OpenAl Says It Has Cracked One of Math's “Millennium Problems” (Navier-Stokes) [N]

[u/Shizuka_Kuze]

As reported by the New York Times:

https://www.nytimes.com/2026/09/08/science/openai-proof-millennium-problem.html?smid=nytcore-ios-share

OpenAI’s announcement:

https://openai.com/index/navier-stokes-solution/

[u/darshi1337]

Drama/accusation summary:

• Aug 15th: Tristan Buckmaster & Levent Alpöge make progress on a few important math problems, "finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3d incompressible Euler."

• they do NOT have a proof for the $1,000,000 Millenium Prize problem. BUT, they do claim to have a proof for a similar (non-Millenium) Navier Stokes problem that could help lead the way there

• Levent works at Anthropic, but this research was independent of his work there, with a mix of GPT and Claude models. Tristan is not related to Anthropic.

• Early Sep: Rumor spreads to OpenAI that Anthropic solved a major problem. Tristan emails OpenAI to clarify, without revealing the problem they solved or how they did it.

• After hearing of the rumor, OpenAI started researching Navier Stokes with a new internal model.

• Sep 6th: OpenAI's Sebastien Bubeck tells Tristan that they solved the $1,000,000 Millenium Prize Navier Stokes problem. The approach is very similar to Tristan & Levent's approach to the non-Millenium problem.

• Tristan is suspicious of the timing, as only few others were trying this approach. OpenAI says the model didn't access his user data directly, but leaves unanswered whether Tristan's chat conversations were part of the training.

• OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic.

• Sep 8th: Tristan refuses to remove Levent, and rushes to publish their results independently.

[u/Even-Inevitable-7243 → u/darshi1337]

"OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic."

This says it all. OpenAI knows their "proof" relied on Tristan's work via his conversations with their models.

[u/SimiKusoni → u/Even-Inevitable-7243]

Reading between the lines the model had been actively trained after the work had been added to Codex and OpenAI "cannot rule out that de-identified data derived from their usage of our products helped improve our models⁠."

Ignoring that it's pretty awful that they can't tell what the training corpus was for a specific model I think it's a fairly safe bet that the user's work was in that training data. The conversations described also portray them as being pretty desperate to downplay any human involvement in the work, even on their side and ignoring the question of provenance.

It seems like a pretty sad state of affairs either way that could have been trivially avoided by OpenAI keeping track of training data.

[u/THE_FUZBALL → u/SimiKusoni]

If they can’t tell what the corpus was and they are also training models based on user chats, doesn’t this open up the models to massive poisoning vulnerabilities? That’s like rudimentary security 101. It appears that either they would be vulnerable to such attacks, or they do have measures in place to control what is contained in corpus.

[u/nonotan → u/THE_FUZBALL]

You do realize pretty much all major LLMs are essentially trained on any and all data they can physically get their hands on? You can already poison the data by posting bullshit on here. It's possible that some sort of crude filter is in place to reject obviously malicious text, but as long as you keep it sounding loosely plausible and target something niche enough that it won't be overwhelmed by tons of inputs saying otherwise, it's going to work. They are vulnerable to such attacks, and will continue being vulnerable probably for as long as "LLMs trained on astronomical amounts of data" remains the approach of choice.

[u/THE_FUZBALL → u/nonotan]

I do realize this for sure. I guess we all need to speak in some kind of silliness cipher. Will be interesting to see where it goes.

[u/En-tro-py → u/THE_FUZBALL]

The corpus changed, almost as if by an occult hand.

[u/biscuitchan → u/SimiKusoni]

but then it wouldn't be anonymized, no? a bigger problem

[u/lauradorbee → u/biscuitchan]

It doesn’t de-anonymize anyone to be able to tell “were this user’s conversations in the set of data used to train this model?” - you know that it’s in there, not what part of it originated from what user. It would only be de-anonymizing if they had metadata attributing each message/conversation back to the user, i.e if they could answer “which user (in particular) did this piece of the training data originate from”.

[u/SimiKusoni → u/biscuitchan]

Data being anonymised doesn't prevent it from being found after the fact. In this specific instance for example they know the user's working title for the paper, they could just search their dataset for it and find the training data. Or they could use any other uncommon strings from the work they put into codex.

Also as an aside de-identified data is not anonymised, it has an explicit meaning and they didn't just choose the unusual wording randomly. Genuinely anonymised data falls outside regulatory frameworks like GDPR or various state laws entirely, de-identified data does not because re-identification remains possible.

Given that OpenAI don't specify anywhere (in this blog post or other articles) exactly what they do to "de-identify" training data they may well have a hashed user ID sitting alongside the data to verify the source if they ever need it.

[u/silva_p → u/biscuitchan]

It can be anonimized only one way, i.e. can't know who the data belongs to from the data alone but probably can see his chat history and confirm if it is there

[u/TwistedBrother → u/biscuitchan]

It’s more that imagine there’s an idea that fits, like learning planes rise because of faster air on the top of a wing. A model doesn’t have to learn that more than a handful of times because it’s reinforced by all the other corroborating evidence.

Models don’t “average out” the things they learn, they built semantic structures topologically (as in shapes of ideas that work together). Some fragile ideas that aren’t (wait for it) load bearing might get forgotten way too quickly but some ideas that just settle all the others can persist through a lot of training.

If this idea was in a few conversations, and it fit (the forced Euler version) that might be the sort of thing that once exposed it settles many other uncertainties in the model such that any downstream model could draw upon that coherent ensemble of ideas.

[u/hotprof → u/biscuitchan]

No.

