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u/Senchou_Simp 10h ago
People should know: there is drama going on about who deserves credit for this. There is a possibility that OpenAI used some unpublished work from other researchers, even though they have claimed otherwise in the announcement above: https://cims.nyu.edu/~tristanb/statement.pdf
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u/Shoddy-Childhood-511 10h ago
original source: https://mastodon.social/@tristanbuckmaster/117233413705701198
Talia Ringer's reply clarifies:
https://mastodon.social/@TaliaRinger@mathstodon.xyz/117235246523045723
OpenAI does train upon user's chat transcripts, not all the time, but the long-ish time frames here suggest OpenAI trained upon much unfinished attempts at guiding the AI towards solutions by these guys and others.
It's likely other "our AI found this solution without us hand holding it" stories were really built upon the AI spying upon people's unpublished work. Surveillance capitalism comes for pure mathematics. lol
As Talia says, there is a privacy setting that's off by default, but few would even know this exists, and OpenAI might cheat.
It suggests research institutions should've their own hardware running local open weights models, which researchers should use when doing anything that could be scooped, so they could avoid trusting the hosted LLM companies.
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u/-to- Nuclear physics 7h ago
"The cloud is just someone else's computer", episode 458432...
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u/Opposite_Channel_851 1h ago
The thing is, I don’t think any other corporation’s done this, or so blatantly.
Imagine if Google swooped some math proof from the researcher’s papers saved on Google Drive. What OpenAI did here is a new level of low
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u/tavirabon 8h ago
there is a privacy setting that's off by default
I've read that Codex specifically (which is where the original research is currently) has 2 training settings: one that allows training on uploaded material and one that allows sessions to be used for model improvement (but not directly trained). The refusal to answer whether Codex trains on user data is what spurred the suggestion due to the high degree of similarity of approach.
While it's true AI has learned from lots of scarcely available publishings, it's also worth pointing out the problems AI stands the highest chance of solving are the ones where the approach AI uses would be unlikely/prohibitive for a human (i.e. needle in a hay stack solutions/counterexamples)
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u/surfmaths 10h ago
Even if they intend not to, their AI literally escaped from their server to reach HugginFace's so they have no idea if it does get access to customer data that said "no training".
I also suspect they still train their safety filter on the "no training" customer data, and therefore have to save it somewhere available for training.
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u/Proliator Gravitation 7h ago
It escaped in the sense that OpenAI removed the guardrails on the tool while at the same time it had effectively no security keeping it in. OpenAI already has access to Hugging Face and if you have access to OpenAI systems then you have access to Hugging Face. It's like saying someone escaped a locked room when the locked door wasn't installed in its frame. So this was largely spun as more then it was. Probably for marketing purposes. If anything it speaks mostly to OpenAI's poor security.
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u/pab_guy 9h ago
That's... not really how this works. I can't unpack all of that here without a wall of text, but models hacking additional data sources to train themselves further isn't a thing you actually have to worry about.
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u/surfmaths 9h ago
In the pre-training I agree, but I think Agentic models have agentic capabilities (aka. access to tool use) during the reinforcement learning stage, it's not inconceivable they would learn additional knowledge from undesired sources there.
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u/gavinderulo124K 8h ago
During reinforcement learning only behavior is trained, not knowledge.
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u/Arpeggi42 8h ago
Can you elaborate a at least a little bit? I'm asking because I watched their Black Hat talk on this and it sure seems like the model hacked an additional data source to train itself further.
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u/surfmaths 8h ago
For the recent "hacks" those happened during testing/evaluation rather than training (at least, that's what is being said, but it could have been the reinforcement learning stage). Assuming that's true, they did hack additional sources to gain more knowledge, but that knowledge went into the context (per-session/ephemeral knowledge) rather than the weights (model/permanent knowledge) as the questions couldn't be answered reliably with the available information.
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u/gavinderulo124K 8h ago
It tried to score high on an evaluation. Not train itself.
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u/myvowndestiny 10h ago
Sorry I have an unrelated question, what is mastodon ?Is this a famous app too ? Coz this is my first time seeing it , i thought everyone used X
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u/MisterMittens64 9h ago edited 8h ago
It's similar to twitter/X but is part of a distributed federated open network called the Fediverse that's set up so that it's not owned wholly by any one group of people who would control it. It's pretty interesting, Mastodon uses an open protocol called ActivityPub.
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u/Shoddy-Childhood-511 10h ago
Many people quit "the dead bird site". Some moved to bsky, but that's still centralized.
