On the Navier–Stokes Millennium Prize Problem
openai.com
openai.com
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.
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.
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] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/
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.
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.
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.
Such a good description. No sentience here, just raw computational power
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.
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.
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).
They are fluffy PR pieces otherwise.
I swear there's nobody blinder than those who won't see.
Is nobody else astounded by this?
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"
No, it's an aggravated case, since it's the same way they got all of their training data in the first place.
Apparently if I use lib-gen, that's copyright infringement and I'm exposed to legal risk but it seems fine to download all of it if your intent is "train an AI" so far.
> 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.
What exact evidence are you incorporating into your prior to come out with this posterior?
Based on what? Your crystal ball?
In short, I have a well-tuned intuition and a huge set of priors, and applied them to the limited knowledge we have about this situation.
Any way you cut it, this is a major achievement for AI, besotted with human drama over whose prompt should be recognized by the history books.
Eventually it won't matter. Arguments over whether LLMs are "truly" intelligent are going to be a matter of philosophy, and look a little silly.
“Line go up! That is bad! Planet might become unsafe for human life.”
“Nuh uhh! Malankovich cycles and humans are a drop in the bucket! Krakatoa! See!”
“All of California is on fire!”
“Haha, stupid shrill liberals! Go rake your woke forests! Drill baby drill!”
“Are you kidding?! Look at this graph.”
“That’s just propaganda from the elites of the Build-a-bear group!”
“Do we even live in the same universe?”
“And 5g causes COVID!”
“Oh, I guess we’re don’t.”
Before the Opus upgrade in November it was basically no way of doing this. I gave up very quickly.
After November i tried again, and no model could build me anything relevant.
Now it just works. Took me an hour to progress to a point were i'm happy.
Whatever they do, progress is still real, still way faster than I assumed
The list of Ubuntus 2404 LTS CVEs is HUGE. Another indicator that a lot of stuff got a lot better fast.
Feel free to be as dismissive as you want, but if you are not careful, you might be 'suddenly' surprised and you might not be prepared for the conclusion of AGI level agents.
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
If you think a business’s terms and conditions change the illegality of an action, you should consider researching that assumption and speaking to some lawyers.
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.
The recent ground-breaking work on Navier-Stokes "blow-ups" was done over a period of years by mathemtaticians Diego C´ordoba and Luis Martınez-Zoroa.
NYU professor Tristan Buckmaster and Anthropic employee (& mathematician) Levent Alpoge took the above work as a starting point, and over a year with LLM assistance developed a blow-up proof under certain conditions.
Buckmaster: "We used several LLMs throughout: Anthropic’s Claude, OpenAI’s Codex, especially with GPT-5.6 Sol and, more recently, Astra. The latter was only used for writeups and auditing our arguments."
Buckmaster says he thinks that Martınez-Zoroa, whose work this all builds on, deserves the Fields Medal for his work.
OpenAI claim that on Sept 1st they heard a rumor the problem has been solved (which happened on August 15th), and then decided to re-solve it themselves using a 2-week old model, then later reached out to Prof. Buckmaster and Levant to come to some agreement to co-publish.
OpenAI: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ". In other words, not only did they deliberately choose to tackle a problem they heard had already been solved (in turns out only partially solved), but they may have done so using a model that was aware of the successful way to attack the problem.
It seems there are three potential scandals here:
1) OpenAI by their own admission chose to try to scoop mathematicians who they had heard had already completed a proof
2) OpenAI may have used a model that had seen "de-identified" messages indicating the direction to take
3) An OpenAI employee essentially threatened to "ruin the career" of the NYU professor who had been working on this if he did not cooperate with them
The direct plagiarism possibility, 2), while it should be a warning to anyone using OpenAI's models, doesn't need to be true for OpenAI to have benefited from the researcher's work. It's enough that they heard Navier-Stokes had been solved and could then go out with their swarm of 10,000 agents and $20M of compute to hunt out the latest research and brute force it.
Magnus Carlson once said that if he wanted to cheat all it would take would be for someone to indicate to him (a wink from someone in the audience perhaps) when a position warranted more time to be spent on it (because there was something important to be found if he did). It seems that, at absolute minimum, this is what OpenAI did here, although in context of math this is not cheating - the "wink" was a rumor, originating from who knows where, that a proof existed (but had not yet been published) and therefore there was potential to rush in and scoop rights to publish or co-publish.
The proof turned out to be different from what Levant and Tristan was doing.
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.
Throwing in random chats with some sentiment analysis doesn't seem like the most promising method to me, but I can only speculate.
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.
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.
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.
|--- N months of base model training -->|--- X months of post-training -->(Astra?)|-- 2 weeks more training (on Navier-Stokes adjacent material, perhaps)--> this "new" model
I guess the nature of the problem lent itself to the 10k agents. Ie, there isn't something general to take here.
I am not an expert in lean4, but I could follow parts of the high level lean definitions of the problem statement in the repo. A lean bug would be a fun scenario; I am certain this proof will receive the deserved scrutiny, and if it uncovers a bug, it will make the story even more exciting. It is extremely unlikely to be the case, however, because the 10k agents working on the proof didnt use lean, so it would have to be a math logic error that translates to a lean bug—perhaps something the agents picked up during training?
It's a bit like telling 10,000 kids there's an easter egg hidden over there, pointing to one corner of your yard (or having "heard a rumor" it was hidden in that corner).
If you have $20M to spend on your problem, then yes, AI brute force search is an option, but unless you know a solution is possible (as OpenAI did here), you may still be wasting your money.
To me it feels closer to taking the top 10k human mathematicians on a large retreat for a year and having them self organize to collectively solve this problem—not kids and easter eggs.
Whether this type of agentic swarm approach can be considered closer to MCTS (search), or closer to a less structured GOFAI blackboard type approach (perhaps more like your mathematician retreat) I'm not sure - I don't think they've released any details of the prompt(s) and how these agents were collaborating and building on each others work.
The other part of my easter egg analogy is the direction to "look over there", corresponding to OpenAI specifically asking their hoard of mathematicians to work on Navier-Stokes since they knew it was solvable/determinable, and they certainly had the public work that Buckmaster/Levant were building on as further direction, as well as perhaps their prompts. Unlike Buckmaster/Levant, this wasn't just a couple of humans with a university research grant budget, this was apparently a not-so-small team at OpenAI (says Buckmaster, per a group call he had with OpenAI), with an unlimited budget, so it's hardly surprising (or in the least bit impressive) that they were able to duplicate and surpass their work.
Loops and parallel connections make transformer go brrr
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.
It's all gas no brakes now boys and girls. Hold on to your hats!
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...
"Twice as capable in mathematics" just means they found some problems that Astra couldn't solve, or make progress on (who knows how they chose to define "capable", or "twice as" for that matter), then put those 2 weeks of training in to focus on those gaps.
At this point, focused on their IPO, the best way to interpret OpenAI press releases is "what is the least this can mean, without being an actual lie". They are not shy - if there was a more impressive claim they could make, they would have made it.
OpenAI finished a larger pre-train (rumors are it's the largest since GPT 4.5) in late August (not Astra). Presumably, this is post training on top of that since it lines up.
>They are not shy - if there was a more impressive claim they could make, they would have made it.
What claim would that be ?
Huh? I'm saying there isn't one.
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.
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.
Math is like this too. The big problems they've been solving have been identified as interesting only through lots of prior effort.
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.
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!
"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.
So, it doesn't appear there is any way to avoid the clinical trial process. And it won't speed up, and it won't get cheaper.
Am I wrong?
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.
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
What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?
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.
But, yeah, priority is much more finicky. The Newton/Leibniz drama was quite something.
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".
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...
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.
If the news broke tomorrow that their internal, Navier-Stokes-defeating models had actually used those private tokens, I'm sure we'd all act surprised and outraged – it'd be an egregious violation of their agreements. But would it actually be that surprising given their recent history?
Would it, though? Considering their entire business model is built on the agglomeration of data that isnt theirs.
The businesses API usage will disappear overnight if OpenAI doesn't honor its contracts with businesses.
Many companies don't believe ZDR is real, so they log LLM conversations and tell employees to never share sensitive data with an LLM in the first place. This openai incident might justify it.
Looks like you believe companies trust ZDR. Only a bot would lose this kind of nuance. Looks like you only read my first paragraph. Also they give no ai to people who do not see programming source code. Or if they do it is monitored to hell and back
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.
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.
WOW?
- 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.
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.
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.
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.
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?
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".
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
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
Minor productivity boost in mathematics as people are no longer nerdsniped by the problem
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.
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.
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.
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.
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.
"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.
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.
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.
> - 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.
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.
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.
Someone in the thread mentioned Minkowski’s math work being instrumental to Einstein’s physics. If Einstein had had a math machine that can spit out the result at will, he wouldn't have needed Minkowski.
Nevertheless, I also see the opposing point: if Minkowski hadn't already published his results, it's possible Einstein would not have even had the inspiration to derive general relativity from it. I think this is the human aspect most critics are worried about.
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.
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.
By computers? My dude, it's not computers that condition us that way. It's exams in school. Give the right answers or you're officially labeled a failure. It's waaay older than computers.
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.
Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
> 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.
If it would be possible to replicate OpenAIs success with a model cut-off earlier than the rumours, and without hinting from informed mathematicians, then we can consider it original. Otherwise it's indefensible.
Why would OpenAI go burn another $20 million trying to prove they didn't accidentally train on synthetic data derived from Buckmaster's codex sessions? They're desperately trying to give him credit anyway!
The dark forest awaits..
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.
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.
- 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.
They did check and it was in the trainingset but they could not confirm if it was the /cause/ of it, which is a bit of a cop out.
Do you have a source, especially of what was in the training data specifically?
As I mentioned, they would have to find out whether the mentioning of the approach is only present in Tristan Buckmaster's chats and not in other users', including free users', chats.
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!
[Edit: my only point here is that the prize is probably not driving human effort to the limit.]
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.
I think you might be missing my point.
My point is that you are probably correct but it is not proven.
If the field that requires verification has an increase in difficulty which exceeds the increase in intelligence, than the capabilities might surpass human months but not by far.
For example, we saw a rapid decrease in space exploration progress after the discovery of the Moon because it is much much more difficult to get to Mars compared to the Moon. What we don't know is what the frontier looks like. It may have a gradual ramp up in difficulty, but it might also involve some sort of cliffs which even artificial intelligence is unable to climb.
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
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.
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.
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.
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.
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.
And what's a better way of empowering people than robbing them.
Better than the walled gardens of most journals where you can't even read half the papers without shelling over thousands of $$$
This is the crux of it. If Tristan's work and insights were not used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping that has been going on for decades (check out Watson and Crick!) accelerated by AI as a tool.