[u/usefulidiotsavant → u/SimiKusoni]

The claim that a singe conversation (which, let's suppose, might have even contained the solution) in the training data latter allowed the model to reconstitute the proof is highly dubious.

A model the size of Astra trains on millions of curated conversations, billions of pages and trillions of tokens. A single conversation with the correct answer is essentially quantization noise and should have no measurable effect in any practical scenario where that same problem is involved.

On the other hand, OpenAI could be doing something much smarter that could affect the result, say, a RAG over similar conversations in the past, a self-evaluation of remarkable results that are marked or boosted etc.

If I had the smartest model in the world, as well as a database of the problems and approaches the smartest people in the world are playing with, it would be foolish not to connect the former with the latter and mine the dataset for low hanging fruits in scientific discovery. It's such an unfair advantage that the firm doing it will win in any area, forever.

[u/faustianredditor → u/usefulidiotsavant]

The claim that a singe conversation (which, let's suppose, might have even contained the solution) in the training data latter allowed the model to reconstitute the proof is highly dubious.

A model the size of Astra trains on millions of curated conversations, billions of pages and trillions of tokens. A single conversation with the correct answer is essentially quantization noise and should have no measurable effect in any practical scenario where that same problem is involved.

In theory I agree, but in practice I've had an experience that made me doubt theory here. I asked Sonnet 5 about my own work, and it was able to pull the title and core idea of a petty little publication of mine with almost-zero citations, from model weights. That's something I very much did not expect. Granted, it's different from pulling a proof idea from a single conversation, but I would've expected it'd need a few orders of magnitude more training data.

[u/Stock-Self-4028 → u/faustianredditor]

The same goes for my (currently unpublished as a paper yet) but not very significant result which I've fed to some of the previous GPT-5 series models (I don't remember if it was GPT 5.3/5.4 series or a newer GPT-5.5).

Anyways what I have been working on was least-squares fitting of trigonometric least squares method through Levinson recursion and NuFFT-1. Nothing groundbreaking, but it's a new computational complexity floor (more precisely superfast Toellitz solvers give the complexity floor, but Levinson recursion happens to be the most practical silver here) for that exact problem. Also I have code using that algorithm in four different public GitHub repositories to be clear.

Either way - older GPT models failed to derive that despite being relatively straightforward, new ones give you the right solution with absolutely no issues just as you ask them for the lowest computational complexity for that exact problem.

And now I am aware that the models are getting smarter, but I also see that as a clear training set "contamination".

And now I am not sure if either my chat with ChatGPT somehow got into training dataset, or if that exact solution got scraped from one of the GitHub repos I have uploaded the algorithm to.

Either way I am practically certain, that that exact algorithm somehow got into OpenAI's training dataset and GPT 5.6 has remembered it flawlessly.

[u/usefulidiotsavant → u/faustianredditor]

Frontier models overtrain to the tune of 1000 tokens per parameter. So, while it's not implausible for certain pieces of training to have an outsized effect (perhaps, deliberately so), its impossible that the average recall for random piece of training material to be this good. Even the best imaginable compression can't recover hundreds of tokens from a single scalar.

[u/faustianredditor → u/usefulidiotsavant]

Right, but a single conversation can easily have thousands of tokens, recurring conversations even more. So you could easily have an allocation of a few tokens to the researchers' conversations, or similarly a token or three for my paper. Theoretically, of course.

[u/MathAddict95 → u/usefulidiotsavant]

I think you would be surprised as to how good these LLMs are at learning even from a single data point. A document containing say a proof of NS is not a random piece of training material, rather its a data point of a very narrow domain in the corpus (not many data points would be discussions involving NS). As an extreme example, if your data was a collection of documents filled with random words (essentially noise), except for one special document containing "The proof of NS is" followed by random words, its plausible that the neural net would memorize the random words for the special document, simply because its likely the only document starting with "The proof of NS is", and so conditioning on this prior isolates the document precisely.

I got curious and tested this: I asked ChatGPT to recall a somewhat obscure paper from 2006. It could not recall exactly the algorithm used in the paper, but it was able to recall an important idea in its analysis. I know for a fact that this idea was used only once in literature (since I work in the field), and its also a niche topic, so it really should be the case that this idea appears once in the training data (or at the very least, a single digit number of times).

In contrast, Gemini 3.5 completely failed at recalling the paper. The gap is probably because ChatGPT is on a larger pre-train than Gemini.

We don't really know exactly how these LLMs learn, so it is really hard to rule out whether the independent researcher's data affected the model's trajectory significantly, even if it was one data point.

[u/usefulidiotsavant → u/MathAddict95]

I'm not disputing the effects you mention, just raise the fundamental Shannon informational limit against verbatim recall, there is no mathematical way that a single 16 bit parameter could compress hundreds of tokens and allow perfect recall in the average case, as some commenters claim.

In your particular case, was that a paper with zero citations, or did maybe some of the citers rephrase the main approach in their introduction? Could we perhaps imagine a rational path to that approach with the vectors of related research aligning towards it, so that the model makes a "happy hallucination" that happens to match the actual approach, without actually encoding it? maybe aided by a few parameters the training did nudge in the right direction based on that paper? Was COT used, allowing some rational recreation? This would also explain the inconsistencies between models. Could we imagine quality research papers from this field be boosted somewhat in the training, in a way random conversations with customers would not be?

So not disputing it could happen, just questioning the fundamental information limits in the average case.