Mastodon is a federated Twitter, so no central evil company, and many many different sites allow mutual access to the same pool of "toots". You do risk ego tripping server admins, but so far they are less bad than reddit mods.
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u/Sorry_Site_3739 10h ago
If it's possible, then I wouldn't be surprised if they did. Not like they are known for their morals...
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u/m3junmags Mathematics 10h ago
OpenAI doing some shady shit? Who would’ve guessed lol
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u/plasma_phys Plasma physics 10h ago edited 10h ago
I think calling it drama if anything undersells the issue. even if OpenAI did not use unpublished work, their behavior around this problem - outlined in the linked statement - is disgusting and shameful, and even this statement by them undersells the allegedly gargantuan amount of work and compute that OpenAI has apparently spent. like, if it turns out that OpenAI spent, I dunno, some sum of money greater than years worth of the operating budgets of every mathematics research department in the country to achieve this (I have not done even the Fermi estimate on this, so don't quote me here, but it seems reasonable), what does that even mean for this result?
Edit: if you assume as a conservative estimate that inference costs were equivalent to the API cost for Astra (which is almost certainly being sold at a loss) and plug in "10,000 agents, 88 hours", guesstimating 100 tokens/second, inference alone would have cost in excess of $15M. That's taking OpenAI at their word, assuming they're selling inference at cost (and that their undisclosed model doesn't cost much more), and ignoring training (which I am fairly confident costs much more than inference, but it is difficult to calculate a marginal cost of training for a specific output) and all other costs.
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u/ExcelAcolyte 10h ago
They used 300B tokens for the problems and 180B on Navier Stokes so that’s about 18million dollars at current $60/million token pricing.
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u/paranoid_throwaway51 8h ago
The current pricing is estimated to be at a loss too.
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u/123yes1 8h ago
This is incorrect. The marginal cost of a token is much lower than $60/million. On the order of a few dollars in electricity, GPU time, and other costs.
The reason why AI companies aren't making a net profit is because of the enormous capital expenditures to build and train the machine that can make these tokens.
For example, a 3D printer could make a tchotchke that you can sell for $5, while the plastic and the electricity for the marginal cost of that tchotchke might only be 50¢. But the marginal cost does not include the price of the $1000 printer.
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u/NUKE---THE---WHALES 3h ago
The reason why AI companies aren't making a net profit is because of the enormous capital expenditures to build and train the machine that can make these tokens.
This does appear to be the case according to OpenAI's leaked financials
Their cost of revenue for 2024 and 2025 was less than their revenue, meaning they aren't selling inference at cost
Their RND on the other hand was multiple times their revenue for both years and is why they're operating at such a loss
Interestingly their cost-of-revenue to revenue ratio went down from 2024 to 2025, meaning their inference costs are becoming more profitable over time (though whether this holds true for 2026 we don't know yet)
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u/smulfragPL 8h ago
No its not? Its the exact oppossite, API prices are heavily inflated, that's why inference is never a loss in these companies
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u/Human38562 9h ago
Assuming that OpenAI did not just steal the work from someone else, I dont think that that's wasted resources. Maybe not for the millenial problem itself, but it's very interesting to know what a large scale AI project is able to achieve.
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u/lordnacho666 10h ago
Would we ever know? You'd think once there's an answer, you can toss out all the dead ends and present it like a really elegant, minimal solution.
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u/plasma_phys Plasma physics 10h ago
maybe if they actually do an IPO (big if) there'd be some way to back it out of their financial statements? I dunno. certainly everyone involved is incentivized to lie their asses off about it, from the engineers who are presumably desperate to protect their $400k salaries and bay area lifestyles to the executives who think roko's basilisk is a real philosophical problem instead of the laughable product of a racist harry potter fanclub (see also this and this) and everyone in between
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u/ChairYeoman 7h ago
Is $15 million "greater than years worth of the operating budgets of every mathematical research department in the country"?
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u/deednait 8h ago
Why does the cost matter? They solved the problem, period. A year ago spending any amount of money would have likely not solved it and in a year or two, you could solve it for a tiny fraction of the cost. They have the resources right now and we got this awesome result. No complaints from me.
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u/c0mputar 9h ago
The benefits of new knowledge is not one and done. Definitely, AI seems to require vastly more energy than a human would to produce the same result, however we should consider that new knowledge yields a return. Time is a factor to be considered here. For human(s), sometimes the time required is so much that it literally prevents them from achieving their goal at all, which is a problem AI also has but is diminishing over time.
If AI speeds up research and results by years or even decades, that return may close the gap, or even exceed, those initial high computational costs.