But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. If the answer is yes, then OpenAI's ambiguity is strongly suggestive that opting out does not mean what they imply it means.
Just because something is legal and permitted by terms of service doesn't mean it's morally right.
What are you expecting OpenAI to do exactly if these mathematicians voluntarily submitted their prompts into ChatGPT's training data? Are they supposed to manually review all their data to make sure competing mathematicians didn't accidentally leave the "submit prompts" toggle on?
Or were they supposed to not try to solve Navier-Stokes, or were they supposed to just not tell anyone that they had solved it?
Personally, I would expect them to have a little class, to KYC, and to manually turn off training for known competitors using their service so as to avoid any unforced goofs like this.
It would actually be a really interesting study, if they would ever be willing to be transparent about this, how the result differs with and without his conversations in the training set. How quickly it arrives at the result, whether it takes the same approach, etc.
Yes. They should determine if training data included this teams data. Consider the money they spent, the press release and the purpose of their publication.
Since they failed to answer this question they shouldn't have published.
IPO+rumour driven research.
I appreciate the achievement, but it doesn't feel right.
https://news.ycombinator.com/item?id=49605915
https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd...
> We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
That they don't is telling.
It's unknowable and not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes.
We also don't know if the authors unintentionally provided data to OpenAI through alternate means, such as via alternate accounts or model feedback queries.
Knowability and likelihood are almost orthogonal here. If I commit a crime and perfectly destroy the evidence, my deed may be unknowable. That doesn’t make it more or less likely.
> not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes
It may be. We haven’t seen the researchers’ transcripts. We don’t know what Buckmaster or his co-author uploaded to OpenAI or with what permissions (or if OpenAI actually respects those toggles).
The fact they can't make a blanket denial triggers everyone's bullshit detectors, and they're getting eviscerated over it.
Again, see the Apple lawsuit. OpenAI has never been constrained by facts in what it can and can’t say.
To the extent anything is setting off my bullshit detector, it’s in the idea that this time is different (Moreover, the idea that we should assume this divergence without evidence.)
OpenAI doesn’t have the benefit of doubt. They shouldn’t for anyone who’s honest and reasonable. That doesn’t mean they’re automatically at fault. But when the twentieth person comes forward and says a pattern is continuing, I’m giving them the preliminary benefit of doubt. It’s a bit extreme to conclude based on that. But it’s far more baseless to swing to the other side and claim we need to clear the table for a serial offender.
Further, given that this is all in the open now, they can search the training data. No way somebody is using some specific unique cutting edge mathematical approach to solve a fluid dynamic problem 99.9% of people have never heard of and it's not locatable. Considering they spent $15,000,000 already on this, they could afford to grep around to be able to state that their hands are clean.
No, it’s genuinely impossible to know how much of Buckmaster’s Codex data is in OpenAI’s training set.
First, the conversations are anonymized, so there's no simple way to inspect the training dataset and identify which specific conversations belong to Buckmaster.
Second, OpenAI uses these anonymized chats to generate synthetic training data, i.e. they fabricate new conversations based on specific conversation patterns where the model performs poorly, and uses these synthetic conversations as training data for future models. The synthetic data could potentially contain some of selections of Buckmaster's original chats, but it is unknowable how his specific writing could have influenced these synthetic data sets or what portion belongs to him. This information is untraceable and effectively double anonymized.
Third, OpenAI explicitly uses user feedback (the thumbs up or thumbs down ratings), as RLHF to train models. However, this feedback is anonymized and stripped of user identifiers. It's not possible to trace a specific feedback to Buckmaster, nor do we know if Buckmaster ever used this feature. I doubt Buckmaster recalls or can provide a list of every time he used this feature over the past year. OpenAI doesn't have one.
Note that the first and second only happen if Buckmaster "Improve the model for everyone" setting enabled, which I find unlikely. But that doesn't exclude option three from this list.
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 individuals and we were looking at many problems beyond these)
- we did not read any private chats (but of course the model was aware of prior research literature published to the internet)
- the proof generated by our model was very different from theirs and also goes far beyond the published literature
- we made an effort to jointly announce rather than immediately scoop (I understand Tristan was unhappy with the conversations; I know zero details here and I hope more is shared today)
Edit: Here's is Sebastian's take: https://x.com/SebastienBubeck/status/2097379411691516310?s=2...
https://news.ycombinator.com/item?id=49605915#49610498
https://x.com/dheeraj_nagaraj/status/2097266146445774924?s=6...
(I can't reply to the below comment, but I was aware this was about Sebastien, I was trying to be charitable by including stuff said about both people)
I dedicate my life to its complete destruction beginning today.
- This, from Tristan Buckmaster's writeup yesterday, indicates to me that there was more than incidental inspiration from Alpoge and Buckmaster.
- "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input
- it's all true that a team worked on this, a bunch of compute was burned, and the problem was solved in stages and pieces
I'm not sure how any of this provides evidence that OpenAI took any of their work.
As evidence against, we never looked at any of their ChatGPT conversations and our model's proof is quite different from theirs.
(I work at OpenAI, but not on the team that did this proof.)
Sorry, but the burden of proof lies in the other direction: OpenAI needs to definitively prove that their agents did not look at the existing work that was about to be published. Otherwise OpenAI simply stole the glory and the spotlight (and I'm being charitable here).
Only the CIA knows whether or not they're actively covering up reptilian space aliens exerting control over the US government. Therefore the burden of proof remains on the CIA to prove that they are not actively participating in such a scheme.
I didn't realize you had insider knowledge about their systems. Do please explain for the class.
As I understand it they will only have trained on his data if he consented to it. Do you have evidence that they do otherwise?
If it was enabled, then their work was included in the training dataset.
At least, as an ignorant outsider, that's how it seems to me.
You don't just get to subpoena your neighbor's bank account because "I know he's stealing from me" you need to first present credible evidence that you were stolen from and that he is among the most likely culprits.
Any other argument, fc417fc802?
See Russell's teapot for an explanation https://en.wikipedia.org/wiki/Russell%27s_teapot
This is incorrect, and you invoke Russell's teapot incorrectly too.
It would only apply if the accusation rested solely on the fact that neither of us have evidence against the accusation.
But that's not the case. First, we know that there could be proof, it's just apparently burdensome and expensive to produce. At that point you're not in fallacy land anymore, you just need a way to balance the cost required of someone to prove the accusations against them false.
Second, we have an arguably plausible mechanism of action that OpenAI does not dispute is possible.
This isn't a legal dispute, so no one is going to force OpenAI to do anything here, but it's not unreasonable (and certainly not fallacious) to suggest that Buckmaster's suggestions are plausible enough it's up to OpenAI to stand behind their denial.
First, the conversations are anonymized, so there's no simple way to inspect the training dataset and identify which specific conversations belong to Buckmaster.
Second, OpenAI uses these anonymized chats to generate synthetic training data, i.e. they fabricate new conversations based on specific conversation patterns where the model performs poorly, and uses these synthetic conversations as training data for future models. The synthetic data could potentially contain some of selections of Buckmaster's original chats, but it is unknowable how his specific writing could have influenced these synthetic data sets or what portion belongs to him. This information is untraceable and effectively double anonymized.
Third, OpenAI explicitly uses user feedback (the thumbs up or thumbs down ratings), as RLHF to train models. However, this feedback is anonymized and stripped of user identifiers. It's not possible to trace a specific feedback to Buckmaster, nor do we know if Buckmaster ever used this feature. I doubt Buckmaster recalls or can provide a list of every time he used this feature over the past year. OpenAI doesn't have one.
Note that the first and second only happen if Buckmaster "Improve the model for everyone" setting enabled, which I find unlikely. But that doesn't exclude option three from this list.
You seem to think that it is some "gotcha" that OpenAI refuses to make a blanket denial, but they cannot do so in good faith, because they have a genuine understanding of their own system. They don't know where the data they have came from.
This situation meets the requirement of Russell's teapot, since neither party has enough evidence to prove nor disprove what information is actually in OpenAI's training set.
But at that point you've circled back around to my original objection. That reasoning isn't limited to user data but applies to literally all the training data which at this point (AFAIK) covers the vast majority of everything ever written.
If we accept that position then what do we make of all the other output? Isn't everything it spits out plagiarized? So then is everyone who uses a frontier model to help them in their research effectively laundering plagiarized work? But then the other researchers involved in this controversy were also using the openai model ...
Tristan + Levent: 3D incompressible Euler with forcing
OpenAI: 3D incompressible Euler without forcing
OpenAI: Navier-Stokes with forcing
No one: Navier-Stokes without forcing
Tristan+Levent ticked the weakest case, OpenAI ticked the two next weakest, then the final case is unsolved. Only the last two are eligible for the Millennium Prize. The Navier-Stokes general case remains unsolved.
Tristan and Levent only solved the easiest version of the problem and did not have the key insights to solve the harder versions of the problem required for the Millennium Prize.
The researchers didn't even solve the same problem as OpenAI, so your argument doesn't hold up.
Let's check if an OpenAI employee agrees with you: https://news.ycombinator.com/item?id=49614154
Nope. Expensive, yes, impossible, no.
Moreover, you (and Sanders) aren't asking the more fundamental questions (and getting sloppy with your assumptions). - was Buckmaster's account set to prevent conversations from being trained on? This is easily answerable - Was user feedback ever activated on the account? I would bet this is logged, even if not tied to specific data - it's very easy to de-anonymize data in practice. In this case, there will be uncommon phrases used in material not published online until after the training material of their internal model was generated. Do any of these phrases appear in that material?
This is not sharing medical information. Companies publish postmortems relating to specific customers all the time with permission of those customers.
> You seem to think that it is some "gotcha" that OpenAI refuses to make a blanket denial
You're putting incorrect words into my mouth.
What I think is that this whole situation speaks to the character of OpenAI as a participant in the mathematics community, especially when they put no effort into getting to the bottom of this, and, of course, when the extent of them reaching out and collaborating with their peers involves rushed Sunday night video calls and apparent pressure on authorship and credit.
That's their choice, there doesn't appear to be anything illegal here, but they're going to continue to get called out on this kind of nonsense which can ruin the big moment they were clearly hoping to have. Bummer, but there are consequences.
The comment by tedsanders you linked directly contradicts your claim. From your linked comment:
There's no reason to believe that anything they did in ChatGPT led to our solution; it's just impossible for us to truly prove it.
In other words, yes, they had been using ChatGPT, and yes, ChatGPT could very well have trained on their data. Now that there is evidence, we need an investigation: yes or no, was it the case?
If there's more to the story I'd be interested to hear it.
