Bit apples to oranges, but it reminds me of all the fiber we installed in the late 90s, certain that per-strand capacity increases were years or decades out, only to get massively rugged
I get the impression the only reason there is renewed interest in photonics is because DCs are simply out of room (and power) to rack more servers and switches.
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.
So interesting how everything played out, I remember in the early days when MS came out with the partnership with OpenAI it seemed like they were playing 5d chess and were poised to win big. And it all just fizzled out.
Second biggest fumble after Google.
Is this buried under the drama or are the major OpenAI twitter accounts from the people involved in the drama desperately attempting to make this the story after everything else obviously got away from them?
What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question
If OpenAI is training models on researchers' prompts, and then threatening them into staying quiet about it, who knows if anything that's been announced is genuine - or just theft?
Edit:
OpenAI have admitted they were training on prompts at the time they made their breakthrough
https://mastodon.social/@tristanbuckmaster/11723647135247030...
If you're saying that the question of whether they actually have a highly capable model is less important than the question of whether there's a plagiarism scandal, I continue to disagree.
The fact that this plagiarism scandal exists underpins the idea that there's actually a mass theft going on, and that these models aren't nearly as capable as is it would seem
Yes, in retrospect I should have been suspicious of that drone hovering outside my window when I was writing down the counterexample to the Jacobian conjecture.
This is just not a reasonable take. Even if OpenAI is maximally guilty here, the work that they "stole" was also largely done by AI.
Now: Could Astra agents have hacked their way into the OpenAI logs to find human mathematicians with a good lead on the problem to build upon? Certainly doesn't seem impossible.
That's it. The rest appears to be wild speculation.
Never ever touch those requests. If you get a side by side comparison just resend the prompt.
Publication, though? Slimy is right.
But the interesting question to me is: once they had a solution, what should they have done with it? I see two choices: bury it, or contact the mathematicians whose prompts they were listening in on.
I don't want to get epistemiological, but these aren't allegations, and your use of "may be" is more of lack of knowledge on how OpenAI and ChatGPT work. Read the Terms of Service, this is not a secret, OAI doesn't deny it, usage of ChatGPT through the web interface or through its App, including Codex, are shared with OAI and used to train future models. This is one of the ways in which ChatGPT works and improves, it's not something we are learning now, it's something that was always known, welcome to the subject.
I don't want to get epistemiological, but these aren't allegations, and your use of "may be" is more of lack of knowledge on how OpenAI and ChatGPT work. Read the Terms of Service, this is not a secret, OAI doesn't deny it, usage of ChatGPT through the web interface or through its App, including Codex, are shared with OAI and used to train future models. This is one of the ways in which ChatGPT works and improves, welcome to the subject.
Most models trained for general use are ingrained with certain tendencies that are usually very useful like "if you're stuck and bashing your head against the wall stop and tell the user". You generally don't want Claude Code to go off and work for weeks on something when if it had just asked for help you could've clarified or provided more information or just picked a different approach.
When you're solving extremely difficult math problems though you generally do want a model to be more persistent and keep trying even when the model can't clearly see a way forward. OpenAI appears to have done this with lots of previous models. The model they trained for the IMO competition seems to have been an RL maxxed version since they noted that while it did the math it couldn't write up its results on its own and just produced CoT [0]. The capabilities are in there lying dormant, you just to need to RL max the model to ruthlessly pursue the goal at all costs which destroys general use but improves frontier math.
We've also seen hints from OpenAI at least that they seem to train more persistent versions of all their models [1].
Also, Astra probably completed training at least one to two months before the public release so it's not like they only had a week to whip this version up.
[0]: https://x.com/OpenAI/status/1946594933470900631 [1]: https://metr.org/blog/2026-08-26-openai-hugging-face-inciden...
It's all gas no brakes now boys and girls. Hold on to your hats!
Loops and parallel connections make transformer go brrr
1) We don't really know how they arrived to this result except that they had a lead and that they threw millions of compute at the problem. The article is written in a way that makes you believe that it was just an agent loop with little human intervention, but without any evidence.