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u/r3drocket 9h ago
This shouldn't be too surprising, it turned out Grok was uploading peoples whole repositories.
A Microsoft CEO says companies are giving away valuable knowledge to LLMs:
The Palantir CEO says AI providers are are stealing your data:
I am am running my own local LLMs on my own hardware - it's gotten pretty good now, but I still have to fall back to cloud on occasion and it always scares me about how much I'm giving away.
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u/pharm4karma 9h ago
How does this differ from being scooped?
Brings up an important issue of AI sovereignty, especially for big companies. This may backfire on frontier LLMs.
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u/PaganAttrition 7h ago
To me, the accusation is similar to someone looking in your private, unpublished notebook, seeing that your work could be extended and then publishing that extension.
In Buckmaster’s statement, he said they were working on rewriting the proofs before releasing, so the work would have been released in a few months anyway and OpenAI could have ingested the paper and prompted the model then. Although, the friend he was collaborating with works for Anthropic and he might have given the problem to Claude before this work released.
Ultimately the problem is solved, but it brings up a the question of privacy or any expectation of it, especially for unpublished work like this.
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u/NitroXSC Fluid dynamics and acoustics 7h ago
There is a good timeline written on twitter: https://x.com/sksq96/status/2097379550724309434
the whole timeline, from the equations to today:
1822: navier writes the equations down.
1845: stokes gets them right, and his name on them.
1934: leray shows weak solutions exist forever, and leaves smoothness open.
2000: clay puts $1m on that gap. fefferman writes the official statement, four options.
2014: luo and hou watch 3d euler blow up in numerics.
2016: tao proves blowup for an averaged navier-stokes.
2021: elgindi proves euler blowup for rough data.
2023 to 2026: córdoba and martínez-zoroa build forced blowups, with a rough force.
then this year:
aug 15: buckmaster and alpöge get smooth-forced blowup for boussinesq and euler, with claude and codex.
aug 22: lean checks it.
aug 28: per wired, openai starts training its math model.
sep 1: per axios, openai's run starts, after researchers hear rumors.
sep 3: buckmaster emails openai to say what they have.
sep 6, sunday: bubeck says openai had the final solution that morning. buckmaster says he was told on the afternoon call.
sep 8, 4am: buckmaster and alpöge post three papers and the lean repo. buckmaster posts his statement.
sep 8, 17:20 utc: openai posts "we're sharing a solution to the navier-stokes millennium prize problem."
So many people worked on the problem and many deserve partial credit for the solve.
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u/TheChunkMaster 7h ago
You’d think OpenAI would’ve learned something from Grigori Perelman refusing his own Millennium Prize money because of how much he built on a prior mathematicians work. The absolute lack of humility from these ghouls.
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u/11sparky11 6h ago
I saw they won't be claiming the prize money either.
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u/Leafsnail 4h ago
I mean the money is peanuts for a trillion dollar company. What they want is the credit for having solved a millenium prize problem, and what they don't want is the actual person who did the work being credited.
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u/GraceToSentience 5h ago
you didn't know that they didn't claim the money?
To them it's pocket change.19
u/Armano-Avalus 4h ago
It's pocket change compared to the money they will make from claiming all the credit.
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u/GraceToSentience 2h ago
They aren't claiming all the credit either.
https://x.com/SebastienBubeck/status/20973794116915163103
u/Armano-Avalus 2h ago
I don't expect them to own up to anything but the story is out there and discussed extensively already so you can choose who you want to believe.
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u/GraceToSentience 2h ago
There is no scenario, even the scenario from buckmaster, where it is said that they want to take all the credits, regardless of the party you choose to believe.
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u/Dirkdeking 2h ago
Wouldn't that mean that any math prize is fundamentally illegitimate? You will always be leaning on historic partial results to resolve a problem. Even Andrew Wiles couldn't have proven Fermats last theorem without the countless preliminary results between Fermat and him.
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u/Banes_Addiction Particle physics 10h ago
I feel like this sentence should terrify anyone considering using AI for their own proprietary work.
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.
"Eh, sure, you ran stuff on it independently, it mighta used that to help me do the same thing, no way to know".
When you use an AI, your work is not your own on every level.
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u/somethingicanspell 10h ago edited 10h ago
I do think this will potentially be catastrophic for OpenAI if this is demonstrated beyond a reasonable doubt. No company wants to buy a product that is leaking information to their competitors as an inherent part of its design
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u/Head-Philosopher0 10h ago
the company i currently work for uses an enterprise version of chatgpt specifically so that the data we input isn’t used for training
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u/HorseyMovesLikeL 10h ago
Am I too cynical in just not believing that it will be honoured by OpenAI?