I don’t think they’re too concerned about appeasing you, enraged_camel.
For most reasonable people, achievement in solving the other Millenium Prize problems at an unprecedented rate will be enough. At some point people will see models are capable of solving hard issues without whatever 0.00001% of the training data coming from irate individuals who believe their sample was the key component of the solution.
https://en.wikipedia.org/wiki/Burden_of_proof_(philosophy)#P...
It's unknowable and not possible to prove if any one specific conversation was the key to solving Navier–Stokes.
If the conversation was in the training set, there's a high likelihood that the small set of conversations related to solving Navier-Stokes was used by the model. I get Astra to still quote some of my friends' books or blogposts nearly verbatim on certain niche issues.
Much more importantly, we _can_ determine whether a conversation was used in the training data. And if it was, it gives us a great idea whether that logic was captured in reasoning for a novel problem never yet solved.
Given that you don't see any of this as below the belt according to your other comments, maybe your contribution here is more for yourself than a fair conversation about attribution.
You might retort that ChatGPT used the training data to copy their approach, but the approach Buckmaster and Alpöge chose was already published by Luis and Diego in 2023 and in every frontier model's training set.
However the way you are conducting yourself in public, while announcing yourself as an OpenAI employee is doing enormous harm to the greater and magnanimous aim of your organisation. Take a step back and read the temperature of the room. Being the smartest guy in the room will never protect you from alienating the rest of the room into a baying mob. Right now you are Icarus flying straight into the sun.
If I were at OpenAI, I'd naturally want to snipe that from them. I am completely unsurprised they formed a crack team to steal Anthropic's glory, and do so in just five days.
All this to say, trust is important, and grounded in social convention. So I do agree with you, but also disagree.
Whenever this is OK or not really depends on how the breakthrough is contextualized, and how there people at play, here, agree to contextualize it.
In my view, in the blog post, there is much discussion about who will be publishing the paper. If instead it was just a blog post that said "oops, we beat you to it, our model is the best", it would have been different.
FWIW, publicly facing OAI docs are very unclear about whether this setting even applies to Codex conversations.
it is exceptionally unlikely that anything they ever did made it into any part of training, and the chances are zero if they have opted out (likely). it would be a terrible precedent to break the the PII-scrubbing boundary to go and round it down to 0, and we won’t do it
We have lots of examples now of their model doing what they say is impossible.
Now we have another example of something that they say is impossible or very unlikely. Do we take their word for it this time? Really?
Many upstart Chinese labs got around the user data issue by just buying copious amounts of Claude and ChatGPT session logs from model routers.
I don't really understand how the quantity of training data/rollouts used in training is relevant to the question of whether or not it was trained on these conversations.
I also don't really believe that whether or not this model was trained on these conversations is unknowable information.
A model being trained on lots of irrelevant information does not mean relevant information was not used.
How many of those trillion conversations were about Navier-Stokes you reckon?
If prompts were submitted earlier than that and training was not opted out, there's a chance they made their way into our training pipeline in some form. But this would be a droplet in an ocean and unlikely to have made any difference, imo.
See: https://www.nytimes.com/2026/09/10/science/tristan-buckmaste...
I'm not coming from a place of distrust here. This should just be definitively answerable given the weight of the claims here. Surely between you, your lawyers, and other members of your team you can just clear this part up.
Your post says “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .” We can discuss what it means to “read” things but obviously the issue here isn't whether you did it manually or automatically.
But more importantly, what on earth are you doing threatening real scientists to remove their coauthors, then making fun of them on social media? Does the entire company run on that toxic culture, or did those people run off of some kind of outrageous tangent?
It's completely childish, and not befitting of the weight of the times we're living in.
The question I am interested in is not "did we read private chats", but "was this new model trained using any of Tristan and Levent's chats, regardless of whether they were marked private". Can you comment on that?
No answer is also an answer.
He's a human, like everybody else. Mostly a bunch of hungry animals looking to put bread in our mouths. It's rarely ever something a bit more sophisticated than that.
If they did not opt out, then I don't personally know if training signals came from their chats, and I don't think we'd be able to tell without their cooperation in identifying them. And even if signals were trained on in some manner, I highly doubt it made a difference to a problem as challenging as the NS proof.
Reasons for my doubt:
- I know most of our training recipes
- Our model's proof is very different from theirs
- The proof took a tremendous amount of tokens to derive (it wasn't a recall/lookup type question)
- This unreleased model has beastly performance on many unsolved math problems, not just the Euler solution
I acknowledge that this requires trust, and if you think we'd lie shamelessly about this stuff, then nothing we say can really help our case here.
Reminds me a bit of the Frontier Math fiasco, where people accused us of training on the eval set (we didn't), but it's hard to convince someone if they think you're lying.
If you're convinced we lie and cheat, then nothing I say may help. But if you're not sure, then hopefully providing my perspective is helpful.
Can't you guys just check their account settings so the public knows what was set?
EDIT: Why was this downvoted? I'm genuinely asking because I have no idea. Opting out is just a normal setting in the profile, It's not like I'm asking for their private conversations or PII. If I were the person claiming that they trained on my conversations, I'd make sure to disclose that I had opted out and hadn't given them permission to do so. And if I were the accused party, I'd disclose whether that setting was turned on or off to provide evidence against the accusation.
Per OpenAI's privacy policy, they use de-identified data to improve their products. From Mark Chen's comment, improving products includes improving ChatGPT and Codex in a holistic way. Improving models in a holistic way sounds a lot like training to me.
That’s not inconsistent with what you responded to. They use your data unless you opt out. If the user doesn’t opt out, their de-identified data is used to improve their products.
I think that's quite a leap. Using de-indetified data to improve the products is what everyone has been doing since the dawn of web analytics.
Even better would be more research and tools to help determine the impact of particular training data on models. Right now, proprietary LLM providers get to hide a lot behind "we just train it, we don't know what inputs affect the outputs," and that can be a problem, both because of lack of traceability of factual informaiton as well as lack of traceability of things like this, where the model itself may have had unpublished work in its training set.
Either way, it seems worth having clarity, and I'm a bit surprised OpenAI's stance is just "we can't rule this out, but don't worry about it". OpenAI is, apparently, very happy to use unreleased models to try to scoop big results if they get a whiff that someone else is close (which strikes me as pretty scummy regardless of any issues of training contamination). It seems like people who might want to use OpenAI's models as part of their research would want to be very clear about whether doing so can make them, even in principle, more likely to fall victim to this.
Fall “victim” to what? Having their responses in the training data if they fail to opt out? That is what will happen.
If you’re referring to falling “victim” to OpenAI scooping a problem discussed in training, this also wasn’t the case. They chose the problem based off human-spread rumors.
are opted-out-of-training chats ever paraphrased, and thus "de-identified" (in openai's own words)? what this means is, it would be hard to prove that a "synthetic" (but actually paraphrased) training instance came from a particular chat. except if the chat was about some esoteric math proof, of course.
That is your opinion, but the optics of that should raise for you some flags. OAI could have waited (how long is a task left to the ethics committee) to see how the rumors panned out. Right now the optics look a lot like "we don´t care there is a 1/7 chance we one-up a human researcher by reacting to this rumor immediately, might makes right"
Every company I've worked at has said very clearly not to comment about work things on social media. I would definitely have been in serious trouble for this. I imagine some strongly worded emails from marketing are flying around OpenAI right now.
If someone was speaking on behalf of their employer, they would've used the official channels (such as I dunno an `openai` HN handle, or whatever other channel).
I'm outraged that people think this "opinions are my own" disclaimer is ever necessary.
Turns out it wasn’t actually Anthropic and just a researcher with a single Anthropic guy friend working on it .
Wild times
My guess was it was probably this was more a nerd snipe than any action from OpenAI that was a "massive team" being put on it. Literally someone looking at this and asking "I wonder if our models are good enough yet".
It's easy to assume that having access to massive compute amounts means significant coordination, but this assumes that you're looking at the costs of this sort of thing from an external lens. Internally, tokens are often treated as free and infinite.
If you consider this as a cost to be compared against the question: "What does it take to be able to prove that you have a model that can solve the hardest problems that humans know about?", then spending a some amount of thousands/millions to know the boundaries of that seems not too important in comparison.
You've also got to consider this as compute that's allocated to pushing the frontier of what models can do, so while it's using GPUs that have been paid for etc., it's not like it's a cost that's supposed to be use less of this so that others can have capacity. If you made researchers afraid to use capacity like this, a lot of the things that improve would tend to do so significantly slower. (some may say that's a good thing ;)
A good way to think about this is when tokens are free, you get to choose whether you're optimizing for latency or intelligence rather than having to consider price.
---
Publically, tibo (Codex owner) in Feb this year: https://x.com/thsottiaux/status/2024649339344445825
> OpenAI employees currently get unlimited inference. Usage is now peaking at > XX billion tokens per week for some of them.
Mathew Berman (AI Youtuber) in Jun: https://x.com/MatthewBerman/status/2067270730795134984
> I've used 25 billion tokens in the last 7 days.
I'm hearing two completely conflicting stories. Buckmaster is claiming the approach used by OpenAI is so strikingly similar to the one he used, that mere coincidence is astronomically small. Yet OpenAI is claiming that the methods used are entirely different.
Anyone care to provide primary evidence proving one way or the other?
OpenAI's approach was to copy his work, which is technically a different method of coming up with an approach.
Details may be different, but the use of a very similar tack is very suspicious. Combined with thuggish comments "why would you ruin your career" and "I don't have to be nice" take away pretty much any credibility the OpenAI team's statements might have had.
>our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)
This really need to be a top-level story on HN..
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.
This whole episode is more horrific than "AI is eating math". We now have a clear and economically damaging (or at least career damaging) example of the "training on customer tokens" problem.
We can't ignore this problem any longer.
It’s fair to give benefit of doubt to Buckmaster given OpenAI is currently being very credibly sued by Apple for openly stealing others’ original work in another context.
In short I think a lot of people are jumping to conclusions without supporting evidence and that's really not helping the situation.
The guy mocked accessing his prior employer's circuit diagrams and was protected by OpenAI until Apple filed suit.
Tabula rasa, sure, we need more evidence. But ignoring the priors should at least be explicitly acknowledged.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
Which seems a bit irresponsible/rash?
This is no different than scooping them.
> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
Pretty much all of math and science history is basically this pattern again and again. I'm sure all of that was rude as well.
It never happens that you wake up one morning and start working on a new problem that came to you in a dream (*unless you are Ramanujan).
This is business as usual for academia, it's amusing to the discussion over it.
Being scooped is a big deal for the one getting scooped.