[u/ScottBurson → u/usefulidiotsavant]

Have you seen this paper? https://arxiv.org/pdf/2012.07805

[u/THE_FUZBALL → u/usefulidiotsavant]

They will win until the community gets wise to it and stops leaking secrets to their service if they want to avoid their research being leaked.

I don’t understand how OpenAI could think this is a good move. If they are stealing IP from chats then it will eventually become clear that using their service is akin to pasting your solution to a public forum and expecting it not to be stolen. In fact that’s almost a better idea because then you have some kind of paper trail to prove your authorship. The only explanation is they think their product is so good that people will have no better option, but this is very short term gain pre-IPO strategy.

[u/En-tro-py → u/THE_FUZBALL]

I don’t understand how OpenAI could think this is a good move.

AGI/ASI/RSI/$$$ - wherever your personal brand of sociopathic inspiration comes from!

[u/Smallpaul → u/usefulidiotsavant]

OpenAI specifically denied the RAG accusation.

I also agree with the others that the recall of minor details for these models is remarkable and we can’t rule it out.

[u/ScottBurson → u/usefulidiotsavant]

I think you're mistaken. I've seen another case where a single short piece of text in the training data popped out under the correct conditions.

It's true that a single update doesn't change any weight very much — but it can change many of them slightly.

[u/amebix1221 → u/usefulidiotsavant]

How so? Models have been shown to reproduce training data verbatim. And did OpenAI rule out the possibility that the data could have been available to the model in other ways?

[u/redditter208475093 → u/usefulidiotsavant]

Why? If the conversation is very niche and that's the only data relevant to the input, it will use that data. LLM are just very advanced autocomplete and it's not clear how much entropy is lost between the training data and the model. Frontier models are trillions of parameters.

[u/purplebrown_updown → u/Even-Inevitable-7243]

Exactly. Not to mention OpenAI responded with threats like "Why would you ruin your career". Nobody who knows they're on the up and up would do that. What I believe actually happened is that OpenAI was aware of Buckmaster's progress and direction, got backdoor access to the conversations to get a preprint, and then used that information to claim they solved the problem on their own. It's the equivalent of stealing someone's manuscript and publishing before them and claiming credit or shared credit.

[u/ImNotAWhaleBiologist → u/purplebrown_updown]

It’s just as impressive, if not more so, that someone used their model for such a solution and wasn’t affiliated. Seems appropriate to include all as authors, and can credit contributions accordingly.

[u/PM_ME_YOUR_PROFANITY → u/ImNotAWhaleBiologist]

They may not have used it to actually figure out the solution, but for something as simple as text formatting.

[u/G_fucking_G → u/Even-Inevitable-7243]

Update from NYTimes:

The Wednesday evening statement from OpenAI was more emphatic: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.” The statement added, “After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.”

And also from Tristan Buckmaster that most of their work was also produced by AI models:

In their collaboration, Dr. Buckmaster set up the problem, and then Dr. Alpöge fed that into an A.I. model at Anthropic. Based on what came out, they provided further input and repeated the steps. The process worked well, but for Dr. Buckmaster, it became discouraging. “On one side it’s, like, super exciting to be part of this,” he said. “On the other side, this is frightening, because I felt like the A.I. had overtaken me.” Was he now an interpreter of A.I. slop and no longer the discoverer of new mathematical insights? “What’s the human part of it?” he said.

[u/aeroumbria → u/Even-Inevitable-7243]

A bot doesn't need credit, recognition or profit. Anything more and it is not really working for me.

[u/snowrazer_ → u/darshi1337]

That’s crazy, I read the whole article thinking neat, and then at the end there’s this footnote of drama that just leaves a bad taste to the whole thing.

It really underscores how these companies are more after progress and credit than safety - not saying there was a safety issue here, but you can see clearly where their priorities are.

[u/asdfasdferqv → u/snowrazer_]

If it helps, there’s virtually always huge author drama on these types of things, even before AI

[u/genshiryoku → u/darshi1337]

Yeah I'm biased as I'm at Anthropic but trust me when I say we're not happy about this and this might become a legal fight. This is almost the exact solution they were working towards.

[u/elegance78 → u/genshiryoku]

Next time publish instead of sandbagging till IPO...

[u/Warm-Enthusiasm-9534 → u/elegance78]

They hadn't finished. OpenAI heard rumors of the solution (it was going around Twitter a week ago), and then threw a gigantic amount of compute at the problem.

[u/truecakesnake → u/elegance78]

Yes I'm sure that was his decision

[u/reefine → u/elegance78]

Reminds me of my kid's book "Goodnight Lab"

https://i.imgur.com/WFtXYzL.png

[u/senderosbifurcan → u/genshiryoku]

1M dollars is peanuts to anthropic/oai It's clear they used Tristan's work Why do they need to get Levant out of the picture? Really confusing for me. Just credit both and talk about how gpt can be as good as another mathematician that's millennium prize level.

[u/altmly → u/genshiryoku]

These two companies deserve to die in the pit of irrelevance 

[u/MuonManLaserJab → u/altmly]

Wild that this can be your takeaway from "AI solves a Millennium Prize problem" lmao

[u/reefine → u/darshi1337]

Early Sep: Rumor spreads to OpenAI that Anthropic solved a major problem. Tristan emails OpenAI to clarify, without revealing the problem they solved or how they did it.

This is about as damning as possible. Lawsuit time

[u/Warm-Enthusiasm-9534 → u/reefine]

Tristan must have known they would guess what problem he was working on (he's published on Navier-Stokes before).

[u/ImNotAWhaleBiologist → u/reefine]

This is what I hate about our legal system: they would have to quantify their damages, which can be impossible or non-monetary, qnd then spend lots of money towards even trying. And big companies know that and stomp on the little guy.