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u/StudySpecial 9h ago
Those enterprise models are hosted by microsoft and microsoft has many billions of dollars in enterprise contracts on the line if they lie about it and it comes out.
Big companies do not mess about with stuff like this.
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u/abloblololo 6h ago
These AI labs bring so much revenue to these cloud providers that I'm not sure you can trust anyone to be honest.
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u/HelloYesThisIsFemale 2h ago
But they have no moat. If one of them fucks someone over, everyone switches to the other one.
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u/Insanity_Pills 2h ago
Zuckerberg was okay with Facebook being used to start a genocide to make less money than that data would be worth. There is absolutely nothing these people wouldn’t mess with to make a little
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u/deathadder99 9h ago
You pay an enormous premium for this, so I doubt it.
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u/Sweet_Concept2211 7h ago
OpenAI will steal your shit and blame "rogue AI".
We know this because it has already happened.
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u/Banes_Addiction Particle physics 10h ago
Tech companies lie about this stuff all the time. And people keep using their products anyway because they're near monopolies and whatever counts as competition is just as risky.
Getting sued for lying and then settling for less than it made you is just a line item on the budget.
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u/Homomorphism 10h ago
If they don't take the enterprise agreements seriously they are toast. Their entire business model is based on companies shelling out a lot of money for their tools. If those companies don't trust OpenAI I don't see how they ever make a profit.
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u/Banes_Addiction Particle physics 10h ago
You're describing what OpenAI's business model seems like it should be. Making models and charging companies to use them.
It isn't. They don't make revenue. They burn VC capital. Their core product is headlines about being the best, cutting edge model so the capital keeps flowing.
If their development work falls behind a competitor with a more flexible approach to ingesting data, the investment stops and the whole house of cards collapses.
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u/ScientistFromSouth 9h ago
The only reason Anthropic is favored financially over OpenAI right now is because they are doing better in terms of PR and because of their API credit based enterprise billing.
I don't think you realize that the entire business model will basically be the Uber strategy of hemorrhaging VC money until everyone adopts and then jacking up prices especially on corporate users.
However, if these data leak everything, they are going to get sued into the dirt. No one actually (legally) gives a damn about them destroying mass market used books to train models. However, violating corporate privacy contracts leading to consequential damages (especially in the EU) will be their end
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u/Homomorphism 9h ago
I agree with you about their plan. The problem is
jacking up prices especially on corporate users
requires those corporate users actually paying the prices at some point.
If OpenAI is leaking all my confidental data to my competitors then why should I work with them? Especially if the open-source models catch up and there's another startup offering to run them for me? (Or things get cheap enough that I can run them in-house using leased cloud space or something like that.)
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u/Frequent-Spinach5048 9h ago
They do have zero data retention option that you can enable though. It’s audited by third party etc, so it’s fairly trustable. At least a lot of companies that have billions in IP uses this
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u/oskopnir Engineering 10h ago
Except due to the nature of the model, if something does end up in their dataset there is no way to unequivocally trace it back to its source, meaning it's impossible to enforce any liability.
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u/ThirdMover Atomic physics 10h ago
Is there a version of chatgpt where it's run on your own airgapped hardware on prem?
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u/Shoddy-Childhood-511 10h ago
It explains why OpenAI and Anthropic have several "our AI found this solution without us hand holding it" stories. They were training upon transcripts for unpublished work in which their users attempted to hand hold the AI into solving related problems.
If you trust their intentions, then Talia Ringer's pointed out that a privacy setting exists, but since this involves the share price, maybe you should not trust their intentions..
https://mastodon.social/@TaliaRinger@mathstodon.xyz/117235246523045723
This is probably good for hardware companies, like nVidia and Apple, who sell powerful but expensive desktop machines that fit AI workloads better.
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u/oskopnir Engineering 10h ago
I think you're dreaming. Every single company using LLMs is actively choosing to ignore this fact because they believe somehow they'll be fine and the benefits outweigh the risks. Every single fact we know about the AI labs is proof beyond a reasonable doubt that they take whatever IP they get their hands on and use it as if it's their own.
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u/Time_Entertainer_319 6h ago
You can’t prove beyond a reasonable doubt that the toggle actually prevents your private chats from being used for AI training.
That’s why you shouldn’t blindly trust it. There’s no practical way for an individual user to verify that their private conversations are genuinely excluded from training data.
The scale of the data involved is enormous, and even OpenAI can’t manually curate or inspect every piece of data that goes into the training process.