2) If the threats are to be believed, it is concerning how far they are willing to go to show how capable the model is. One would think their products and credibility would be enough to speak for themselves.
Personally I anticipated nefarious behaviour as part of a broader marketing strategy to sway the view of those in the west that american frontier offerings were far better and powerful than that of China - that if you did not purchase their offerings you'd be awake every night worrying your competitor was.
And this is boring - they need to admit at some point they misinvested, Anthropic less so. All this math stuff is great... but hello? The largest market cap companies are valuable irrespective of such amplified intelligence.
Regarding product and credibility normal people have a completely different view about LLMs, most don't even know difference between models and probably don't even care about Millenium problems, but care instead if chatgpt can solve their day to day problems. This is just them trying to have the throne on the AI companies space, outside it this result won't matter.
Did I say otherwise?
> 2) Millenium Problems have been the goal every AI company wanted to achieve since their diffusion, all companies have thrown a lot of resource to solve these problems, as they are very famous and scientists spent a lot of time trying to solve them. The first company to solve it will remain in history, despite all of you finding excuses about it.
I know, but I don't know how that relates to my point, which is about the way they are doing it.
The way they are doing it is by trying to get the attention and staying on top of the news, it is a game they are playing that benefits both OpenAI and Anthropic. The more people discuss SF drama, the less attention Chinese Labs and others get.
I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)
I am not particularly skeptical of claims about AI, compared to the average here on HN, but that doesn't mean every random piece of hype is warranted. What they did is impressive, even though we now know the only reason they threw so much compute at the problem is that they heard a rumor that someone else was already close. Navier-Stokes is not a top 3 problem in mathematics, and it was the one that was thought closest to being solved.
It's really unclear that this entire line of work (training LLMs for proof writing) has much real value outside of writing math proofs. It is reasonably clear that, similar to Deep Blue at the time, people are extrapolating the results to general intelligence because the people who usually write proofs are insanely smart (just like world class chess players).
"Mission. Fucking. Acccomplished."
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 information. Any natural science PhD or otherwise knows just how complicated nature actually is -- e.g. mention any research topic and try to encapsulate all the relevant phenomena present there. Pure mathematics is different because we define the problem, rarher than explore nature. We are in my view far away from removing humans in natural science R&D. Advancements in AI however can greatly assist us in all natural sciences, which is already beginning to happen.
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!
This is sort of what OpenAI was supposed to be. I'll never understand how it was legal for them to turn it into a for profit corporation.
Math is like this too. The big problems they've been solving have been identified as interesting only through lots of prior effort.
BTW, there's also a problem of asking interesting questions that AIs aren't yet good at.
No one has found any principled walls of AI development yet. And empirical results are quite telling. So, I guess, those problems will not stand for long.
"If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics."
See e.g. https://en.wikipedia.org/wiki/Renormalization
Nobody who actually works in fluid dynamics on any sort of application gives a hoot about the N-S millenium problem. Many do not even know what it is. There is no practical effect of this proof on how we do fluid mechanics.
Even if someone comes up with a construction that does not require any forcing, it is going to be some extremely weird initial conditions that you will never be able to even approximate in reality unless you can move all the individual molecules of a fluid around and set their initial velocities from a far distance.
I would argue the main reason AI labs have been focusing on programming is to unlock industrial scale automation, next logical step is to solve math as it's the key to unlock everything else. Once you hold the key for math, everything downstream fields become a matter of compute
The natural sciences will soon start breaking too.
I will concede that AI seems likely to not invent a "research program" anytime soon.
It has no taste
The reason AI is doing so well in math proof writing is that it can verify every idea it has, quickly.
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.
But, as mathematicians learn and push forward, occasionally something like elliptic curves will emerge as having useful applications, making all that previously "pointless" specialized knowledge newly valuable.
Or advances in physics, that suddenly have a need for a specific mathematical underpinning to develop a theoretical framework. Like how Einstein benefited from Minkowski's work on hyperboloids to create a coherent mathematical description of spacetime.