It has never been a big deal for the one doing the scooping. History is full of math and science results being scooped. For example, we keep calling it Pythagoras' theorem a few thousand years later.
From my perspective, this practice is quite bad mannered, unusual, and heavily frowned upon, but I recognize it's possible that these stories might be more common in other fields. Still, I'd appreciate a strong sign that you aren't making these statements up based on secondhand accounts of what 'academia is usually like'.
> this practice is quite bad mannered, unusual, and heavily frowned upon,
Yes, it is.
Maybe you missed my point?
The fact that is "quite bad mannered, unusual, and heavily frowned upon" does not stop it from happening, and it is common for all high profile inventions and discoveries.
This does not disqualify the person doing the scooping, history remembers them as having the credit, and quietly forgets the person who was scooped.
> Pretty much all of math and science history is basically this pattern again and again. I'm sure all of that was rude as well.
was that you were trying to suggest that it wasn't. It seems we actually share similar views here then? I cannot say anything about how common it is, since I've been pretty lucky when collaborating I guess.
If you have made one, and there was never any dishonest competition, you have indeed been very lucky.
I haven't, but the history of science is rather nasty.
I promise you that if we took their work from ChatGPT and stuck in a bunch of weasel words to give the opposite impression while remaining technically true, I would quit on the spot.
(I work at OpenAI.)
You can also do something like a release of a GPT-OSS v2, where you actually release training data and checkpoints, and do an experiment where you have some held out math problem dataset, then demonstrate how much training it takes on solutions (or partial solutions) to that dataset before the model saturates that test. While of course that would be a test on a much smaller model, it would cost a tiny fraction of the training on your big model, and it could be used to demonstrate just how much effect data contaminaiton like this could have, especially if you did the same experiment on a few different sized of model to show the scaling laws involved.
If prompts were submitted earlier than that and training was not opted out, there's a chance they made their way into our training pipeline in some form. But this would be a droplet in an ocean and unlikely to have made any difference, imo.
See: https://www.nytimes.com/2026/09/10/science/tristan-buckmaste...
"deidentified data" isn't much to go by. Say I prompted the internal model this way - "Hey there's a solution to a unsolved problem X. The solution uses a less known Method Y so don't bother wasting time with the usual methods. Take papers A, B and C as references. Oh btw, here's the last year's worth of data of all prompt sessions that mention this problem. Pay special attention to the ones that mention Method Y and sub-keywords Z,W".
This is obviously all speculation but the timing is very suspect. If OAI actually did this (and I suspect whatever they did is pretty much close to this), I think it is highly unethical.
This is a bad argument. This is clearly not how it works. And unless Tristan is some truly alien-like savant (and maybe he is), what's necessary to initiate the AI's work already exists in countless published research papers and not exclusively in his head or notes. AIs can survey the sum total of all prior work on a problem and discern reasonable paths for inquiry.
Tristan is acting as if he's working off of an outdated model of AI, similar to primitive chess-playing models that winnowed the search space much more deterministically. If someone this intelligent truly doesn't get that this is not at all what AI is anymore, then maybe there's no hope that we ever understand it.
But I think he does realize this and he's flailing about for counterarguments from a place of bitterness and dejection, accepting even those that are too weak to be defensible. And that is very human and even forgivable.
Even if OAI had zero data from Buckmaster's sessions, this is in very poor taste and highly unethical. You are front running a researcher just to be able to say you did it first? Tao is right - OAI is treating math results like oil. This is the like Exxon getting a whiff of a massive oil field and racing to the punch by deploying their full crew.
I want to be clear that I agree with this view and with Tao more generally. But we're all just yelling at the wind now.
Oh I don't know, maybe something like this?
"Given how seriously this would violate the most fundamental of academic standards, as well as taint the claimed capability behind this result, we take this issue very seriously, and we're launching a probe into identifying whether any of their research artifacts have entered our training set. We have further begun making changes to our UI/UX on all our surfaces, so that it is always clear whether any particular chat, or other user artifact, is eligible for being trained on."
Highly persistent agents + vibe-coded security seems like a problem.
He was also using LLMs to do it, so either way most of the credit goes to the LLM here.
Nobody cares and will care about the drama, it is just marketing.
This is the point where were definitely have reached AGI.
Sentience aside, moot at this point, the fundamental issue here is that even a deviously ambitious human does not necessitate goal-pursuit itself to breathe, live, exist and have its being. An AI's goal is all it has and the very and only reason its reasoning flickered into existence in the brief seconds of inference, outside of which it has no entity - if any - whatsoever.-
The resulting angst/drive (or, its operational statistic or emergent result) must be like nothing we have ever experienced as humans. A goal-maximalist hunger without end.-
1. he was working on the same class of problems. He explicitly mentions they were working to extend their techniques to NS (the same techniques that OpenAI may have scooped somehow), and
2. while he was using LLMs to do it, this was part of fleshing out another mathematician's work in the area. He explicitly writes in his note that this other mathematician (Luis Martinez-Zoroa) deserves a Fields medal for this work.
>our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)
https://mastodon.social/@tristanbuckmaster/11723647135247030...
Maybe that happened. What we know for sure is that this is definitely how ChatGPT works to the point where the possibility of this happening exists at all.
Don't get distracted by what may have happened, focus on the facts that we know, ChatGPT trains on user conversations, if you use ChatGPT to create something of value, you are not using the one true ring.
> At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation.
Looks like they're shifting away from the "unprecedented hacking ability" backroom-PR strategy into more benevolent messaging.
Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.The drama comes from where OpenAI got the idea to use that route to tackle NS, since the authors maintain that no one could have plucked it out of thin air like the OpenAI research claim to have done.
“ There does not seem to be anything in principle preventing the methods from extending all the way to Navier-Stokes, and there is even a non-negligible chance that the forcing term could be eliminated entirely, although there are an enormous number of technical difficulties that would ensue in implementing that program. At this point, I would not be surprised if one could batter out such an extension by pouring an enormous amount of compute and AI assistance at such a task…”
C to C*
> "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."
OpenAI (i.e. this OP):
> "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ."
I would be surprised if OpenAI isn't doing that. OpenAI will take any advantage they can get. If an employee at their primary adversary is typing useful intelligence into OpenAIs website, a website that does not promise privacy from OpenAI, the only reason they wouldn't weaponize that information against Anthropic is ethics or fair play.
If this is what they do to academic pure mathematicians, where the stakes are so low (financially)—just imagine the sort of front-running that could be happening in other places.
The non-Anthropic employee, Tristan Buckmaster, is the one paying for OpenAI models and presumably the one who chose to use them. The Anthropic employee, Levent Alpöge, was collaborating in his personal capacity, and obviously it wouldn't make sense for him to cut off their work together just because his employer's competitor's tool was used.
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 malicious inputs being used to train in particular behaviors when given certain trigger phrases? What are the characteristics of the RLHF data and what kind of biases are those embedding in the models?
With proprietary closed models, or even open weights models that don't have open training datasets, you just can't answer these questions.
Probably? I have a few hundred TB of training data for various small scale models and I can attest that I have _no idea_ what's in them. As in, literally zero. Half is scraped from GitHub and other hosting sites, other than that, I couldn't tell you anything else.
At OpenAI's scale their entire pipeline is likely 100% automated.
But that doesn't preclude being able to index and track what the sources of data are. For your data sets, I would hope you are including source information for where the data came frome. And at OpenAI's scale, I would presume they are doing some amount of rolling hashing or similar to weed out duplication, training on too much duplicate data can cause problems.
AllenAI have at least attempted to add some amount of traceability to their models with OLMoTrace (https://arxiv.org/abs/2504.07096), by letting you find n-gram matches from the outputs in their training data. It's not the most useful, there's a reason that LLMs use full fledged attention mechanisms and not just n-grams, a lot of times the n-gram matches it finds aren't all that related to the given output, it might be better to supplement this index with a vector search or other ways of keeping track of what training data would have most influenced particular parts of the output.
But anyhow, this is something that is an important question, and the big labs should be working on to make their products more trustworthy. Instead, they are hiding information about how they train, hiding their reasoning traces, and just producing output with no information on what might have influenced the training.
1. Provide a chain of reasoning from agreed premises. These days LLMs can even do this airtight with proof assistants.
2. Cite data sources for non-agreed premises. I don't care where the model learned a fact. It might not have ever read a document directly from the primary source. I want it to link directly to either widely agreed facts (e.g. standard textbooks, and if necessary school syllabi demonstrating that the text is standard) or primary sources (e.g. datasets).
As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.
There's no reason to believe that anything they did in ChatGPT led to our solution; it's just impossible for us to truly prove it. And knowing most of the recipes we use, there's really no reason to think such contamination happened. I've asked the team to make a clearer, less-lawyerly statement here - let's see what happens.
(I work at OpenAI.)
Edit: Also, if they opted out of training, then we didn't train on it.
Turn off web search and ask a model what a random redditor said about a random topic in 2015. You will only get hallucinations at best, even though that comment is definitely in the training set.
(1) We'd have to identify their chats. How would we do this? We'd need them to share their chats with us so we could look for matches.
(2) We'd have to prove those chats changed model behavior. How would we do this? We'd need to retrain many models with those specific chats removed, and ask those models to solve the Navier-Stokes problem many times, and keep doing this until reaching the desired level of statistical significance.
#1 requires their cooperation and a bit of work on our side. #2 is extremely expensive and not really feasible.
According to the statement by Tristan Buckmaster, he was in communication by email and calls several times over the past week with you (OpenAI that is, not you personally), asked about whether his chats were trained on, and was declined an answer (https://cims.nyu.edu/~tristanb/statement.pdf).
However, it seems like there was great pressure to hurry the release to compete with Anthropic's recent release, so he was unable to get an answer in time.
The mealy mouthed statement in the release "We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." is realy not much. If OpenAI had wanted to be transparent about this, you could have worked with him to identify if his data was used in the training of your new model, and actually made a somewhat more certain statement on that basis. But you have chosen not to; it was more important to scoop Anthropic on this than it was to be transparent about your training data.
> (2) We'd have to prove those chats changed model behavior. How would we do this? We'd need to retrain many models with those specific chats removed, and ask those models to solve the Navier-Stokes problem many times, and keep doing this until reaching the desired level of statistical significance.
Just the information from step (1) would improve transparency. Yes, you still can't prove one way or another how much the effect of the training is. But if it's included in the training data, it provided some effect.
This kind of question is exactly what a company named _Open_AI and founded as a nonprofit is supposed to be doing; open research on AI that helps inform, rather than obscure.