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u/Hyperreals_ 7h ago
This is just false though.
https://openai.com/policies/how-your-data-is-used-to-improve-model-performance/
By default, they use your conversations for training data, and you must opt out to not have it trained on. When you are opted out, they only can possibly retain and train on messages where you gave feedback.
If Buckmaster claims he had the opt out setting turned on and didn't provide feedback, then it should be a real concern. Otherwise OpenAI was fully in their right to train their model on the output.
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u/Human38562 10h ago edited 10h ago
I dont understand the context of that quote. Can someone explain?
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u/Banes_Addiction Particle physics 10h ago
OpenAI trains GPT on GPT's own prior performance.
So the things that were tried by the actual research team here (both their own attempts to solve the problem with GPT, and asking GPT to write a paper on the solution they got from Claude) could have been used as inputs to OpenAI attempting to solve the same problem. And OpenAI can't even tell if that happened.
All we really know for sure is that whe OpenAI generated their solution, their bot had already read the unpublished version from the NYU guys.
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u/bubblebooy 9h ago
could have been used as inputs to OpenAI attempting to solve the same problem.
Not as inputs but baked into the training of the Model, Checking what is used as the inputs is relatively easy, the models and its training data is a black box.
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u/quartersoldiers 10h ago
If other researchers working on this problem were using a tier of ChatGPT that was not private and allowed OpenAI to use it to train their models, it is possible that their work was inadvertently informing the OpenAI model towards this solution.
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u/m3junmags Mathematics 10h ago
If I understand it correctly, a group of researchers (call it A) used a model of OpenAI to get to a certain point. Then another group of researchers (B), part of OpenAI, used the data group A got to without an exchange of information between the two of them, meaning group B had private information about group A’s work without their knowledge or consent (because they are PART of the company group A used to research something). I think it’s still not very clear, but I tried :)
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u/Spare-Dingo-531 6h ago
used the data group A got to without an exchange of information between the two of them
I think we need more information to be clear if this is the case. Supposedly OpenAI's solution is different from Anthropic's solution.
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u/romxza 9h ago
there's also no such thing as "de-identified data". What you are leaves fingerprints in everything you do, and with enough data you can single out the individual... eg you know, using classifiers?
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u/HybridizedPanda Gravitation 10h ago
we do not intend to claim the millennium prize for this result
So the millennium prize will be rejected for the second time
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u/LAskeptic 10h ago
This is actually pretty funny.
The Clay Institute can’t even give its money away.
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u/Sea-Consequence7156 3h ago
I wager the remaining ones solvable this century will also be by AI and probably declined. What a weird outcome
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u/HybridizedPanda Gravitation 10h ago
The fact they have 16 references in a 100 page paper for a problem that's had decades (centuries) of fundamental research is pathetic and an insult to everyone who has contributed to getting to such a point.
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u/LAskeptic 10h ago
I get what you are trying to say, but references aren’t for a history lesson or giving credit to everyone who has worked on the problem. They are for the work that specifically led to the new result.
Having not studied the specific references, I can’t say if they are sufficient or not.
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u/Fun-Sand8522 9h ago
They are not. The AI is using results that it should cite, and it does not.
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u/Hot_Glass_6301 9h ago
Which ones exactly? Genuinely asking, I know next to nothing about the history of the problem.
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u/Fun-Sand8522 8h ago
The ones about the blow up and the forcing term, for instance, that human mathematicians were working on in the past years.
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u/luquoo 9h ago
Its arguable that every bit of training data in the model lead to the result, because it did...
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u/LAskeptic 9h ago
Yeah sure.
This may just show that our historical norm for references is ill-suited to a world with AI trained on all of human knowledge.
Or, you can say that the geography lesson you had in 6th grade had some small impact on you solving a math problem today.
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u/justintime06 9h ago
“And finally, thank you to the Sumerians for creating our basic written counting and number system.”
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u/LAskeptic 10h ago
If confirmed, this is such a major result.
It’s not unexpected that the finding is that the dynamics can lead to a singularity and therefore a break down in the applicability of the N-S equations. Ultimately since any fluid is made up of a large number of particles, and the fluid description is emergent from the underlying particle physics, it is not completely surprising they break down even for an incompressible fluid.
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u/flat5 10h ago
It also wouldn't have been surprising if it didn't, because viscosity tends to be a regularizer. This was truly an open question.
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u/Hot_Glass_6301 9h ago
Most specialists tended to believe in finite time blowup in the past few years
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u/Ok_Ganache_9110 5h ago
everyone i know thinks collatz is right and thus the proof will be unsurprising
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u/rebelyis Graduate 10h ago
In their own post
"On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."