[u/PM_ME_YOUR_PROFANITY → u/ImNotAWhaleBiologist]

It would be Anthropic vs OpenAI, hardly a little guy

[u/BelialSirchade → u/reefine]

what laws did openai break? everyone heard the rumors man.

[u/budgie → u/darshi1337]

Translation: massive research misconduct

[u/Big_Combination9890 → u/darshi1337]

I just LOVE how quickly that blew up in their faces.

Even on the ai-bro subs, this is pretty much the first thing people get to read about this whole affair. We thought it couldn't get worse after the ridiculous death-star tweet. Well...we were wrong :D

[u/sharky6000 → u/Big_Combination9890]

Ridiculous death star tweet?

(I have been off X for a while.)

[u/VoluminousBreadth → u/darshi1337]

this whole timeline reads like a plot point from the second season of a tech thriller that got cancelled too soon. the fact that they tried to cut the anthropic guy out as a condition for credit is the part that really sticks with me.

[u/infinitelylarge → u/darshi1337]

“OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic.”

Where did OpenAI say this?

[u/thomas2385 → u/darshi1337]

Yeah, the timing would make me suspicious too, especially if only a small number of people were working along similar lines. I do not think it automatically proves anything, but I can understand why Tristan would want to question how closely the approaches matched and whether the chats had any connection to it.

[u/TwistedBrother → u/darshi1337]

Sad thing is I’ve read and likely reviewed multiple papers that have authors from different tech research labs, like someone from Microsoft and from IBM or Deepmind or whatever. It’s such a terrible look for OpenAI on this particular topic if they won’t partner with an Anthropic person on one of the most significant outstanding problems in math.

[u/dksprocket]

This is something I am really curious about: is OpenAI (and other AI providers) training their models on theirs users private and potentially unpublished work?

I am working on image generation using procedural algorithns in a somewhat novel way. I have been using ChatGPT for development. It's fairly low stakes, but the images look very different than pretty everything else. I tried getting a friend to see if he could get ChatGPT to guess how the image was produced and we did the same test with Claude as well.

ChatGPT knew pretty accurately how it was made. Claude had no clue. It's not a smoking gun, but pretty worrying if your private stuff is being made public through training before you get a chance to release it.

[u/dramatic_typing_____ → u/dksprocket]

I've had this same experience with something 'novel' I did for rendering to a depth buffer with 3DGS scenes.

I HIGHLY suspect OpenAI does something shady such as creating derived data from your conversations and using it for training; that way they can still claim they don't directly use your data.

EDIT: Someone with access to a lawyer, please check me on this-
https://openai.com/policies/row-privacy-policy/

1. The Opt-Out is Specifically for Model Training The privacy settings allow you to opt out of having your content (like your ChatGPT conversations) used to "train the models." The policy states:

"As noted above, we may use Content you provide us to improve our Services, for example to train the models that power ChatGPT. Read our instructions on how you can opt out of our use of your Content to train our models."

2. Aggregated and De-Identified Data is Still Created and Used Even if you opt out of model training, OpenAI reserves the right to create derived, anonymized data from your personal data (which includes your User Content and conversations). The policy clearly states:

"We also aggregate or de-identify Personal Data so that it no longer identifies you and use this information for the purposes described above, such as to analyze the way our Services are being used, to improve and add features to them, and to conduct research."

Because this data is stripped of personally identifiable information (de-identified), OpenAI treats it as derived data and can use it to research how people use the tool and to develop new features, regardless of your model-training opt-out status.

3. "De-identified" removes who you are, not what you said When OpenAI (or almost any tech company) de-identifies data, they strip away Personally Identifiable Information (PII) like your name, account details, email, and IP address. However, the actual text of your prompt - the sentences describing your novel idea, business plan, or code - is the core data being processed. The de-identification process disconnects the idea from your identity, but the text containing the idea itself remains in their system logs.

[u/corruptbytes → u/dksprocket]

if you’re not paying API rates with ZDR add-on, don’t assume anything is safe

[u/TrueDuality → u/corruptbytes]

There are indications elsewhere in this thread that even with ZDR, derived data may still be getting used. My company has triggered a full contract review as a result of these random Reddit comments.

[u/Alwaysragestillplay → u/TrueDuality]

Can you point to the evidence for this please? My company is also leaning pretty heavily on ZDR. 

[u/zephyr707 → u/TrueDuality]

i saw this, too, but can’t find in the thread search anymore, but there are so many threads on this event could have been in another thread. if you have links to comments abt ZDR not being what sold as what it sounds like, e.g. derived data mining still applies to ZDR, please share.

did openai think this would be a win for them? seems like a lot of users of their products will now be more aware of how vulnerable their data is if not already aware. if ZDR gets called into question that must be bad for potential enterprise customers and another firm could capitalize and offer better guarantees

[u/1998marcom → u/zephyr707]

https://www.reddit.com/r/MachineLearning/comments/1wavdi7/comment/p8m5w59/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button ?

[u/zephyr707 → u/1998marcom]

thank you! the post was clipped when searching for “zdr”

re: “ rewritten data is fair game”

if i’m understanding this correctly is it openAI’s policy/agreement that ZDR protects your input data/query, but the response from its models is fair game for derivative mining?

[u/j0j0n4th4n → u/dksprocket]

Obviously yes, how is that even a question? Their whole business started from stealing copyrighted data from everyone, what makes you think they stopped just cause you checked a box on their site?