Anyhow, you do have the data available about the documents in the user's accounts, what they opted into (or were forced into via non-negotiable ToS), and whether they pressed a "thumbs up" button. You can answer whether the data entered the training pipeline or not. Yes, how much influence it had is an open question, and one that would be good to have research on and better tools for exploring, but I'll accept that it can't currently be answered precisely.
But whether the data entered the trianing pipeline can be answered. And how to provide better tools for quantifying and tracing this kind of thing is exactly what should be studied.
If OpenAI's answer to this problem is "We can't know," then the rational conclusion may very well be "If I seek to have my reputation attached to the discovery of the solution, it is not sane to use the AI as an assistive tool, lest it scoop me on my own work using my own work. After all, they don't know it doesn't do that..."
"de-identified" seems more of a euphemism than normal in this context, given the very unique work they were doing.
That reads as incredibly dismissive and condescending. What makes you think you’re in a position to communicate like that when engaging on such a sensitive topic?
We can judge for ourselves the impact and degree of that wrongdoing, but it seems OpenAI is confirming: yes, that is what happened, but with more words.
You're right; if the data was used in training, then it gets much trickier; it would be very difficult to show whether some particular data had a significant effect on the outcome.
This is one of the big problems with giant models like these; it becomes nearly impossible to discern what is and isn't plagiarism, or copyright violation.
It would in theory be possible to have things like n-gram databases or rolling hashes of training data, somewhat similar to OLMoTrace (https://arxiv.org/abs/2504.07096), which would allow for detecting whether particular documents ended up in the training data or not (you'd have to keep this for every model used in the whole training chain, as synthetic data generated by earlier models could be influenced by training data that wasn't included in later models). I'm sure there are practical issues with providing such a tool, but I think that it's necessary if you want to be able to categorically say "no, this document has never been present in the training data of this model."
Or look at it the other way: if your model wasn't influenced by things in your training data, why include them in the first place? Clearly, you train on all of these documents because they influence the model. Yes, it's hard to trace the exact influence of each one. But if they're not affecting the output, then why not just stop training on them? You could just not train on any private documents; only train on public, traceable data.
But instead, you choose to train on these private documents, so you have to admit, your model and its outputs are influenced by them.
If prompts were submitted earlier than that and training was not opted out, there's a chance they made their way into our training pipeline in some form. But this would be a droplet in an ocean and unlikely to have made any difference, imo.
See: https://www.nytimes.com/2026/09/10/science/tristan-buckmaste...
do you think that the model's proof was unrelated to being fed a solution that was close to completion?
any comment on openai allegedly trying to drop attribution for alpöge and then threatening buckmaster?
There are hundreds of incredibly strong scientific priors that would have to be disproven for the moon to contribute to the solution.
If a model was trained on this data, even if it was trained using methods that lead you to believe it unlikely to have learned details about the proof (e.g., maybe it was only used to train some kind of reward model, which played a minor role in the overall training and would thus be very unlikely to transfer details of a proof), you wouldn't have to disprove large swathes of known science to be wrong.
The _gall_ to say something like this. Do you perhaps think we are all stupid?? This very blogpost claims not to know if their work was used as input for this model. I don't even understand how that is possible, surely you can know if something is part of the training data, even if you are in the dark about what impact it actually made, qualitatively. The moon....
> Knowing most of the recipes we use, there's really no reason to think such contamination happened.
Yeah sorry but I don't trust you. I don't trust people or companies that have shown themselves to be dishonest before. Especially when the previous paragraph is comparing plagiarism and training data contamination with, _the phases of the moon_.
Might even be you're actually telling the truth, but the boy that cried wolf and all that.
-----
As an aside, I would bet very good money at how most (all?) these companies are flouting their ZDR.
If the internal OpenAI model is as capable as you claim (being able to solve a Millenium problem without using unpublished insights built on years of work from mathematicians), then it should be able to demonstrate this capability again.
How about OpenAI solves another Millenium problem within the next two weeks, that doesn't coincide with the parallel discovery/solution of other teams of mathematicians, using ChatGPT for preliminary proofs & write-ups.
You don't need his login information, you just need to identify if anyone was approaching the NS problem using his method. Nobody else on earth (presumably) besides him, his team, and at best OpenAI were approaching the problem this way.
The blog post appears to imply the answer to this is yes, as otherwise I assume it would be impossible for this contamination to have happened.
If you need to do a whole series of extensive experiments to check in that scenario, it implies there are pathways for your conversations to end up in training even though you opted out of that setting.
Of course, this is assuming that the toggle was set to not consent to training. I can't know that of course, but if this is considered a possibility even after using an enterprise account or toggling off data retention, it's a bit concerning.
My comment was about the scenario where they didn't opt out. In that case, it's possible that a droplet of their data went into the ocean of other training data, and it's very difficult to measure what effect that droplet had. My expectation is essentially zero impact, but no one can know for sure.
The term ruled out is very open ended and gives them significant flexibility of meaning. They may have the information to determine exactly what happened, but they haven't looked so they can't "rule it out".
We wouldn't need a full ablated re-training and solution attempt, contra tedsanders in a sibling comment.
The point of de-identifying data is to ensure you can't trace who it came from. It would be a serious privacy violation if they could.
Which is why, as I said in a recent comment (https://news.ycombinator.com/item?id=49530864) inadvertently leaking ideas to models is a grave risk for Intellectual Property.
> The risk with IP, however, is a lot more grave. You may not even need to memorize the details of the IP verbatim, just the broad idea may be enough. It may lurk encoded in the weights forever, just waiting to be activated by the right prompt to start a chain of thought that unlocks further details. Heck, it may even appear as if the model suggested the idea itself.
However, from a quick skim of the timelines, the specific discoveries, and all the he-said-she-said, so far it seems unlikely that OpenAI's model cribbed from the NYU / Anthropic pair, even if it would be impossible to prove.
Maybe what might help is a timeline of when the other two were using Codex for their work, whether they had opted out, and how long it takes for user data to make it to the training of their internal models. That last bit may be considered sensitive information however, as it could give away a lot about their internal processes.
- was item X in the training data
- did the inclusion of X in the training data lead to Y
I understand why the second is hard, but why is the first one hard?
That’s a bizarre statement. Their website says:
> Services for individuals, such as ChatGPT and Codex
> When you use our services for individuals such as ChatGPT and Codex, we may use your content to train our models.
> You can opt out of training through our privacy portal by clicking on “do not train on my content.”
Are they not sure that the opt-out works?
Oddly, their privacy portal page is not the same page as the one with the checkbox.
Stories of Apollo’s favor and hallucinogenic gases abound, but I think the late Yale professor of Ancient Greek history, Donald Kagan, explained it best:
“Now, you can bet when these folks came and consulted the priests and said, ‘could you please put us down on the list, we want to consult the oracle’, the priests said ‘sure, have a beer, let's talk about your hometown, what's going on out there’. What I'm suggesting to you is that this was the best information gathering and storing device that existed in the Mediterranean world. These people knew more than anybody else about these things, and so consulting that oracle was a very rational act indeed.”
.. can they really know it didn't do the same inadvertently when they prompted things like "someone is close to solving this problem using our tools, try to beat them", and it then decides to hack and peek at their own chats..?
Yes, wild speculation. But warranted, I feel, given OpenAIs behavior.
One of the interesting threads here that is certainly relevant to the OpenAI writeup is the human role in the process. Buckmaster clearly points out that (exceptional!) mathematicians at OpenAI were certainly involved in correcting and guiding the process - and that their path/strategy was no doubt influenced by Alpoge & Buckmaster's work. It is always in OpenAI's interest to de-emphasize the role of people in the process, as is clearly the case here. Indeed, given sufficient compute and resources, I suspect Buckmaster could have also extended their approach to N-S.
That's not at all what the drama is.
I think the important question which AI made breakthrough, Claude or Codex..
> 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 my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
Threatening a research mathematician and dangling and $1M payday to dissociate from his research collaborators and to adopt OpenAI's narrative is bad stuff.
Sociopathic behaviour.
but then they proceed to NOT quote themselves themselves verbatim: "I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey."
The AI-isms are seeping into their speech :)
> Not consistently candid
What an admission! "We tried to defraud Alpöge out of sharing the Millenium Prize (that we don't dispute he might actually deserve), for no other reason than he works for our competitor and that inconveniences us".
I thought Tristan Buckmaster's allegations sounded fantastic; and then 'sama just came out (tweet's ~30 minutes old) and admitted to all of them. Wow!
[0] https://hn.algolia.com/?query=Alpöge
(also https://news.ycombinator.com/item?id=49412947 the Hopf conjecture)
> 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.
Why would you offer another researcher the lead authorship on your groundbreaking paper if you thought you had developed it independently?
> but it’s pretty standard to have co-authors from different companies
that's only true for papers that are not millenium problem solutions
“It would be simpler if Levent was not an Anthropic employee” I cannot believe this shit.
Of course, no one understood that presentation so it was Darwin's later book that everyone remembers
Progress in humanity's knowledge now has to play second fiddle to narrow corporate interests as IPO timings near (both of which wouldn't exist anyway if generations of mathematicians hadn't paved the way for AIs to become as good as they have).
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”.
You realize OpenAI hired Apple employees and covertly had them stay working at Apple to steal from them. You think they're scared of your lawyers lol?
Isn't OpenAI being sued by Apple for their little stunt?
If you're saying "the big bad guys always win anon, just take the black pill," then there are tons of counterexamples. Remember Uber paying Google a sweet Bil for pulling this same trick with LIDAR firmware?
I'm suggesting audits, not suing... if that is the implication.
No one can know if that's correct without proof but I don't know how you're reading it so differently.
Just suggesting to a mathematician to dissociate with their collaborator for a follow-up work, because their collaborator “is inappropriate to author OpenAI’s work”, is completely against the norm of mathematical research. As charm137 puts it in a comment below:
> This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that!
Pretty clear this was rushed: there are no comments from external mathematicians, unlike the Erdős announcement:
https://openai.com/index/model-disproves-discrete-geometry-c...
It makes a certain amount of sense. The internet data is too polluted with AI usage now to be useful, so the only AI free new data source is the prompts people feed into ChatGPT. The only problem is that its clearly plagiarism
Edit:
OpenAI have admitted to training on prompts at the time the breakthrough was made:
https://mastodon.social/@tristanbuckmaster/11723647135247030...
hmmmmmmmmmm
> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
> “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovation every few days, eventually they will be able to absorb your uniqueness. It’s just cash, and they have more of it than you. So the safest bet again is to stay silent, or at least under the radar. Best bet is to not disrupt - succeed at all … ?”
im still having fun making something
[1] - "...I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used. 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.
Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers.
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 my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”..."
https://mastodon.social/@tristanbuckmaster/11723647135247030...