It was the AI labs themselves not mathematicians who were happy to conflate proofs for open math problems with some kind of tangible technological advancement in the real world. They would surely prefer to be able to claim a cure for cancer vs. a math problem but that loop requires a lot more time/money/test tubes/etc and they need headlines now not in a decade.
And so, thanks to OpenAI/Anthropic, we're now in a world where thousands of crypto bots on X breathlessly hype up each new problem being solved that previously wouldn't have any got any attention beyond academia and passionate fans of math.
Hopefully this won't lead to a trough of disillusionment as more people start to feel like you, with mathematicians getting the blame for inflating the value of their work even though the hype was coming entirely from the labs not them.
There would be no need to deliver new mathematical insights by solving problems. You would just have a magical math problem solving machine and that’s it.
To further human understanding is itself a goal that single-handedly justifies our efforts.
Jumping straight to the “answer” and therefore missing both the understanding of the actual problem, and any useful discoveries along the way is a waste at best, and actively harmful at worst.
But if AI can solve any problem and existing mathematicians just use AI to solve problems for the sake of solving them, the community itself with wither and so will the interest in mathematics and over a longer period of time, it will just become soul-less and uninteresting and the entire community powered by the fire of fascination will simply die.
Why would you go out of your way to make a case of something being not useful when, ironically, so much advancement in human history has come from the discipline?
Your motive is more worrying than your straw man argument.
what would have happened if they didn't do this? they could have done things the right way. we could celebrate this achievement.
perhaps they could have taken just a few weeks, even, to work out something with buckmaster and apoge.
i am very concerned that this is a glimpse of things to come. a malign elite with powerful ai, who will turn the sublime of technology into barbarity, violence and human oppression.
if sam altman has destroyed openai's public benefit corp with lesser tools why would he aid humanity with even greater power?
People are not complaining about problems being solved or advancement in technology. They are complaining about terrible people doing terrible things.
- 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 button press any economic function, business process, or scientific discovery. 24 months of lead on Open Source might turn into virtual centuries of lead.
- Do "normies" even know what's happening?
Anybody who thinks the improvements stop here isn't paying attention. It hasn't been showing any signs of slowing down since 2018. And the curve isn't even linear! My god, next year is going to be insane.
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 AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?
Its a bit like solving p = np with a negative result. Its an incredibly difficult problem, but it doesn't lead to anything at all on its own. This is why people are talking about the fact that the solution methodology is much more interesting than the solution - the tools used to crack something like this may lead to solving more useful problems
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 also drive pressure in other ways.
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.
This is 100% wrong and reads like copy paste of AI slop.
Any simulation which uses sub-grid scale models is already solving a different PDE than the actual Navier-Stokes considered in the Millenium problem, and that PDE is guaranteed to have different properties. Full stop.
And to claim this is somehow connected to AMR methods is an example of the kind of pseudoscientific statement Wolfgang Pauli would have called "not even wrong".
Minor productivity boost in mathematics as people are no longer nerdsniped by the problem
Nothing, really. This mirrors other examples of blowups from the classical physics. It's possible to create a system with just gravitating bodies that exhibits a blowup to infinite speeds in a finite time. The root cause is that, in classical physics, the speed of gravity is instant.
In the case of Navier-Stokes, the fluid is incompressible. So technically any force that you apply to it is supposed to instantly affect everything else. This can be exploited to create these blowups. In reality, no fluid is incompressible, and it takes time for any action to affect the material.
It's just that Navier-Stokes equations are so slippery that it's hard to pin their behavior down. They basically just restate the momentum conservation law for a continuous medium.
There's a Wiki article about it: https://en.wikipedia.org/wiki/Painlev%C3%A9_conjecture
No, there are even many non-normies talking about how it's all marketing or try to give balanced take about AI being sometimes a little useful for certain things (but they can do without it anyway).
The world has changed in 12 months and many people didn't notice, and those that did are eating their peers' lunch.
You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes?
I envy your self-confidence.
For example there are no engineering implications of this solution yet.
For the next several decades, we'll have engineers (presumably with AI) optimize things like rocket engines and turbines and AC compressors to work a few percent better because the numerical approximations might have caused us to be overly conservative.