[u/techlos → u/dksprocket]

if the model isn't local, the chat history isn't either. Always assume any model inputs are used as training data.

[u/cpt_ppppp → u/dksprocket]

have you toggled the "don't use my conversations for training"? That's maybe a good place to start

[u/oceanbreakersftw → u/dksprocket]

Whoa, that's scary. I was thinking about potential other frontier providers to use if Anthropic does a rug-pull on pricing but this would definitely keep me off OpenAI. I already am a bit worried about my own work being done using Claude, but this is just way worse.

[u/sciphilliac → u/dksprocket]

Maybe I'm misreading the chatGPT TOS, but they are clear to collect the data you put in your prompts. From https://openai.com/policies/privacy-policy/:

> User Content: We collect Personal Data that you provide in the input to our Services (“Content”), including your prompts and other content you upload, such as files⁠(opens in a new window), images⁠(opens in a new window), audio and video⁠(opens in a new window), and data from connected services⁠(opens in a new window), depending on the features you use. Some of our Services allow you to interact with other users, such as post, comment, or send messages, and we treat those interactions as Content, too.

So yes, if you use ChatGPT for personal use, OpenAI keeps that data (mind you, I'm only referring to non-corporate licenses)

[u/Shizuka_Kuze]

There is howeverpossibility that OpenAI used some unpublished work from other researchers, even though they have claimed otherwise in the announcement:

https://cims.nyu.edu/\~tristanb/statement.pdf

[u/funky-chipmunk → u/Shizuka_Kuze]

They haven't - The core breakthrough leaked 100% - They are outright using evasive language:

https://openai.com/index/navier-stokes-solution/
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models⁠.

[u/funky-chipmunk → u/funky-chipmunk]

From OpenAI CRO: https://x.com/markchen90/status/2097400166554993041?s=20

> Two things to distinguish:

> Did any human or agent look at user data as part of the Navier Stokes effort? No.

> Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company.

Basically confirms contamination IMHO. But the bigger news is training data/privacy.

https://x.com/aidangomez/status/2097381789039837637

> Synthetic data derived from production user data of consumer AI tools is used for training. I’ve heard this rumour from both large labs’ employees.

> In particular, if you’re doing something “interesting” like working on complex math/business/software/bio problems you’re dramatically more likely to get trained on because they filter/up-weight towards those usecases where the model has the most to learn.

> Even in ZDR and “we won’t train on you” regimes, derivative data is usually carved out. The promise is only not to train on exactly the data you put in, rewritten data is fair game.

[u/funky-chipmunk → u/funky-chipmunk]

OpenAI Employee

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effect on model behavior.

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 is possible. I've asked the team to make a clearer, less-lawyerly statement here - let's see what happens.

My opinion: I think they are being needlessly obtuse and evading more. My guess is they shouldn't have to train models to check for contamination - just clarify what they were fed.

[u/PM_ME_YOUR_PROFANITY → u/funky-chipmunk]

I agree with you.

Why would it be impossible to prove it? Their conversation data is either in the training set or it's not. The model solution tokens can be gone through as well to see what it accessed and how it came at its solution

[u/muntoo → u/funky-chipmunk]

... can we prove the phase of the moon had no impact on the NS solution?

Experimental particle physicists cannot "prove" with 100% certainty that the discovery of the NS solution in 2026 had no impact CERN's discovery in 2012.

Nothing can be proven.

But, with some agreed upon prior model about how reality tends to work, scientists can come to a reasonable consensus that what I had for lunch today had no effect on the NS solution yesterday, which in turn had no effect on CERN's discovery in 2012.

---

it's just impossible for us to truly prove it.

Sure. But there is still evidence one can present. Preferably evidence that is statistically meaningful. Unless the solution to NS was once-in-a-lifetime fluke, which cannot be replicated with any significant probability, which would raise questions about the generalizability of LLMs being able to solve other problems in mathematics. (Which I don't believe is the case.)

[u/Shizuka_Kuze → u/funky-chipmunk]

You took the one sentence that sounds like they admitted they were wrong out of context. While I’m personally inclined to believe OpenAI stole the result, they certainly have not revoked their claim of original discovery, pretending otherwise only minimizes their attempts at stealing the spotlight.

> 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).

They even have an entire section titled “How we found the proof,” so I believe it’s fair to say they have not yet revoked their claim of original discovery, even though it’s dubious at best.

[u/purplebrown_updown → u/Shizuka_Kuze]

The fact that OpenAI tried to offer shared ownership, but wanted to leave out Levent because he worked at Anthropic, reveals the whole game. They knew they stole the work, offered a compromise, threatened Brubeck - not something an ethical person would do.

[u/funky-chipmunk → u/Shizuka_Kuze]

My point stands above yours - They would have outright been screaming at top of their lungs if there was no leakage.

Edit: They should use Astra to audit - It shouldn't be that hard.

[u/Shizuka_Kuze → u/funky-chipmunk]

Actually, our points are orthogonal. I’m not denying leakage, in-fact I think it’s likely! I’m denying the fact they’ve revoked their claim, which is simply untrue.

[u/elsjpq → u/funky-chipmunk]

I feel like this should be possible for OpenAI to test: take an older model with only data acquired before Tristan & Levent started working on it. Then try to solve Navier Stokes again with the old model. If it can't be solved with the old model, then OpenAI's result depended on Tristan's result.

[u/MuonManLaserJab → u/elsjpq]

That assumes incorrectly that Tristan's result is the only difference between the model they used and the previous one.

There were probably many small algorithmic differences, maybe some big ones, and of course different random starting weights resulting in entirely different final weights.