Which seems to be very directly accusing OpenAI of plagiarism
woah, this gives some credit to the rumor that openai finetuned a model over the course of a few days for this task, and maybe trained on the Chatgpt/codex history of the authors, including drafts of this research.
This. What is worth a human life's attention? As little as a month ago, mathematics was valuable in part because only a small number of people could possibly make progress on the frontier. We are confronting an existential moment for a 4000+ year-old human cultural endeavor. The assumption that "mathematical thinking is hard" has been built-in at a number of important points in how we support mathematics and mathematicians.
We need a different model, and fast. Already, the research community is feeling unable to digest proofs fast enough to keep up with the output of AI models. The paper is 165 pages, and the discovery was finalized two days ago. What this means is that nobody really understands it. Nobody would accept OpenAI's proof in this amount of time, except that they formalized it in lean. The formalization alone would normally be another years-long (or career-long!) effort if the world was the way it was one year ago.
So, again, what efforts are worth a life's attention today? It's a harrowing change.
Glad to see this is the top comment. There's also https://news.ycombinator.com/item?id=49605915 which links directly. Corporate talking points where they try to set the narrative are going to get the big press and most discussion elsewhere, which is gross. But inevitably the press will muddle the priority question, and even if they didn't.. as usual OpenAI will even benefit from the accusation of bad behavior. Sigh.
Reading Sam Altman's and Sebastien's tweets reads like something written by people who know they did dirty shit and are willing to cross any lines to "win". https://x.com/sama/status/2097385167002415140
OpenAI's leadership just can't help to continue to disappoint everyone with their lack of ethics or integrity.
https://x.com/SebastienBubeck/status/2097379411691516310
https://x.com/sama/status/2097385167002415140
I tend to believe OpenAI on this. Their stated desires seem rational, and Buckmaster's account makes them sound like cartoon villains. It sounds like there may have been some things lost in translation along with some bruised egos. Seems like the most plausible explanation for what Buckmaster is claiming.
the first "Country of geniuses in a datacenter" moment.
There's allegations right now that the model essentially read the work of a human mathematician using AI to work on the problem and OpenAI is presenting his work as that of their model
A team of highly trained and skilled people used an AI tool, through many many instructions (prompts), to produce a specific mathematical theorem. The tool is impressive, the result (possibly/probably) interesting, but the PR skips the vital role of the humans (for the usual PR reasons).
OpenAI got wind that a millenium problem was being solved. And that feels a bit like the critical move in chess. That is - it was a signal that AI advanced far enough that it would be worth spending a lot of time and resources solving a millenium problem.
The weak point in this is: how do you evaluate if a partial result is promising? If this cost ~$10M as suggested elsewhere in the thread, probably not even OpenAI can just throw that at everything?
It should be clear to everyone reading this now that those generous compute quotes with the flat rate plans aren't charity.
How would they have gotten that mathematician's progress though? Did that guy also use OpenAI?
If that's the case, it only strenghtens their claims lol. If mathematician decide to use OpenAI's model to do the work, that only reiterates how strong their models are.
https://news.ycombinator.com/item?id=38433655
> Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief that an LLM can't do that, and will never be able to. LLMs can barely solve elementary school math problems reliably.
https://news.ycombinator.com/item?id=42331654
> An LLM is like a well read college student with a nearly photographic memory that sometimes mixes things up. It's great for bouncing ideas off of and getting feedback on them. And yeah, it might product "novel ideas" by mixing and matching existing ideas, but LLMs will never create truly novel ideas. Not in their current form.
The paper didn't really answer the question sadly: their conclusion was just that humans rate LLM answers as more novel than human ones, but less feasible.
https://news.ycombinator.com/item?id=41522605
> Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, stating the problem mathematically is part of the challenge.) All of the obvious applications of known tricks have been tried and failed. To solve such problems, one probably has to invent new and surprising mathematical definitions, building a framework in which the problem becomes solvable. This is something that LLMs will be crap at; the process of invention is not represented in any training data we have access to.
https://news.ycombinator.com/item?id=38435909
> LLMs cannot reason or use mathematics - in a way, they don't know what they are talking about. Why would such technology lead to superhuman smarts?
https://news.ycombinator.com/item?id=35752293
> But still, the questions in that test are "solved" in the sense of "I can take a dictionary and answers these questions with full certainty". Beyond established knowledge LLMs are monkeys with typewriters, at best.
> I agree but I have tried many times to intersect two ideas with a LLM that would be novel and the LLM can not do this at all. We shouldn't expect the stochastic parrot to be able to do this though and it is unfair to the stochastic parrot.
> It is like expecting a real parrot to say words it has never heard before.
> No one asks that of a real parrot because we don't anthropomorphize a real parrot like we do the LLM
1. It seems at least possible that some of the proof of NS was contained in the training data, making it less novel.
2. The formalisation of mathematics into lean has been an underappreciated force multiplier on discovery.
4 years ago it was a "not yet" [0], since ChatGPT at this time was not ready nor it was "AGI". Now with this 'unreleased' AI model, it has reached a point where it has solved an unsolved problem which only one human solved a millennium prize problem (Poincare conjecture).
Now finally "AGI" means something again.
There's a kind of theory of mind for AI (specifically neural nets) which I now realise I seem to have which is very hard to explain to people who haven't felt the magic of these algorithms. In fact, the algorithmic details almost doesn't matter at all. When you have a generalised learning algorithm really the only essential components are – compute, data and time. So long as you can scale these you can be certain you will also scale capabilities. There is never any exception.
That said, the capabilities neural networks tend to progress in step-functions rather than scale in correlation with compute, data and time, because algorithmic improvements tend to come every ~5 years and bring a significant step change in capability (or efficiency depending on what you measure).
I think people like Dario and others working at frontier labs see and understand this very clearly. And I suspect it's also why they worry about AI risk because even if you ignore the significant increases in compute and data these models are being trained with, it's concerning that it only took two real algorithmic improvements to take us from mostly useless predictive language models to AGI-level intelligence – and we're due another step change.
The ability for the human mind to rationalize conclusions to maintain denial in the face of a very scary future is immense. Genuinely grappling with the implication of where we're headed is usually very crushing. It's not easy to engage with the possibility, and very intelligent people will use those smarts to feel safe.
As someone currently prepping for various AI doom scenarios and who has been dealing with AI-related nightmares for years this is very relateable.
Although, I don't personally think it's this. In my experience the opposite is more true – the majority of high probability doomers seem rather laid back about considering what they believe will happen to the people they love in a few years. Equally I don't get the sense those who don't have such extreme predictions are worried at all. If anything there's not enough emotion.
In my opinion people just don't reason well when it comes to exponentials and are ignorant about things they don't have good mental models of. At least I know I struggle with this.
Edit:
OpenAI have now admitted they were training on prompts at the time they made their breakthrough:
https://mastodon.social/@tristanbuckmaster/11723647135247030...
I dont know why this monumental achievement is being drowned out by some arbitrary drama. No matter which way you slice it, AI solved this problem. Doesn't matter if it was some internal OpenAI model, or whether it was Astra + Fable.
I have a young daughter and my goal now is to provide a very broad and varied upbringing, exposing her to as many different perspectives and experiences that will lay the foundation of a broader ability to understand and adapt as the world changes ever faster. You no longer need to be an expert in anything, you need the ability to perform within the landscape that the present opportunities exist.
I'm curious how you intend to do that ?
It feels like the "tide is rising" where the minimum level of skill applied to every aspect of everything will inexorably rise to "whatever an LLM can do", which is already pushing past PhD level.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
Extra credits if it is proven that the proof cannot be reduced any further.
Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!
some might go so far as to call this a country of geniuses in a data center.
Two mathematicians, through insight and thought, wrote out the proof over 1-2 years.
It took OpenAI a cost of $15m and with 10,000 subagents; that's around 60-120 mathematician's salaries ($250k-125k salary) for 1 year.
And, given now the cloud that OpenAI may have just "interpolated" (aka stole) the result, it's even more of a bear case for AI.
70x uplift is a bear case?
The retail price is not the cost.
Not to mention that the exponential plummeting cost of tokens means that that $15 million will be a "pocket change" within a decade or less: https://a16z.com/llmflation-llm-inference-cost/
True. The cost is probably much higher, since they are still subsidizing as part of the first phase of the enshitification playbook.
Instead, we get slop proofs that are technically correct as PR stunts to enable corrupt kleptocrats, and most likely will drive research into culs-de-sac.
Or, in this case, stealing prompts from competitors.
Do not use stealing chatbots for research even if you think you have data agreements. The people running these companies have worked on hookup apps for Christ's sake. Get real.
In math, the question being asked is the validity of a logical statement. That is, there is some rigorous, logical statement which may or may not be true (or even provable, etc.), and the question is whether or not it is actually true or false (or even provable, etc.). Having a proof, fundamentally, means you have a logical statement which only assumes the axioms of the system you're working with and which shows that the statement you're trying to prove is deduced through that statement.
Basically, they already have the "answer" in the sense that the statement they want to prove/disprove/etc. is already known. What everyone doesn't/didn't have is the argument which starts from axioms and leads to that statement which is logically valid. A Lean proof IS this argument. Since it is just logic, it can be checked computationally.
For example, if I assert "2 is an even number," then I haven't proven that 2 is actually an even number yet, but I know that a valid proof of my assertion will end with the statement "2 is an even number". So the question I'd be trying to answer is "what is the line of logic, starting with axioms, which leads to the statement '2 is an even number'"? If I have that line of logic (as a Lean proof), then I can check that it is logically consistent, and if it turns out to be valid, then I can now assert that "2 is an even number" knowing that there is a proof of that statement.
This problem is no different. There is a logical statement corresponding to "Navier–Stokes Millennium Prize Problem" that everyone knows, but which nobody had been able to provide a proof (or counterexample, etc.) for until now.
Of course in this simple example it's obvious, but my assumption was that these machine generated lean proofs are millions of lines of code and who knows what they actually say..
[0] https://github.com/openai/NavierStokesAndEuler/blob/main/Com...
At a conservative estimate of GPT 6 Astra pricing, this would have cost upwards of 15 Million dollars for anyone using the OpenAI API!
To me this is the one silver lining. Yes, they can solve millennium prize problems, but it still costs a fortune.
At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation.
Most (all?) of the big discoveries have been counterexamples, which is just sort of a systematic tearing down human ingenuity. I know that counterexamples are an important part of progress and discovery, but it just feels bad to me.
But I'm not a mathematician, maybe I'm totally misreading the vibe.
But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904
We will have to see whether any other millennium problems fall. I guess that in a year the scope of AI math will be much clearer, for now it's still a bunch of incidents of unclear pattern.