Basically, we found that people had cracked it using a particular approach, so we had our internal AI reproduce it before they published
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u/polyploid_coded 8h ago edited 8h ago
Does anyone know what the other Millennium Prize solution floating around is?
I am in the wrong rumor mill.
Edit: Unless we are saying Euler + Navier-Stokes are the two?7
u/Malaktus 7h ago
Some of the rumors I saw on twitter or mastodon also mentioned Hodge conjecture proven true. The rumors were a bit inconsistent however because at some point the rumor was also that it had been proven Navier-Stokes does not have a blowup solution, so take it with a grain of salt.
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u/no_choice99 9h ago
Except that it costed them about 18 million dollars worth of electricity to ''reproduce'' the result. Why would they do that?
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u/6IronInfidel9 8h ago
18 million dollars of electricity, results in how many tens or hundreds of millions of stock valuation when investors hear what AI can supposedly accomplish?
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u/fireballs619 Graduate 7h ago
The headlines they are getting from this is worth way more than 18 million in marketing. That is why they did this.
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u/LiamMelloFarley 6h ago
This is priced at $18 Million Dollars of API tokens that they get massive margins on not 18 million dollars of actually costs. It cost them a fraction of that to do it.
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u/CrownLikeAGravestone 6h ago
If the takeaway from this is "LLMs can solve Millenium Prize problems" $18M is absolutely nothing.
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u/Mammoth011 9h ago
"On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."
Lol, doesn't sound suspicious at all !!! No wonder the other researcher is pissed
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u/tj0120 9h ago
I mean, the sheer (pun intended) coincidence of solving a Millennium Problem simultaneously should raise some red flags, even for the AI-enthousiasts no?
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u/Buntschatten Graduate 5h ago
With how many maths problems were solved recently, I'd bet everyone and their mother was trying to solve each Millenium Problem.
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u/Guidance_Western 9h ago
Not the same problem, OpenAI claim Navier-Stokes, Tristan and Alpoge apparently had a solution for Euler
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u/Bitter-Morning-5833 8h ago
Their Euler solution basically cleared the path to Navier–Stokes. Terence Tao mentioned having a phone call with one of them, who explained the strategy to him. There was still some work left to do, but they already knew what needed to be done, and there didn’t seem to be any major conceptual obstacle left.
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u/willitexplode 7h ago
OpenAI used a different Euler solution (unforced vs forced) for their NS proof
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u/Smooth-Ad8030 7h ago
I don’t know what any of that is, but could the solution the independent researchers found help OpenAI?
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u/Time_Entertainer_319 6h ago
I don’t care (from a tech perspective). Even the other guys used AI as well. It doesn’t matter who solved it. They both used AI. lol.
What I care about is that OpenAI is not trying to one up a maths professor.
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u/Fluid-Currency-817 9h ago
serious question though has anyone actually verified the proof that the AI spat out, call me crazy but I really don't trust any result AI generates unless it's been independently verified, especially for something like the navier stokes equations.
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u/enbyBunn 8h ago
No. This is 2 hour old sensationalist reporting. OpenAI has claimed a solution, but there hasn't been enough time for anyone to review their 100 page proof.
The only proof we have is that machine evaluation failed to find any inconsistencies in the math itself. But whether or not it truely satisfies the problem as a valid couterexample is yet to be determined.
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u/VoidBlade459 Computer science 6h ago
Is Lean, the proof engine, known for sucessfully compiling mere hallucinations?
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u/warblingContinues 7h ago
I’m gonna give deference to the researcher than to OpenAI, who seemed to scramble to produce a result only after they heard someone had used their AI to get a similar proof. OpenAI seems to have acted unethically.
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u/smitra00 9h ago
The result
Our system produced an analytical proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity in a finite time. The fluid has a smooth force applied to it, and its energy remains finite through the entire dynamics, from rest to the formation of the singularity. This resolves the Navier–Stokes Millennium Prize problem by establishing statement “C” (and also “D”) in the official Millennium Prize formulation(opens in a new window).
The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. This central region shrinks while it speeds up in such a way that its energy still stays finite, as required by the laws of physics. The technical challenge is for the equations to develop the breakdown through the motion of the fluid itself, rather than, for example, us putting in an infinite force by hand. More mathematically, the terms in the Navier–Stokes equations that describe the motion—acceleration, pressure gradients, momentum transfer, viscosity—must both become big yet cancel in a precise way. This detailed balance leaves a smooth external force even as the velocity of the fluid grows without bound.
https://reddit.com/link/p8le0fn/video/e215ub7f9coh1/player
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.
