[1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/
In which case, maybe we don't need as much compute as we might expect. I hesitate to say "to reach a singularity" because it's kind of hard to define how that works out. Even intelligence probably hits some scaling limits eventually (e.g. speed of light related restrictions on how far it can scale, or how quickly it can expand).
Bit 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 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.
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...
That's it. The rest appears to be wild speculation.
If you're saying that the question of whether they actually have a highly capable model is less important than the question of whether there's a plagiarism scandal, I continue to disagree.
The fact that this plagiarism scandal exists underpins the idea that there's actually a mass theft going on, and that these models aren't nearly as capable as is it would seem
Yes, in retrospect I should have been suspicious of that drone hovering outside my window when I was writing down the counterexample to the Jacobian conjecture.
This is just not a reasonable take. Even if OpenAI is maximally guilty here, the work that they "stole" was also largely done by AI.
Loops and parallel connections make transformer go brrr
1) We don't really know how they arrived to this result except that they had a lead and that they threw millions of compute at the problem. The article is written in a way that makes you believe that it was just an agent loop with little human intervention, but without any evidence.
2) If the threats are to be believed, it is concerning how far they are willing to go to show how capable the model is. One would think their products and credibility would be enough to speak for themselves.
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.
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.
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.
"Mission. Fucking. Acccomplished."
https://news.ycombinator.com/item?id=49605915
https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd...
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...
- 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.)
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?
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"
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?
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.
> 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).
>our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)
1. It shows what even this wave of AI can actually do.
2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model.
3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including information. Any natural science PhD or otherwise knows just how complicated nature actually is -- e.g. mention any research topic and try to encapsulate all the relevant phenomena present there. Pure mathematics is different because we define the problem, rarher than explore nature. We are in my view far away from removing humans in natural science R&D. Advancements in AI however can greatly assist us in all natural sciences, which is already beginning to happen.
So I'm greatly excited what AI will bring about in physics, more so than in math, because in physics it's clear that our fundamental theories are missing a big piece of the picture, and given how easily AI crunches through Millenium prize problems I think it's possible that AI will come up with a viable grand unified theory uniting quantum mechanics and gravitation, or produce new predictions in other areas. There's enough contradictory or unexplained observational data available to make a ton of progress on the theory side I think. Exciting times ahead!
"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."
Math is like this too. The big problems they've been solving have been identified as interesting only through lots of prior effort.
BTW, there's also a problem of asking interesting questions that AIs aren't yet good at.
No one has found any principled walls of AI development yet. And empirical results are quite telling. So, I guess, those problems will not stand for long.
WOW?
This.
I do dislike the AI oligarchs as much as the next person, but I do find the thread full of complaining a bit depressing still.
If the result holds (and it looks it does), this may be one of the, if not the, biggest things to happen in computing to date. A lot bigger than e.g. Deep Blue beating Kasparov in chess or AlphaGo beating Sedol in Go.
But, as mathematicians learn and push the field 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 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.
Which hopefully won't end up with 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.
- First off, to reiterate, WOW.
- Second of all, when does this end? Are we at the dawn of the singularity now?
- People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them?
- Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can button press any economic function, business process, or scientific discovery. 24 months of lead on Open Source might turn into virtual centuries of lead.
- Do "normies" even know what's happening?
Anybody who thinks the improvements stop here isn't paying attention. It hasn't been showing any signs of slowing down since 2018. And the curve isn't even linear! My god, next year is going to be insane.
3) I'm still processing the drama, just found out about it after reading the blog post. If that happened based on private data, that's horrible. If that happened based on public tweets, then it's still abuse of power as OA employees access to compute (launching 10k agents) is quite heavy weight in boxing terms.
But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?
Its a bit like solving p = np with a negative result. Its an incredibly difficult problem, but it doesn't lead to anything at all on its own. This is why people are talking about the fact that the solution methodology is much more interesting than the solution - the tools used to crack something like this may lead to solving more useful problems
There's unlikely to be any engineering applications since even if the solution can be approximated, you still need to set up the initial conditions but at that point you can also drive pressure in other ways.
Proving out the combination of scaling inference-time compute and agent collaboration to solve previously intractable mathematical problems is WOW. By pairing creative candidate generation with automated proof checkers (like Lean) we are leaning into a repeatable framework for AI-driven scientific discovery.
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.
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).
You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes?
I envy your self-confidence.
For example there are no engineering implications of this solution yet.
For the next several decades, we'll have engineers (presumably with AI) optimize things like rocket engines and turbines and AC compressors to work a few percent better because the numerical approximations might have caused us to be overly conservative.
AI is not going to magically solve all random problems. Pick a career where you are in the driver seat.
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?
> - 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 is an impressive result, but there is absolutely zero evidence of "the singularity".
Singularity doesn't "dawn". That's the whole idea. It happens all at once.
Absolutely not. Even to a lot of techy/nerdy people it's still just a chatbot that they sometimes use to help them at work. Even on here people will do whatever they can to downplay.
The lack of fucks given is staggering.
The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.
"People" are just misinformed and keep spreading misinformation.
He very much is accusing them of stealing his work
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.
So OpenAI weren't even working on Navier-Stokes, but heard the rumor that "someone else" (Anthropic) has solved it, so rushed in to steal their thunder.
Are we meant to be impressed by this ?
Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees
> 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee.
> 3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.)
https://xcancel.com/SebastienBubeck/status/20973794116915163...
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
The dark forest awaits..
2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi-paradox-and-the...
When doomposting please actually say something substantive. Negative news always gets clicks/updoots; fight that human tendency.