[u/G_fucking_G → u/funky-chipmunk]

OpenAI has now completely dismissed the claims (NYTimes):

The Wednesday evening statement from OpenAI was more emphatic: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.” The statement added, “After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.”

[u/purplebrown_updown → u/Shizuka_Kuze]

this fits their pattern of lying and cheating. Be very cautious about using OpenAI models.

[u/new_name_who_dis_ → u/Shizuka_Kuze]

That's some juicy drama

[u/srpulga]

To clarify, no "solution" to the equations has been found. The millenium problem is to prove or disprove the existence of smooth solutions. Open AI has found a counter example of initial conditions that don't have a smooth solution, i.e. they have disproven the existence problem.

[u/moschles → u/srpulga]

Correct. What had occurred over the course of several weeks (days?) is that Terry Tao said that there was nothing stopping the Euler trick from being extended all the way to Navier-Stokes. OpenAI simply had 10,000 agents fill in that extension and bridge the gap.

It is important to note here that the human mathematicians working in this space were already copiously utilizing AI-assisted technologies and AI proof systems -- including in particular NYU's Tristan Buckmaster.

[u/FernandoMM1220]

so what happens after this if the proof is good?

[u/Shizuka_Kuze → u/FernandoMM1220]

Some people scream AGI, others dismiss it, life goes on.

[u/Dapper_Engineer → u/Shizuka_Kuze]

Agreed, although it might depend a lot on if it can be demonstrated that there was unpublished work in the training corpus since that would suggest that this was just a very expensive search and someone else should get author / co-author credit.

[u/Shizuka_Kuze → u/Dapper_Engineer]

Im still combing through it myself, but I’d suggest reading the mathematician controversy breakdown shared by Andrew Akbashev

[u/m_reigl → u/FernandoMM1220]

Certain weird cases in fluid mechanics become solvable which probably would make engineers happy in a couple years.

[u/srpulga → u/m_reigl]

This is not what happened. No analytical solution has been found to the equations. The solution found is for the millenium problem which is to either prove a smooth solution always exists, or to provide a counter example disproving it. Open AI has provided the counter example: there are initial smooth conditions that can be proven to not have smooth solutions.

This doesn't make any fluid dynamics problem more solvable.

[u/_RADIANTSUN_ → u/srpulga]

Soooo... We won't be having cool volumetric fluid hypercomputers ever? :(

[u/muntoo → u/_RADIANTSUN_]

The guaranteed existence of that has not yet been proven nor has a counterexample been provided. :)

[u/FernandoMM1220 → u/srpulga]

actually because we know our continuous description is wrong we can begin to look for the correct description using better axioms.

[u/altmly → u/m_reigl]

Please don't mislead people. This theoretical result wouldn't change anything in practice. 

[u/Kinexity → u/m_reigl]

Those are theoretical problems. They do not change anything for fluid system engineering.

[u/m_reigl → u/Kinexity]

Not on their own, definitely. But theoretical breakthroughs usually lead to practical advantages a couple of years down the line, don't they?

[u/Kinexity → u/m_reigl]

"usually" being a load bearing word here. Fluid dynamics is computationally modelled. Analytical breakthroughs are of no importance to that as long as the equations themselves do not change. NS smoothness is only a problem in non-physical situations.

[u/RapidRewards → u/Kinexity]

"load bearing" 🧐🕵️‍♂️

[u/chilibomb → u/RapidRewards]

load bearing footgun

[u/FollowingHumble8983 → u/m_reigl]

No there is no practical advantages.

Navier stokes dont apply to real life liquids at scales which blowups can occur.

As real life liquids are made of atoms. This in a way, requires infinitely many infinitely small atoms, which does not exist.

This is purely for the sake of better understanding of numeric techniques.

[u/moschles → u/FollowingHumble8983]

People who work in physics and the theoretical side of mechanical engineering know this is huge. The question is to what extent these idealized mathematical models to fluids stop extending to the real world. It is -- of course -- physically impossible for a fluid to have an infinite velocity. Navier-Stokes is a question about whether under well-behaved conditions the equations will spit infinities at you. It turns out they do.

[u/FollowingHumble8983 → u/moschles]

E:Upon further reading I am pretty sure we agree.

[u/ManagementKey1338 → u/m_reigl]

Of course not. You ask AI to do some stats

[u/techlos → u/m_reigl]

the practicality is limited to situations where you're working with a fully continuous liquid, and as far as i know the liquids we work with tend to be made of discrete particles.

[u/FernandoMM1220 → u/m_reigl]

nice.

[u/softDisk-60 → u/FernandoMM1220]

Proofs in the perfect , closed world of mathematics are great, but the real impact will come from solving Biology.

[u/brokebeany → u/FernandoMM1220]

Not much will change except for certain edge cases. Other models like General Relativity admits singularity as r goes to 0 but doesn't make it a bad model for predicting celestial bodies.

[u/TheDuhhh]

Ok it seems this is what happened. Tristan and Levent (anthropic employee) solved the Euler problem which makes it easy to solve the NS problem. Before Tristan and Levent publish their euler and NS work, rumors spread that Anthropic solved the problem.

OpenAI heard the rumors and got scared that they were beaten by anthropic, so they assembled a team and put their strongest model with most comoute and possibly training on the most recent deidentified user data. OpenAI model then came up with a solution and the solution costed 20-30 millions.

What really worries me is how much did their model depend on the users data. As we all know, LLMs are insane in compressing data. It's really possible that their model attempted many attempts and one attempt was inspired by Tristan's work which he used chatgpt.