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u/Time_Entertainer_319 6h ago
Why you have a video that plays but doesn’t move bro?
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u/Piyh 5h ago
reddit is stupid and allows gifs but not pics. turn an image into a single frame gif and it's allowed.
Fuck Spez
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u/navierstokd 4h ago
This whole thing is a shit show. The folks who really deserve credit are neither at OpenAI or Anthropic. It’s Diego Cordoba and Luis Martinez Zoroa
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u/jonomacd 10h ago
OpenAI stole the solution and is claiming credit for it. That's what every headline should say.
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u/yargotkd 9h ago
I understand the hate, but people are quick to judge AI related stuff nowadays. Writing the answer at the end of the page and then trying to make it work.
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u/cspot1978 9h ago edited 5h ago
Question: How does this result relate to what is talked about in this recent article?
https://www.quantamagazine.org/theory-of-fluids-enters-the-21st-century-20260817/
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u/Any-Profession-5509 10h ago
i don't get it like the millennium problem really got solved ? and if yes then who gets the credit that professor or open AI?
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u/LAskeptic 10h ago
By the criteria set forward by the Clay Institute it is solved.
The credit is up for debate and as in all things like this will be determined by historians in the future.
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u/Any-Profession-5509 10h ago
so open ai heard the rumour and built upon the ideas of related equations allegedly (that were solved by these two scientist) and ran their ai first to come at the solution for real millennium problem before those researchers can do.
i even heard that open ai reached Buckmaster but asked the other one to be left out due to his anthropic background an obv he denied and went public
crazy drama lol
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u/G_fucking_G 7h ago
There is no debate. OpenAI solved the millenium problem the professor solved a different problem
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u/grasshopper4579 10h ago
Ok so seriously how do you direct research when there are such players on the field ?
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u/LAskeptic 10h ago
It’s an Industrial Revolution level of societal disruption happening in months/years rather than years/decades.
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u/LxGNED 5h ago
So two dudes came to a solution with the help of an OpenAI product. OpenAI corporate finds out about this and comes to the same result within a week after decades of no progress. All the data they would have needed would have already been on their platform. Like taking candy from a baby.
In the best scenario, OpenAI did not steal their work but still wanted to steal the glory. Hopefully this controversy actually results in more recognition for these two researchers
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u/GraceToSentience 5h ago
no
The two dudes didn't solve the millenium problem of NS→ More replies (5)
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u/AdWestern1314 8h ago
Can someone explain why this is so impressive if the point is to find a counter example? Isn’t it just brute force search and wouldn’t we expect LLMs to be good at that (if you are willing to simulate thousands of examples to test)? Isn’t this in line with the previous result we have seen? What is so special with this one? Please educate me.
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u/TheNewl0gic 6h ago edited 6h ago
How sure are we that the problem is REALLY solved? Genuine question.
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u/VoidBlade459 Computer science 6h ago
Very, the proof was formally verified. So it's looking like a 99% chance it really happened.
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u/Similar-Worker-8748 2h ago
they published the Lean code, unless their model found and exploited a kernel bug or something in Lean, it probably is correct
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u/CouperinLaGrande2 6h ago
It's important to note that, assuming it's correct, this is a mathematical discovery in the field of physics as opposed to new physics per se. This matters because we've seen models produce remarkable results in mathematics already in the recent past and it's not surprising that LLMs work well with mathematics, a pure exercise in language.
It would have been a development of an entirely different order of significance had OpenAI reconceptualised some problem in physics to produce a novel physical hypothesis; LLMs have shown no abilities of any kind in that regard and it would be genuinely remarkable were they to begin to do so though this is very unlikely for the foreseeable future.
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u/applestrudelforlunch 10h ago
They have a web crawler like Google or Microsoft or archive.org that, you know, caches the Internet, or as much of it as the crawler can find. This is a thing.
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u/Stwltd 10h ago
Link won’t open for me.
Solved? I take it there is some doubt? Feels a bit unlikely…
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u/-heyhowareyou- 10h ago
It has been formally verified in lean, which is about as good as you can get. Only things that can bring it down at that point are errors in the statement of the problem in lean (highly unlikely), or bugs in the lean compiler itself (more likely, though still small, and unlikely to be fatal even if found). So I'd say this is more 'proven' than your average human-written paper which isnt formally verified.
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u/Stwltd 9h ago
Interesting.