I agree that we have not solved the Fermi paradox; I disagree that comments highlighting immature behavior from people who wield enormous power in our world are unproductive.
Separately, I disagree that intellectual work has ever been free of "dark forest"-style secrecy. Scientists everywhere have worried about being scooped; AI just magnifies that (as all tools have; e.g. Leeuwenhoek lenses).
And thirdly, if you want to make a stronger case for "I feel even less confident in them as a team to be shepherding this much capital and compute", you should give citations and arguments. From what I've seen, there's drama, it's much OpenAI trying to avoid scooping, and Tristan being stuck in a game of telephone, and Levent being incommunicado.
If you have a better analysis, you should say so instead of being vague.
I appreciate your upholding of ideals, and since I respect that, I will honor with final replies:
1. Locktime has passed.
2. Yes, intellectual work has always had elements that incentivize secrecy. If you want to say we were already in a "dark forest", so be it. My suggestion is that the multiplier AI adds to the possibility you get scooped is a step-change, and therefore we now enter a new "dark forest".
3. This is a big thread, and the twitter antics are well-documented, so I would assume someone else has cited them. If not, I think most are aware at this point that the online antics of AI researchers, especially when announcing or citing mathematical advancse, have regularly been childish.
3. ctrl-f "x.com" in this thread only yields https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 https://x.com/OpenAI/status/2097375276384567642
and frankly, I'm unwilling to give Elon any more traffic to dig up drama that ultimately doesn't matter. I'm not seeing anything especially childish, but y'know... I'm not sure I care.
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.
What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?
If you need privacy, then you are going to have to pay full price for those tokens (API). This has been true since day one. Everyone knows it, I guess though this is the first time that it has become "real".
But, yeah, priority is much more finicky. The Newton/Leibniz drama was quite something.
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.
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!
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.
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
- 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!
> 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?
"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.
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."
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.)
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.
> 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.
Highly persistent agents + vibe-coded security seems like a problem.
This is no different than scooping them.
IPO+rumour driven research.
I appreciate the achievement, but it doesn't feel right.
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.
He was also using LLMs to do it, so either way most of the credit goes to the LLM here.
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.
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.-
https://mastodon.social/@tristanbuckmaster/11723647135247030...
>our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)
> 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.
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.
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
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.
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.
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.
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.
the first "Country of geniuses in a datacenter" moment.
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.
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.
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..
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.
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?
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.
What's the other one?
I guess solution had not yet appeared in training set.
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.
Cure all illnesses Utopia or Robot Wars Dystopia, both are pretty exciting.
Turns out actually living some terrible catastrophe is only fun in the movies.
(This is the alignment problem of course)
[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)
>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...
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.
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)
That file should be https://github.com/openai/NavierStokesAndEuler/blob/main/Com... in this case (286 lines).
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.
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.
If this actually holds up, solving a Millennium Prize problem in 88 hours is mind-boggling.
If the singularity is in the physical space?
Is this just a result of ignoring things like friction and energy dissipation via heat, etc?
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.
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?
>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.
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.
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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!
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.
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?
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.
OpenAI doesn't need a million dollars.
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...).
Or will access to internal frontier models provide a big boost?
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 they should be able to unravel whether or not any sessions by Tristan or Levent went into the training data for this model.
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
Interesting detail. A heavily pruned version, I assume?
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.
this is surely the line which confirms they plaigiarised the solution.
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.
There you go, the suspicion of the "concurrent work" (https://cims.nyu.edu/%7Etristanb/statement.pdf) mathematicians might not be that unfounded after all...
We've seen in the past they will go to any means to satisfy the desired outcome
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.
Cause OpenAI will hear about it and beat you to publishing.
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".
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.
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.
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.
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.
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.
> 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.
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.
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.
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!
Just saw this a few mins ago.
> 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.
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”.
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!
I'm suggesting audits, not suing... if that is the implication.
FYI, they are getting away with IP theft, whistleblower "suicide", hacking web servers already. The Kushner family is invested in OpenAI.
What exactly do they have to fear?
The thing that makes someone not a conspiracy theorist is evidence.
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...
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).
[0] https://hn.algolia.com/?query=Alpöge
(also https://news.ycombinator.com/item?id=49412947 the Hopf conjecture)
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...
> 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.
hmmmmmmmmmm
> 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?
Of course, no one understood that presentation so it was Darwin's later book that everyone remembers
“It would be simpler if Levent was not an Anthropic employee” I cannot believe this shit.
Sociopathic behaviour.
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!
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
> "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 ."
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.
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.)
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 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.
Edit: Also, if they opted out of training, then we didn't train on it.
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.
(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.
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.
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?
"de-identified" seems more of a euphemism than normal in this context, given the very unique work they were doing.
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?
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..."
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.
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As an aside, I would bet very good money at how most (all?) these companies are flouting their ZDR.
They aren't keying queries by phase of the moon. But if, for example, more people talk about camping outdoors when the moon is full, and they're using conversation topic and timestamp as signal in what eventually becomes training data, it's not impossible the model has learned something about moon-phases.
That's the kind of thing that's hard to prove had no impact on an answer.
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.
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".
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.
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.
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.
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.
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.
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.
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.
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.
> “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 … ?”
https://ryelang.org/blog/posts/cognitive-dark-forest/
https://news.ycombinator.com/item?id=47566442
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.
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…”
[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 just for this, and possibly trained on the Chatgpt/codex history of the authors, which included drafts of this research.
That's not at all what the drama is.
I think the important question which AI made breakthrough, Claude or Codex..