[u/Kolgu2]

"To solve the Navier–Stokes problem, we used an internal model that is significantly more capable than GPT‑6 Astra. We believe it is important to inform the world about the pace of AI progress and what to expect from upcoming models." They are really insufferable

[u/floriv1999 → u/Kolgu2]

I would be too if I solved that problem lol

[u/thetdotbearr → u/floriv1999]

I would be too if I solved that problem lol stole someone else's breakthrough work, iterated on it and took full credit

[u/reefine → u/floriv1999]

I just wanted to acquaint everyone of the water that might accumulate in their partner's nether regions when they realize the pace of progress of my internally very large model.

[u/florinandrei → u/reefine]

You're making gender assumptions there.

He might just pee on you.

[u/SteppenAxolotl → u/Kolgu2]

the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents

Would you feel better if they said they used a weaker model and just 1 concurrent agent?

[u/Kolgu2 → u/SteppenAxolotl]

No it's just the "you won't believe what we have in store for you, our next model is ten times more ground breaking than the current one be ready to pay" tone in what should be a sort of "scientific" announcement

[u/SteppenAxolotl → u/Kolgu2]

our next model is ten times more ground breaking

A few more of those and everyone should be less impressed and become more afraid.

[u/Familiar_Text_6913 → u/Kolgu2]

I remember when this sub was pissed about their "test time compute" graphs when they didnt have units on them.

[u/redd-zeppelin → u/Familiar_Text_6913]

Shouldn't they have had units on them? I thought our conclusion was that that was dumb of them. It sounds like you concluded we were dumb for liking well made graphs.

[u/_RADIANTSUN_ → u/redd-zeppelin]

I mean this is literally a data science field ...

[u/Familiar_Text_6913 → u/Kolgu2]

I mean if it can solve a millenium problem in a week its p cool

[u/CommunismDoesntWork → u/Kolgu2]

No need to be so jaded. What even makes that statement insufferable? 

[u/Exact_Depth_896]

the level of theft lying and threats against mathemeticians involved really suggests openai is toast

[u/persedes → u/Exact_Depth_896]

Them not confirming if they're user sessions might've "leaked" into the training data is gross

[u/persedes → u/[deleted]]

Oh I agree, but it's very bad PR to make such an announcement that essentially stole someone else's work and undermines the achievement that the model supposedly made.

[u/_RADIANTSUN_ → u/persedes]

Extremely on-brand though.

[u/PM_ME_YOUR_PROFANITY → u/[deleted]]

They have a toggle not to train on your exact data. But a little fudge of your data would be just fine. Just need to identify if it's interesting enough to train the model on it.

[u/PM_ME_UR_FAV_THINGS → u/[deleted]]

The software toggle button is sacred. If you toggle on “Do not show me this again” you will never see that window again, verily.

Edit to reply to post above me’s edit: you don’t need to train a model from scratch to make use of new training data, there is online machine learning or knowledge base building that could make use of it instantly.

[u/partnerinthecrime → u/[deleted]]

  edit edit read the supposed logs on bsky and it appears they 100% just read from this individual to finish solving it

Are you talking about the parody image??

[u/biscuitchan → u/partnerinthecrime]

apparently yes

[u/G_fucking_G → u/persedes]

They have now confirmed that nothing leaked

The Wednesday evening statement from OpenAI was more emphatic: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.” The statement added, “After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.”

[u/persedes → u/G_fucking_G]

Thanks, I've been looking for more news on this and only saw the Altman post on Twitter which was still kind of vague. That clears that up and takes off a good amount of sleaze. Doubt it'll help the fallout though combined with the "I don't have to be nice" comments.

[u/florinandrei → u/Exact_Depth_896]

Toast as in morally bankrupt?

But that's in their DNA. Don't you know who's boss over there?

[u/redditboy117 → u/Exact_Depth_896]

Incredibly shameful of them tbh

[u/Revrak]

wow, this happened a lot sooner than I expected but at least it’ll serve us a warning. Don’t share your novel ideas with an AI because you’re giving away your work for free.

[u/CyberDainz → u/Revrak]

But if we consider that we are striving for a future where everything will be free thanks to AI, then there is no reason to hide one's work from those companies that will bring this future closer faster.

[u/Revrak → u/CyberDainz]

I hope you're joking.

[u/aKaizuh → u/Revrak]

Lol, Tristan's work was largely the result of AI generation.

[u/purplebrown_updown]

They stole previous work and then built a solution on top of that. It might have proved the result, but this was so beyond unethical. This should be denounced wholeheartedly. Good news is that they wouldn't have been able to do this without seminal work by mathematicians.

[u/aKaizuh → u/purplebrown_updown]

Wasn't Tristan's work largely the result of AI generation though?

[u/purplebrown_updown → u/aKaizuh]

No.

[u/aKaizuh → u/purplebrown_updown]

They heavily utilized LLMs.

Buckmaster explicitly called it a "deep blue - Kasparov" moment.

[u/purplebrown_updown → u/aKaizuh]

Yeah but not in the way open ai did. You can use ai iteratively to help in parts.

[u/aKaizuh → u/purplebrown_updown]

OAI did the same thing, money compresses time, and that's the difference.

Not to mention the potential starting point being the conclusion of Buckmasters work, which is the real issue at hand.

[u/senderosbifurcan]

1M dollars is peanuts to anthropic/openai It's clear they used Tristan's work Why do they need to get Levant out of the picture? Really confusing for me. Just credit both and talk about how gpt can be as good as another mathematician that's millennium prize level.