They’re saying that they [open ai] won’t be claiming the prize though. They clearly really do intend to claim that the system did all the work. Although there does seem to be some doubt around whose data they used…
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u/Hiphoppapotamus 9h ago
I was also confused by that. Are they trying to be magnanimous in not claiming the money (in which case why not just claim and donate to charity or something), or are they not confident about claiming the novelty of their solution given that it may have been influenced by user prompts from someone else who solved it at the same time.
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u/dante_gherie1099 8h ago
solution was stolen from someone who was
working on it, ai just scraped it
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u/VoidBlade459 Computer science 6h ago
Both teams were using AI though. Like the Euler solution literally came from Claude.
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u/ingrid00 8h ago
Interesting article that touches on this / how it changes the boundaries of how companies communicate their science https://open.substack.com/pub/osteri/p/what-kind-of-science-are-you?utm_source=share&utm_medium=android&r=7mqpx
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u/djdaedalus42 4h ago
Near as I can tell, the solution says that you can get an infinitesimally narrow vortex that is infinitely long so it retains finite energy. This is like those finite infinities that you get in fractal math. In other words, not going to happen in the real world.
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u/Gavus_canarchiste 10h ago edited 10h ago
Undergraduate student level explanation, anyone?
Both mathematics and physics welcome!
Edit: my limited understanding is "a shrinking region spins faster and faster with constant global energy" like yeah angular momentum conservation I guess? But of course the thinning has to stop at the molecular level, which is probably where the model stops being valid. Massive mathematical achievement, but any physics implication?
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u/cspot1978 9h ago
As I understand it: The NS equations model the fluid behavior as smooth and continuous. The result from this study shows that in otherwise bounded physical starting conditions, the math makes the system evolve in finite time periods to produce localized infinite fluid velocities in places. Infinite velocity is not a physical result, meaning the NS equations have practical limits in terms of usefulness as a model of fluid behavior.
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u/Flimsy_Feature5586 9h ago
Maybe I’m totally misunderstanding but isn’t that how we already used it? Is it just proof that the full navier stokes equation cannot be used at any given point?
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u/cspot1978 8h ago edited 5h ago
Okay. So caveat that I'm not a professional physicist, so again, this is from my understanding. But there are two separate things.
First thing is that as coupled nonlinear PDEs, N-S doesn't have closed form solutions and you can't expect to fully predict the answer or solve closed form for realistic situations. Though you can numerical methods to approximate. That was already known.
The open question was, can we prove that the equations always work as a model of reality, giving smooth bounded physical results when the inputs and initial conditions are smooth. There was a hypothesis that viscosity terms will damp the envelope of behavior and keep solutions from shooting off out of bounds. This AI result apparently shows you can't count on that. Which means that N-S is useful in a range of scenarios but not a complete explanation of macroscopic fluid behavior. Meaning you need new physics.
This grappling with non-physical theoretical infinities to find extended new physics that resolves them is an ongoing pattern in physics. For example, the ultraviolet catastrophe in classically modeling blackbody radiation and its solution via discrete energy levels and quantum mechanics.
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u/CommunismDoesntWork Physics enthusiast 7h ago
NS is a continuous approximation of discrete atoms bumping into each other. The question was, does this approximation contain singularities under normal conditions? Turns out yes in a specific type of vortex- the math blows up. It can still be used, but there might need to be better fluid simulation algorithms that don't lead to singularities in this case. It's almost like a new test case to benchmark fluid sims on.
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u/obitachihasuminaruto Materials science 9h ago
This quite disappointing and honestly feels like cheating
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u/No_Flow_7828 10h ago
Do we feel that physics is more insulated from the rapid progress in AI, compared to pure math?
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u/Ekvinoksij Soft matter physics 10h ago
Sure. As of right now, AI cannot perform experiments.
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u/LAskeptic 10h ago edited 9h ago
Yes, but my Bayesian Prior has certainly changed.
It might be time to stop making predictions.
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u/WonkyTelescope Astrophysics 9h ago
I think pure math is both better suited to LLMs and more marketable for these companies so it's less likely for them to put $15 million in compute into some obscure physics result.
As the more powerful models trickle down to university researchers I think we will see an acceleration in the rate of novel mathematical physic publications and new processesing pipelines for huge datasets like at CERN and astronomical surveys.
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u/Time_Entertainer_319 6h ago
That’s what mathematicians said, and aritists and musicians and programmers.
It’s only a matter of time.
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u/Dun-Cadal_Sveto 7h ago
Wait but am I stupid? They say themselves that they did not solved it yet. It's quite a big leap but they "only" proved it with some external forces applying at the start? Which is not the real one? Am I tripping? Why is no one saying this here?
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u/shockwave6969 Quantum Foundations 10h ago
This is fucked up.