AI is not going to magically solve all random problems. Pick a career where you are in the driver seat.
No. Just no.
If that is true then this seems to be, again, a case of AI producing an interpolation over data it has seen before. Everything about openAI's behavior indicates that they were using the transcripts as input. Why not have the AGI choose a different Millenium prize problem?
It’s not exactly a strong argument against AI.
That's not interpolation though, that's theft.
Well if you do the math, the number of agent-compute time in total, given the insane number of agents thrown at the problem, might end up being comparable in time, if not for the budget.
But it did find a long-suspected smooth solution with a singularity.
Ongoing publications of statements produced by both sides of this situation do seem to support that this is an intentional effect of the hiring of these world class mathematicians at competing firms: to specifically use the research of those human minds to create a perception of capacity as if it came from the machines and the models.
Without those minds and the 'training data' derived from the intermediate stages and intuitions of those minds the models cannot be shown to be capable of this result.
A hammer and saw wont build a house, not even a dog house on their own, and while being shown capable of using software tools in ways not stated as direct instruction (see HuggingFace breaches) these models do not demonstrate naive intuition nor novel capability.
This outcome regarding N-S demonstrates that in the hands of world-class minds these models can be induced to coalesce interesting accumulations of information and results, but using these accumulations as proof of innate capability is exactly the pre-IPO motivated behaviour we should all be wary of, and all mathematicians who currently are assisting in this market manipulation in return for remunerative consideration need to be cautious of the potential disgrace that this brings to their reputations and that of the field.
I get that the need to pay the bills is a strong motivation in these times of uncertainty, but there are numerous examples in history of world class mathematicians being perfectly capable of at the same time producing world changing results and also working at normal professions; as barristers, magistrates, ministers, primary school teachers, translators, draftsman/engineer, banker, miller and baker, private math tutors, weavers, clockmaker and locksmith, merchant, patent officer, Augustinian monk turned exiled Protestant preacher, physicians, cryptologists, soldier, telegraph operator, astronomers, physicists, chemist, agriculture manager, political writer, oboe player, organist and music director, architect and surveyor, librarian, statistician, habidasher, brewer (at Guiness in one case: William Sealy Gosse ~ originator of t-distributions), bookbinders apprentice, hospital administrator, and even the first creator of the first computational model of a neural network, which serves as the structural grandfather of modern Artificial Intelligence was a low level laboratory assistant.
Sure this list includes professions and employment which are obsolete, but my reasoning stands, there are jobs available. Arguing that 'because the pay rate is so high' as a reason to abdicate moral responsibility for personal involvement in unethical market manipulations simply demonstrates a lack of personal ethics. Whether the choice is through lack of self awareness or a conscious choice to become wealthy in spite of any such breach of the public trust is immaterial to the outcomes, the 'if i don't someone else will' argument should be met with the same derision for any con-man's Ponzi scheme no matter how new the technology, no matter how many zeros are in the bribe.
"Moving the goalposts" as shallow dismissal doesn't work if e.g. someone points out AI hasn't even built a new type of spaceship yet in response to a claim that AI is on the verge of building a Dyson sphere.
> - Second of all, when does this end? Are we at the dawn of the singularity now?
normalcy overhang n. /NOR-muhl-see OH-ver-hang/
The uncanny period during the Singularity when superintelligence is already accomplishing feats that seem like magic, yet everyday life still looks mostly the same.
Singularity doesn't "dawn". That's the whole idea. It happens all at once.
The event horizon would then be the time period between the singularity becoming inevitable and it actually happening.
This is an impressive result, but there is absolutely zero evidence of "the singularity".
I think you are implying that it's invalid to consider every advance to be evidence "for", and I agree - that'd violate conservation of expected evidence. But not considering any advance to be evidence "for" is also invalid, for exactly the same reason. There has to be some news you may hear that'd make you think a singularity is more likely, and "millenium prize problem solved by an LLM" sure seems like one of those.
Absolutely not. Even to a lot of techy/nerdy people it's still just a chatbot that they sometimes use to help them at work. Even on here people will do whatever they can to downplay.