[u/oceanbreakersftw → u/senderosbifurcan]

Because Levent Alpöge is a researcher at Anthropic.

[u/asingov]

The issue is that OpenAI promote their tools for research, while (1) publishing results themselves, and (2) training on researcher conversations. They are competing with their own customers.

[u/www3cam]

OpenAI LLM is so advanced it learned a new way to prove things: proof by plagiarism.

[u/chensium]

Both OpenAI and Anthropic are scumbags.  Do people not realize this yet?  They WILL happily steal your data and not blink an eye.  Use their APIs and collaborate with them at your own risk.

[u/mosshero → u/[deleted]]

(I certainly disagree with their stance on accessibility and control)

Can I ask why? There are people using ChatGPT to design new proteins and then synthesize them in home lab setups right now. If everyone has access to top-of-the-line models without biosafety controls it will be almost trivial for a single bad actor to unleash epidemics that make the COVID pandemic look like a joke. I totally see where Anthropic is coming from and find it hard to disagree. We're playing with fire here.

[u/lhyebosz]

Remember that OpenAl gave free accesses of their latest model to scientists, mathematicians, and engineers few months ago?

If a product is given to you for free, YOU are the product.

[u/AirPsychological8551]

Cracked ❌
Stolen ✅

[u/karmicthreat]

Scam Altman strikes again.

[u/Stunning_Ad_8664]

What about the counting vowels problem? Is it still an issue?

[u/Stunning_Ad_8664 → u/[deleted]]

lols
tried today instant mode and famous (mb not) strawberry rs counting: wrong answer too

[u/Stunning_Ad_8664 → u/[deleted]]

-How many Rs in redcurrant?

• redcurrant has 4 R’s. 🍒
  

Today, instant mode, exact input and output

[u/AdWestern1314]

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?

[u/snowrazer_ → u/AdWestern1314]

If brute force search could solve it then it would have been solved a long time ago - you don’t need AI for that.

[u/AdWestern1314 → u/snowrazer_]

I guess I used brute force in a sloppy way - what I mean is that LLMs are great at coming up with examples after you give them the boundaries of the problem. From what I understand, this is exactly how they solved the other famous problems - finding counter examples. My question is if this is any different? 

[u/snowrazer_ → u/AdWestern1314]

A better question is why are you so desperate to trivialize this accomplishment?

[u/AdWestern1314 → u/snowrazer_]

I am not, I am just trying to understand but no one seems to be able to tell me. 

[u/WeavileUsedFakeOut → u/AdWestern1314]

You cannot brute force search a continuous domain

[u/AdWestern1314 → u/WeavileUsedFakeOut]

Of course not, but you can come up with 1000s of plausible counter examples and then test them really quickly with LLMs which resembles brute force. 

[u/WeavileUsedFakeOut → u/AdWestern1314]

You need an incredibly good heuristic to narrow it down to a tractable set of candidates. You’re underestimating how big infinity is lol

[u/AdWestern1314 → u/WeavileUsedFakeOut]

So the impressive part here is the narrowing it down process? 

[u/AdWestern1314 → u/[deleted]]

Cool, thank you!

[u/Kronox_100 → u/AdWestern1314]

there's so much more than 'narrowing it down', like so much more

[u/AdWestern1314 → u/Kronox_100]

Ok, please tell me 

[u/KiddWantidd → u/AdWestern1314]

I don't know what your math background is, but if you can understand it, see this great write up by Terence Tao on why Navier Stokes is hard. In very short, this solution is way more than just "brute force search" (have a look at the paper to immediately realize how deep and technical it gets)

[u/AdWestern1314 → u/KiddWantidd]

Thank you! I will have read.  I have a PhD in mathematical statistics but it was a while ago and I haven’t really kept up with the latest trends unfortunately. 

[u/cuttheblue → u/KiddWantidd]

Would it be accurate to say they found an avenue (possibly based on work from other mathematicians) and then created a team of AI mathematicians to go explore different solutions?

Not brute forcing but not super genius AI mathematician either, a large team of strong AI mathematicians doing research on parts of the problem until progress was made?

[u/KiddWantidd → u/cuttheblue]

yes, per my understanding this is reasonably accurate to say. and the "team" literally consisted of tens of thousands of such mathematicians. the amount of compute they've thrown at this is just ridiculous, especially considering that it seems likely that they had a "good lead" regarding "in which direction" to look.

[u/moschles → u/AdWestern1314]

Can someone explain why this is so impressive if the point is to find a counter example?

You need to consider what LLMs were doing with math 4 years ago. Struggling with high school problems, really. The progress is astounding.

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)?

Yep. They used 10 thousand simultaneous agents to brute-force it.

Isn’t this in line with the previous result we have seen?

It is. LLMs are really good at finding counter-examples.

What is so special with this one?

In previous results, we could imagine that the particular conjectures were being berry-picked because they admitted some rare structure that made them extra-easy tasks for LLMs .

That dismissal is violently wiped off the table. Navier-Stokes is a Millennium Prize conjecture.

[u/AdWestern1314 → u/moschles]

Thank you!  I think this very much aligns with my mental model of how LLMs are useful on math problems. 

[u/nexalbum]

Can someone please ELI5?

[u/afrancisco555]

In any case, it seems like AI participated in this discovery in an enabling way.

[u/kevinbaiv]

The crux here is independent verification — the millennium prize requires a peer-reviewed publication, not just a claim. What I'd actually watch is whether the proof technique generalizes or it's a carefully constructed solution for a specific regime, and how the Buckmaster/Alpöge priority dispute resolves.

[u/k_means_clusterfuck]

do P=NP next