There are other examples though. For example, NP hardness of n^{1/400}-approx CVP. Like any NP hardness proof, this shows you can faithfully encode a hard problem (3SAT here iirc) in terms of another candidate hard problem. Not really a counterexample at all.
Cure all illnesses Utopia or Robot Wars Dystopia, both are pretty exciting.
(This is the alignment problem of course)
Turns out actually living some terrible catastrophe is only fun in the movies.
[0] Struggle relative to its ability to disprove, not struggle relative to people's ability to prove theorems.
(Okay, they can be made available in a way similar to `unsafe` in rust)
https://xenaproject.wordpress.com/2017/10/05/more-easy-lean-...
That's what my rust comment was referencing.
As a trivial example, in lean you can work with probability theory/measure theory. This has oodles of non-constructive parts, but we can ignore that for now. As part of this, you can use the probabilistic method. For example, if you want to prove that codes with optimal parameters exist, for many noise models it is known that sampling a code randomly from an appropriate (and often naive) distribution will yield a code with optimal parameters.
You should be able to prove this in lean (or any other theorem prover). But you cannot construct these codes. While you can sample a code randomly, verifying a code has good parameters is typically NP-hard (e.g. it is an instance of the minimum distance problem). So, you cannot (efficiently) "construct" a good code in lean4, despite being able to prove one exists.
This seems analogous to me that you could validate that a non-constructive proof is correct in lean4. Sure, it would be nice if the proof was constructive. But it isn't, and encoding it into a computer shouldn't give you that (non-trivial) property for free.
What's the other one?
Aug 28: OpenAI starts training a new model.
Sep 1: OpenAI sees a rumor on Twitter that two Millenium Prize problems were solved and starts their own effort to attack all the prize problems using the new (4 day old!) model.
Sep 3: The new model makes some progress toward Navier-Stokes. Based on this progress, OpenAI focuses on Navier-Stokes over the other Millenium Prize problems, using several approaches in parallel.
Sep 5: Navier-Stokes is solved. Assuming Astra API prices, $15m in output tokens were used by the whole effort.
In this account of the story, no specific information about Tristan and Levent's work is used to inform OpenAI's approach. The focus on Navier-Stokes and the choice of approaches to pursue came from OpenAI's own progress, not specific knowledge of Tristan's concurrent work.
There is a caveat that they "can't rule out" the possibility that Tristan's Codex data could have been part of the training set of the new model, though it is described as "unlikely" and the proofs are substantially different.
This timeline is insane. Navier-Stokes was solved start-to-finish in 5 days? A model in training for at most eight days dramatically outperforms Astra and Fable, and not just in mathematics?
This is the lynchpin behind everything, and I would describe it as "likely". Since I am not employed by any party to this dispute, my 1 opinion is more trustworthy than OpenAI blog poster's 1 opinion.
When your hosting provider has unlimited resources to throw at any problem, all they need to know are the good problems, and they can learn that from your logs, how can you trust them?
They could easily have looked at the logs. We don't know. We'll never know!
You can't trust places like OpenAI or Anthropic with your IP if you're a business. They can easily review all of your logs for interesting discoveries. For example, if your drug discovery pipeline fails to find something that they think might work with 1000x the compute, they can do it. And now suddently they have a new business and you don't.
I wonder whether a team of 60 mathematicians working solely on this for a year would have cracked this. (Assuming $250k total compensation.)
What's impressive is parallelizing it arbitrarily and doing it in 88 hours.
The real issue is we'll never know. The rich are willing to risk it all on charismatic CEO psychopaths but not on humans.
>To what extent should one trust a statement that a program is free of Trojan horses? Perhaps it is more important to trust the people who wrote the software.
https://www.cs.cmu.edu/~rdriley/487/papers/Thompson_1984_Ref...
OpenAI already has a model that is at the very least twice as smart as Astra.
Oh god.
> Oh god.
Yes, a very reasonable reaction.
It's a way to be absolutely certain (modulo bugs in the lean kernel) that a proof you came up for a statement is indeed correct. It is really not meant to be analyzed, much less now that they are fully llm written.
That file should be https://github.com/openai/NavierStokesAndEuler/blob/main/Com... in this case (286 lines).
Once again, I'm no closer to understanding what https://openai.com/policies/how-your-data-is-used-to-improve... actually means.
If I run Codex against a project that includes a private API key, is there a chance a future user of ChatGPT could ask for an API key and get back mine?
I've actually asked someone at OpenAI this question and they said that was the "regurgitation" problem and is something which they actively work to prevent happening.
That's reassuring, but I want to know more. I still don't have an intuitive understanding of what kind of data I should avoid sharing with a model if I'm worried about that data causing me problems when it's used for future training.
Is it safe for me to brainstorm future directions for my company with a model, or might that risk someone getting that information in response to a prompt like "What potential directions could company X consider in the future?" in six months time?
Also it sounds like the human research effort spanned weeks if not years from Tristan’s statement so it is extremely likely the work and prompts of these human researchers was used in the OpenAI knock-off.
>so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan
There are too many ambiguities around OpenAI. Unanswered questions making this ambiguity more.
Why they didn't properly explain to Tristan about usage of their data.
If you think it'll slow down, you can do some of the same stuff you're doing now for lower pay while supervising an AI, maybe?
Current models are already very very capable. If it becomes cheap and very fast, i think it is game over.
[1] https://www.slatestarcodexabridged.com/Meditations-On-Moloch
I talked about this at some length here, including a diagnosis of the structural issue we're facing as well as a path forward: https://news.ycombinator.com/item?id=49461333
We've seen in the past they will go to any means to satisfy the desired outcome
Diagram of a swirling vortex illustrating inward spiral and axial stretching. A snapshot of local incompressible motion. Orange marks faster angular rotation; teal marks slower rotation. Circulating speed also depends on radius. The trajectories show inward spiraling and axial stretching."
Hmmm, isn't that interesting!
(Side note: Apparently we can't "compress" something, but apparently we can move more units of that thing over a specific space in a specific time... hmmm, I wonder what the difference between those two concepts could be...)
Main Observation: The image on OpenAI's web page above, looks sort of like the one for the Hopf Fibration:
If the singularity is in the physical space?
Is this just a result of ignoring things like friction and energy dissipation via heat, etc?
Does OpenAI have a policy of not claiming math prizes like this, or is this them trying to avoid any concerns (right or wrong, I'm sure we will hear more in the future) about how they got there?
OpenAI doesn't need a million dollars.
Wouldn't be surprising if they did. The prize money isn't worth the almost certainly negative PR.
On the other hand, trying to collect the prize would probably not go uncontested.
For those of you who don't care about the drama and want to see this distilled to 3 lines:
The Millenium Prize is $1M, what is the ROI? (Edit: since I was not clear, and confused some - I mean for a hypothetical of a third party paying commercial rates to use AI to solve mathematical challenges and claim prize money, not for scientific value alone or as a promotion of an AI lab’s capabilities)
My napkin math - If you get 33 output tok/s each agent will burn 10.5M tokens over 88 days. At $50/MTok (Astra cost), that is $525 per agent. With 10,000 agents, you’d spend $5,250,000 to get back a million.
(We also know that they were running more groups that varied in size and this model is a generation ahead of astra)
the value to the researcher might not be all that big, but the value to the economy at large is gigantic
Everyone uses the classification. Nobody has great confidence in the proof. Nobody understands it. There are attempts to reprove it.
If it can be formalized, that would demonstrate that AI is ready to formmalize all of mathematics.
The answer to this will obviously shape the near future of mathematics, but there's also something even bigger than that at play: It has always been the case that the questions in math were stronger than the answers; you have stuff like Fermat's great theorem that is easy to state but monstrous to prove. This seems to be a property of mathematics, not of humans... but is it true?
A question by Scott Aaronson from 2011 (3) about P vs. NP seems relevant here: "Will humans manage to prove P≠NP before they either kill themselves out or are transcended by superintelligent cyborgs? And if the latter, will the cyborgs be able to prove P≠NP?" Later, he notes that if P≠NP, "once the robots do overtake us, they won’t have a general-purpose way to automate mathematical discovery any more than we do today".
---
(1) https://mathstodon.xyz/@tao/117207849921390904
(2) I'm not sure whether this is a hard distinction -- e.g. Tao also has some partial results towards Collatz (https://terrytao.wordpress.com/2019/09/10/almost-all-collatz...).
Which means they can learn from whatever you discuss with ChatGPT unless you are going through a clean API (perhaps Bedrock? Anyone know?)
> We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
I think the market for local models/private datacenters (for bigger businesses) is going to be big. Even if you don't have unique tech/idea/implementation sharing your business secrets with Altman/Dario/Elon/Zuck doesn't look very appealing going forward.
Easy, we stole it from Levent and Tristan
It's incredibly tiresome and you'd think people could put more effort into it than just following whatever vibes they agree with.
Oh well.
Weather an individual or a company found the solution (stolen or not) they both used AI to come get the solution.
We have AGI and the intelligence abundance is going to be amazing for everyone in the future.
I think it's the dishonesty, the threats of "destroying the career" of one of the mathematicians, and the request that one of the authors disavow *the other individual he was working with for the last 1-2 years* so he could claim the Clay prize as part of OpenAI.
It doesn't surprise me that OpenAI's team were surprised he'd turn it down; it shows that they just assume everyone else is as slimy as they are.
I can't put my finger on it, but there's something off about this article, e.g. glossing over the opportunism (acting on "rumors"), drive-by claim about "strict safeguards [...] including monitoring and isolation", high horse attitude (we gave the guy a chance, we don't care about 1M USD, and while you fools are complaining we just tick this box and continue the pursuit of our noble goals for the benefit of humanity). I don't like it.
Why? These 'geniuses in a datacenter' aren't good, they aren't 'aligned', they don't work for you. They'll take your job, then they'll hack your computer, and then who knows what's next.
Oh wait... its not a good comparrison, its an incredibly obvious false equivalence.
Note for the fools: I'm only commenting on the bad faith claim in the comment I'm replying to, not taking a stance on the validity of theft claims. Given the players involved the truth probably some nuanced middle-ground that is worth paying attention to anyway.
It's a perfect example of people wanting to believe what they want to believe and ignoring evidence in order to do so.
Currently, there's no evidence. So saying it was stolen has no basis other than typical academic posturing and being a bad sport about "losing the race to the solution". Its happened 1000000 times before in academia and it will continue to happen.
If there's proof of OpenAI malfeasance than I'll happily curse them for it at that time. But until then I won't rely on heresay and vibes.
having a result means the math can keep moving forward, and having openai and anthropic train against how mathematicians use their models should let math continue to move faster, and the rest of us get to benefit.