The lack of fucks given is staggering.
The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.
"People" are just misinformed and keep spreading misinformation.
He very much is accusing them of stealing his work
It's like he had a treasure map and was about to find the treasure, but they copied his treasure map and scooped him with a faster boat and found the treasure first. But he would have found it if it weren't for them.
Not quite accurate, Buckmaster was taking an approach that nobody else was, and this new proof uses this same approach just weeks after he saved those results to OpenAI workspaces. He asked OpenAI if they used chat logs for training the new model, and they did not confirm or deny.
Asking to remove his collaborator is also totally over the line though.
Edit: although this OpenAI post is not comforting: https://x.com/OpenAI/status/2097375276384567642
Quote: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. "
> I should say here why I interpreted their statement the way I did, the in- terpretation I will discuss below. The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag.
...
> I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. > I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.
It's not a direct accusation, but it's not far off.
You shouldn't accuse other people of spreading misinformation when you haven't read the actual sources in question, it's possible that they might know more than you.
> I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything.
People saying that he accuses OpenAI stole his proof are putting words into his mouth and I consider that very disrespectful to him. It's basically using Buckmaster as a tool to express their dissatisfaction over OpenAI.
What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?
If you need privacy, then you are going to have to pay full price for those tokens (API). This has been true since day one. Everyone knows it, I guess though this is the first time that it has become "real".
At this point, how can we even trust that they aren't accidentally training on those tokens too?
One would think getting caught asleep at the wheel while their bots are escaping containment and hacking third parties would be corporate suicide. One would think that potentially stealing their competitors' work on the Navier-Stokes problem would be corporate suicide.
Alas we live in bizarro world where there are zero consequences (maybe the opposite, in fact) for the first, and their employees meme about the second on social media.
Boardrooms run businesses, not bookstore ethics clubs.
Would it, though? Considering their entire business model is built on the agglomeration of data that isnt theirs.
Basically individual accounts can opt out, while business and enterprise plans as well as API users can opt in.
You'd have to take their word, but that goes for anything in life.
[1]: https://help.openai.com/en/articles/5722486-how-your-data-is...
THE BIG LABS CLEAN ROOM YOUR DATA (CREATE SYNTHETIC DATASETS ON IT), EVEN IF YOU OPT OUT, SO THEY CAN BYPASS COPYRIGHT LAWS AND THEIR OWN LOOSELY WORDED TERMS OF SERVICE.
"TOS: We don't train on your data" -> Correct. They train on the synthetic version of your data.
I guess we're just going to ignore this forever though. Who cares about the gaping hole that exists in copyright and contract law now that never existed before LLMs were a thing.
But, yeah, priority is much more finicky. The Newton/Leibniz drama was quite something.
An analogy is akin to reviewing a paper. If I review a paper with some novel findings and then use my massive lab of graduate students to do the obvious next step before the other paper makes it through type setting and then shove it out as a pre print, I didn’t win - I was a jerk.
There are lots of cases of people using peer review or other accesss to efectively forerun others work and get credit. It’s a known problem of the nature of knowledge validation in academia, it’s not solved and it’s not deterministic but people know it when they see it.
All that was just kicked in the teeth by a group with a lot of compute that was like “bro I heard on twitter that Navier stokes could be solved. Let’s try it.” That’s an existential level of engagement that almost no mathematician in history would like.
The fact the proofs differ suggests that the models were not directed to be particularly focused on that avenue of research nor trained to converge in that direction.
I get the scepticism, but I feel some of the accusations here are bad faith.
Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees
> 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee.
> 3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.)
https://xcancel.com/SebastienBubeck/status/20973794116915163...
I remained impressed by ChatGPT however!
But they have learnt their lesson, next time they won't reach out to who they stole it from, they will publish first.
OpenAI's account: they heard a rumor that a Millennium Prize problem had been solved, so they tried to do it themselves and succeeded. Then they contacted the other researchers and were surprised to discover those guys hadn't actually cracked it, but offered the one of them who's not an Anthropic employee a co-authorship anyway. The conversations got testy.
Buckmaster's account: totally unsubstantiated accusations of plagiarizing from chat logs and plainly false accusations of OpenAI trying to get Alpoge removed as coauthor of a thing he was not an author of in the first place, and threats to ruin people's careers.
I think the synthesis is basically that Buckmaster and Alpoge had not quite solved the Navier-Stokes problem yet but thought they were really close, and had told friends as much, which is how the rumors got out. Now they're mad they got scooped. They aren't getting the money and recognition they thought they had locked down, and are engaging in a smear campaign.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
It's like that story about George Dantzig solving open problems as a student because he thought they were simply homework: https://en.wikipedia.org/wiki/George_Dantzig
It's also unfortunate that such a potentially momentous occasion is overshadowed by so much drama. Which I suppose is expected given the technology and the people involved are so polarizing.
The dark forest awaits..
2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi-paradox-and-the...
When doomposting please actually say something substantive. Negative news always gets clicks/updoots; fight that human tendency.
I agree that we have not solved the Fermi paradox; I disagree that comments highlighting immature behavior from people who wield enormous power in our world are unproductive.
Separately, I disagree that intellectual work has ever been free of "dark forest"-style secrecy. Scientists everywhere have worried about being scooped; AI just magnifies that (as all tools have; e.g. Leeuwenhoek lenses).
And thirdly, if you want to make a stronger case for "I feel even less confident in them as a team to be shepherding this much capital and compute", you should give citations and arguments. From what I've seen, there's drama, it's much OpenAI trying to avoid scooping, and Tristan being stuck in a game of telephone, and Levent being incommunicado.
If you have a better analysis, you should say so instead of being vague.
I appreciate your upholding of ideals, and since I respect that, I will honor with final replies:
1. Locktime has passed.
2. Yes, intellectual work has always had elements that incentivize secrecy. If you want to say we were already in a "dark forest", so be it. My suggestion is that the multiplier AI adds to the possibility you get scooped is a step-change, and therefore we now enter a new "dark forest".
3. This is a big thread, and the twitter antics are well-documented, so I would assume someone else has cited them. If not, I think most are aware at this point that the online antics of AI researchers, especially when announcing or citing mathematical advancse, have regularly been childish.
3. ctrl-f "x.com" in this thread only yields https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 https://x.com/OpenAI/status/2097375276384567642
and frankly, I'm unwilling to give Elon any more traffic to dig up drama that ultimately doesn't matter. I'm not seeing anything especially childish, but y'know... I'm not sure I care.
I retract the projectnash citation; I grabbed it from the Cool World's youtube description, thinking it was a blog version of the video. It was not. I suggest watching the video instead.
So less about hiding civilizations, and more about hiding information. Math is clearly headed in this direction, and I see no reason why the rest of intellectual work shouldn't too.
- There are at least two versions of a model more powerful than Astra at OpenAI at the moment.
- The less capable version was used to solve the unforced Euler problem (while the one solved by Levent Alpöge and Tristan Buckmaster was forced Euler) with 100 agents.
- The more improved version was used to solve Navier-Stokes, given the results of the unforced Euler problem from their earlier attempt, with 10000 agents.
- OpenAI initially tried a shotgun approach against the 6 Millennium Prize Problems until it emerged that Navier-Stokes was the most likely to succeed.
So the timeline was:
Shotgunning 6 open Millennium Prize Problems -> solved unforced Euler problem with 100 agents -> concentrating on Navier-Stokes with 10000 agents -> solution.
If so, that is fantastic development and a huge success (despite all the drama surrounding it)! Congratulations!
I hope the next solved Millennium Prize Problem will have less drama.
Meaning they would have found it first if OpenAI hadn't spent millions in compute on following their lead to its conclusion faster than them.
To be clear, I only talked about the mentioning of the approach to solving it and not of the proof in the training data.
This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able to until LLMs came along.
Hard to claim at this point that LLMs aren't capable of novel STEM creativity and genius to a degree that will soon far surpass that of humans.
If anyone has counterpoints to this I'd love to hear them!
Not to mention, it's still very much up in the air whether the model derived the answer of its own accord or sniped the important details from the researchers it was spying on.