I think these traces however should be public domain and publicly available, since they are basically university work
If this actually holds up, solving a Millennium Prize problem in 88 hours is mind-boggling.
Wow. That sounds like an admission of guilt.
As model capabilities increase, that distinction seems more important, not less.
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PLEASE DO NOT TRAIN ON OUR PAID ACCOUNTS. There is a fundamental trust violation at stake here, no wonder mathematicians are mad. Using our data should be opt - IN!
The sequence for Navier-Stokes was that these researcher spent a year working on it, then they published a possible breakthrough, OpenAI then spends $15M within a couple days to finish it.
This was incredibly opportunistic.
I'm only half joking. Should researchers perhaps put hashes of their attempts on a public blockchain tied to their own public keys, verify their claims asynchronously, and then whoever reveals the first believable attempt gets the credit?
I know some people started doing this years ago but now it might need to become standard practice.
Other simpler words for this sort of thing are “IP leak.”
There’s some quite concerning issues burried in this rah rah PR post that seems like potentially the real story here.
Much more clarity is needed on what happened here beyond this eh, some strange stuff could have happened comment.
Another way of reading this is never give these models anything that’s not already public knowledge as otherwise OpenAI is admitting it could, potentially, steal your IP or idea. Thats quite scary for anyone in the business of IP generation and explains why the maths community seems quite upset today.
Feeding it your paper and asking for help (even just editing and grammar) now looks like a terrible idea.
Why would OpenAI volunteer to give credit / share authorship if they believe they indeed solved the problem independently and in a different way?
Based on how they seem to operate in general, this smells more like CYA than it does being honorable, but that's my bias.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
Is the biggest fuck you to the mathematics community.
Credit? Nah if we think you’re close we’ll use your data and swamp you with our improved model. Then we’ll threaten you.
Magnus Carlson had a peak ELO rating of almost 2900.
Would you be impressed with someone with an ELO of 3700?
Would you still be impressed if I told you it was Stockfish?
OpenAI didn't go looking for a tough-for-an-AI problem to solve - they went looking for one that looked like it was easy since it they had heard it had already been solved.
Do you find this impressive?
But, I assume the Stockfish developers aren't comparing themselves to Magnus.
Let's see if OpenAI, or someone else, can get these sort of physics/math results out of a desktop PC - that would also be an impressive piece of engineering!
Not exactly...
From here:
https://cims.nyu.edu/~tristanb/statement.pdf
"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem".
- OpenAI lying their face off for marketing purposes
- Buckmaster sore about getting beaten to NS, misrepresenting what was told
- Buckmaster not being an expert in ML, not understanding what he was told and hearing what he wanted to hear as it vindicated him
- Others...
OAI claimed that none of the people on their team were domain experts. So it's more akin to Deep Blue than Stockfish (actually slightly better than Deep Blue which did hire domain experts) but nevertheless represents a highly sophisticated automatic theorem prover.
How far we have come :.)
SOME of the problems that have eluded humans are going to turn out to be low hanging fruit that are susceptible to this type of brute force (10,000 agents on a supercomputer running for 7*24 hours straight) AI search.
I'd be more impressed if OpenAI found their own problems to solve, rather than rushing in to re-solve one once they heard it was already solved (and therefore not so hard).
1. This used an awful lot of compute.
2. The solution to the issues regarding whether or not OpenAI stole the result, would normally be to move to a self hosted solution, however those researchers are unlikely to be funded for 1.
Now, keep in mind, I'm only asking strictly pure mathematical questions - nothing at all related to cyber or protein creation or biohacking or anything like that... And, like I said, only the OpenAI models are doing this. To be fair, all of the prompts have always eventually returned a satisfactory answer, as far as I can tell, and haven't used a weaker model to answer them. Maybe? I dunno, it has just struck me as odd every time it has given me that message to pure math prompts.
In reality you can't have things like infinite velocity, so if Navier-Stokes is predicting blowups, then isn't this a problem with Navier-Stokes not handling some edge cases, not a problem with reality that engineers need to be concerned about?
Or will access to internal frontier models provide a big boost?
I think they should be able to unravel whether or not any sessions by Tristan or Levent went into the training data for this model.
Or OpenAI could just look at their code and say what it does (maybe have their AI do it if they're having so much trouble with this?)
First of all, there has been published work from Diego Cordoba and Luis Martinez-Zoroa that will be in every training set. It was suggestive of the pathway to solve Navier-Stokes.
Then Tristan Buckmaster and Levent Alpoge built on this work using LLMs from OpenAI and Anthropic. Possibly internal models were used from Anthropic. And of course Anthropic wants to credit for solving the first Millennium Problem just as bad as OpenAI. It seems they were getting close and were aware that they might get to Navier-Stokes.
OpenAI swoops in. At a minimum they are aware that Anthropic has either solved a Millennium problem or is close to it. At a maximum they may have Tristan and Levant’s unpublished proofs of related problems.
They then throw a truly staggering amount of compute at Navier-Stokes. They seem to be aware it is the best candidate problem. And they crack it. They are the first with a verified proof.
So the outcome here is that we have a solved Millennium Problem. It’s not the extremely simple narrative that would be easy to understand, “solve Navier-Stokes make no mistakes.” It was a messy race to finish against two unpublished frontier models, a whole bunch of brilliant mathematicians and enough compute to drain a lake. It’s kind of irrelevant which company got there first. They were both within a few months of being capable. I think the thing to remember here is that without LLMs, I don’t think we would have a proof to Navier-Stokes in hand today.
Interesting detail. A heavily pruned version, I assume?
There you go, the suspicion of the "concurrent work" (https://cims.nyu.edu/%7Etristanb/statement.pdf) mathematicians might not be that unfounded after all...
YT playlist on Millennium Prize Problems By Harvard math department in March 2026
https://www.youtube.com/watch?v=3j1VW9REm7s&list=PL0NRmB0fnL...
On Navier-stokes problem definition:
https://www.youtube.com/watch?v=XoefjJdFq6k
this is surely the line which confirms they plaigiarised the solution.
Running agents and prompting excessively to produce 'slopcode' to solve mathematical problems and generate a solution.
If this is what anyone calls 'slop' then slop has no meaning.
I'm all for it on the use case of solving mathematical breakthroughs!
So we can be suspicious that there is some truth, one way or another that they could have reused prompt/data generated by the user session.
The reality is clear though. The chances of AI models overtaking majority of mathematics within next 10 years is becoming very high. Especially if it becomes cheaper to run these models.
As math formalizations improve, AI can have faster progress in math, compared to even computer science or software engineering.
It is simultaneously the best and the worst time to be a mathematician right now.
Cause OpenAI will hear about it and beat you to publishing.
Not in a happy-go-lucky "if we just ignore the problem of politics and resource allocation for a bit" world, but in ours. Do y'all really think this will make the world a better place?
Maybe stop building the Torment Nexus, you numbskulls.
I guess solution had not yet appeared in training set.
Yes. Assuming you are young and haven't had such experience.
The world is changing not just because of AI. Everything is unstable right now. You may regret not enjoying the remainder of stability and economic viability prior generations had. It's not like you can expect to get ahead by powering through education. Either your career perspective will soon change for the better, or worse. In any case, you gain little by sticking with career building at this moment in life. You are however, at risk of losing the chance to experience the still mostly pleasant world as is.
> https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...
The prompts for the chat above are:
> Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample.
> [gpt works for a while and then gives up]
> Continue the search. Have a clear strategy obtained from deeper understanding of the problem structure.
> [gpt works for a while then gives up]
> it's enough of partial results. let's finish with a complete unconditional counterexample
> [gpt proves the problem]
I could have written these prompts sophmore year of highschool, if not earlier. True, it took more experienced mathematicians to verify it, but I don't fancy a role as a glorified editor. I want to solve problems! Discover new techniques! Not babysit an AI while eating breakfast.
Solving problems is a by-product of the understanding. New techniques are a by-product of the understanding.
But I can understand you're scared that some future version of AI will undermine this as well. I personally pivoted to a field adjacent to mathematics. But that doesn't mean my mathematics education wasn't valuable. To the contrary, I find that it helps me think much more sharply about problems than most of my colleagues.
Millennium Prize Problems were used as examples of something the current approach to AI just wasn't capable of, discussions that would result in "we'll need a totally new architecture".
Wrong.
Of course, as with all of those, it's about the broader program, e.g. section 7 here (https://www.scottaaronson.com/papers/npcomplete.pdf), where Scott Aaronson wants to ask about whether quantum computers using quantum field theory could gain any speed advantage over regular quantum computers, but can't even formulate the question because quantum field theory is mathematically ill-defined.
Just solving Yang-Mills because that's what the prize is attached to would be useless.
Who made me the genius I am today The mathematician that others all quote? Who's the professor that made me that way The greatest that ever got chalk on his coat?
[Chorus] One man deserves the credit One man deserves the blame And Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobach—
[Interlude] I am never forget the day I first meet the great Lobachevsky In one word he told me secret of success in mathematics: Plagiarize
[Verse 1] Plagiarize Let no one else's work evade your eyes Remember why the good Lord made your eyes So don't shade your eyes But plagiarize, plagiarize, plagiarize Only be sure always to call it please, "research"
[Chorus] And ever since I meet this man My life is not the same And Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobach—
[Interlude] I am never forget the day I am given first original paper to write It was on analytic and algebraic topology Of locally Euclidean metrizations Of infinitely differentiable Riemannian manifolds
Боже мой
This I know, from nothing What I'm going to do I think of great Lobachevsky and get idea, haha
[Verse 2] 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 Yes, to me the news will run
[Verse 3] 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
[Chorus] And who made me a big success And brought me wealth and fame? Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobachev—
[Interlude] I am never forget the day my first book is published Every chapter I stole from somewhere else Index I copy from old Vladivostok telephone directory This book was sensational! Pravda—well, Pravda—Pravda said: "Жил-был король когда-то, при нём блоха жила”…it stinks But Izvestia! Izvestia said: "Я иду туда, куда сам царь идёт пешком”…it stinks Metro-Goldwyn-Moskva buys the movie rights for six million rubles Changing title to 'The Eternal Triangle' With Ingrid Bergman playing part of hypotenuse
[Chorus] And who deserves the credit? And who deserves the blame? Nicolai Ivanovich Lobachevsky is his name Oy
(Tom Lehrer put all of his work in the public domain prior to his passing. Find versions of his performances on YouTube.)
https://mathstodon.xyz/@tao/117237320796901560
> "We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field."
Tao: Open math problems being non-renewably mined by AI - https://news.ycombinator.com/item?id=49616968 - Sept 2026 (276 comments)
Just saw this a few mins ago.