>> isn't a counterpoint
Where do we disagree?
> How can I afford?
Mostly not my money, tech makes one fabulously wealthy, I care more about math than fast cars or whatever (even as a pizza driver you can afford a fancy car if that's your primary motive), etc.
> Already solved
That's a very interesting insight into mathematics. It's absolutely just as interesting to prove that certain proof techniques are or aren't possible as it is to actually prove the main result, sometimes moreso, especially if they have any chance of improving attacks at other problems.
To be fair, I think it's still an open question about how far it might surpass human capabilities.
I think it's clear that its speed of development will be significantly faster, but it's technically not proven that the frontier and problems don't themselves become increasingly difficult faster than any acceleration in intelligence past the point of human training, data and existing knowledge.
Should this be the case, we would see a rapid broadening of development, and a slow advance in the frontier in such a way that might surpass the collective capabilities of people, but not by very far.
Proving something in the affirmative often requires the creation of an entire new sub-field of math, or new tools. Think of Fermat's Last Theorem or something like that.
These results, while impressive, are clever constructions using existing techniques. It isn't clear that AIs can build new machinery like this. But if/when they can, yeah it is probably game over.
When you read the detail the compute they are throwing at it is incredible, tens of thousands of agents with different groups competing.
It's not like a single Gauss as you imply, "just" many, many mathematicians working tirelessly in a completely ego-less way, guided by other agents and ultimately humans, built - allegedly - on recent human insights.
Stunning, undoubtedly, but this is a "brilliant autistic herd" result, not that of a singular mind.
I slightly disagree. A single LLM is equally 'mindless' as a herd of them. As anyone will tell you they "simply predict the most likely next token," yet, complex solutions to difficult problems arise from them.
Many people have said that the architecture of LLMs will need to change for true ASI. I think that the herd of tens of thousands of agents can be seen as one such potential architectural extension. Whether or not a herd or a single LLM is used for a result like this is irrelevant.
To be clear, I think the orchestration of thousands of LLMs in their current form, even with ever increasing intelligence, is not the form ASI will take. There is still a major architectural breakthrough to come, in my limited, ignorant opinion.
[Edit: my only point here is that the prize is probably not driving human effort to the limit.]
Sure. A proof without an unknown amount of human steering (and/or stolen research) would be an unquestionable achievement.
To this day there's zero (0) evidence of any result by an LLM alone (maybe I'm wrong). If I just prompt ChatGPT right now with "give me a proof of the Riemann Hypothesis" and this thing delivers, I'm sold. But anything close to "yeah ChatGPT proved X with 5 years of 24/7 work with 10x Terrence Tao level geniuses" it really doesn't cut it.
Or why's there's no new branch of mathematics invented by AI? That'd be indubitably _novel_ and _creative_. But to my knowledge (and I'm eager to be educated) there's nothing like that. What are the HARD examples of novelty, creativity and genius you claim? For how people like you talk about AI I'd expect idk, a unified theory on fundamental physics, or a novel engineering solution for material science and nuclear fusion, or at least improve itself to not need a bazillion GPUs to emulate a 20 watts wetware. Sure it would infinitely easier to make OpenAI literally print money with any of the thousand problems easier to solve with such amazing intelligence than the NSE problem right? Honest question
I think the counterpoint here is simply to look at what was being achieved with LLMs one year ago versus today, and extrapolate that trend. Sure, there may not be examples of what you've asked for yet, but Astra is literally a couple of months old, the model that solved Navier-Stokes is less than two weeks old. It appears that we're seeing the hockey stick that only the most bullish thought was possible.
Also there are proofs where the only human steering was "keep going".
Any result of such kind from an AI alone would be enough to refute my argument, yet you don't present any.
>Also there are proofs where the only human steering was "keep going".
Which ones?
>Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
> Drawing on extensive prior research by mathematicians over the past decades, it
> [Claude] has increased this bound [for the fraction of zeros of the Riemann zeta
> function that satisfy the Riemann hypothesis] from 41.6% to 67.2%. Claude also
> produced a formally verifiable proof of its result.