10 ms·

The Navier–Stokes Millennium Prize Problem

233 points by tosh 8d ago

michalsustr 7d ago
If you'd like to explore what the Navier–Stokes blow-up construction looks like visually, I vibe-coded an interactive 3D visualization based on the published result for fun :) Demo: https://minfx.ai/navier-stokes/ https://minfx.ai/navier-stokes/ Source code: https://github.com/minfx-ai/navier-stokes-blowup https://github.com/minfx-ai/navier-stokes-blowup
1vuio0pswjnm7 7d ago
08 Sep 2026 05:42:28 UTC | Navier-Stokes Tristan Buckmaster [pdf] | http://cims.nyu.edu/~tristanb/statement.pdf http://cims.nyu.edu/~tristanb/statement.pdf | https://news.ycombinator.com/item?id=49605915 https://news.ycombinator.com/item?id=49605915 | 823 comments 08 Sep 2026 07:50:24 UTC | I talked to deep buddy about AI solving Navier Stokes rumors | http://www.echohive.ai/deep-talk-buddy/navier-stokes http://www.echohive.ai/deep-talk-buddy/navier-stokes | https://news.ycombinator.com/item?id=49606955 https://news.ycombinator.com/item?id=49606955 | 0 comments 08 Sep 2026 14:40:37 UTC | Major breakthrough made on Navier-Stokes Problem | http://www.newscientist.com/article/2588115-major-breakthrough-made-on-famous-millennium-maths-problem/ http://www.newscientist.com/article/2588115-major-breakthrou... | https://news.ycombinator.com/item?id=49610993 https://news.ycombinator.com/item?id=49610993 | 3 comments 08 Sep 2026 15:02:35 UTC | Has OpenAI model solved 80-year-old Navier-Stokes problem? | http://www.firstpost.com/tech/has-openai-model-solved-80-year-old-navier-stokes-problem-mathematician-raises-questions-14044080.html http://www.firstpost.com/tech/has-openai-model-solved-80-yea... | https://news.ycombinator.com/item?id=49611362 https://news.ycombinator.com/item?id=49611362 | 3 comments 08 Sep 2026 17:13:21 UTC | On the NavierStokes Millennium Prize Problem | http://openai.com/index/navier-stokes-solution/ http://openai.com/index/navier-stokes-solution/ | https://news.ycombinator.com/item?id=49613262 https://news.ycombinator.com/item?id=49613262 | 1129 comments 08 Sep 2026 17:26:44 UTC | Navier-Stokes and the Future AI Acceleration in Science | http://blog.valency.io/posts/navier-stokes-ai-science http://blog.valency.io/posts/navier-stokes-ai-science | https://news.ycombinator.com/item?id=49613469 https://news.ycombinator.com/item?id=49613469 | 0 comments 08 Sep 2026 18:41:41 UTC | We're Sharing a Solution to the Navier-Stokes Millennium Prize Problem | http://twitter.com/OpenAI/status/2097374640582668336 http://twitter.com/OpenAI/status/2097374640582668336 | https://news.ycombinator.com/item?id=49614788 https://news.ycombinator.com/item?id=49614788 | 1 comment 08 Sep 2026 19:35:46 UTC | Improve the model for everyone: OpenAI and the NavierStokes problem | http://twitter.com/danimberman/status/2097379292367802672 http://twitter.com/danimberman/status/2097379292367802672 | https://news.ycombinator.com/item?id=49615732 https://news.ycombinator.com/item?id=49615732 | 1 comment 08 Sep 2026 20:28:33 UTC | Show HN: Browser viz of OpenAI's "spaghetti" NavierStokes vortex (illustration) | http://3d-retro.com/experiments/vortex http://3d-retro.com/experiments/vortex | https://news.ycombinator.com/item?id=49616564 https://news.ycombinator.com/item?id=49616564 | 1 comment 08 Sep 2026 21:31:38 UTC | Global regularity problem for the incompressible three-dimensional Navier-Stokes | http://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/ http://terrytao.wordpress.com/2026/09/07/finite-time-blowup-... | https://news.ycombinator.com/item?id=49617372 https://news.ycombinator.com/item?id=49617372 | 0 comments 08 Sep 2026 22:56:30 UTC | Navier-Stokes Proof | http://medium.com/@m.alfaro.007/open-sourcing-the-universes-code-navier-stokes-eight-pages-and-the-speed-of-light-cbbf4ee84464 http://medium.com/@m.alfaro.007/open-sourcing-the-universes-... | https://news.ycombinator.com/item?id=49618321 https://news.ycombinator.com/item?id=49618321 | 0 comments
1vuio0pswjnm7 7d ago
09 Sep 2026 02:11:50 UTC | Statement from AMS Leadership on Navier-Stokes Problem | http://www.ams.org/news?news_id=7686 http://www.ams.org/news?news_id=7686 | https://news.ycombinator.com/item?id=49619946 https://news.ycombinator.com/item?id=49619946 | 1 comment 09 Sep 2026 03:02:22 UTC | Navier-Stokes Sebastien Bubeck | http://twitter.com/SebastienBubeck/status/2097379411691516310 http://twitter.com/SebastienBubeck/status/209737941169151631... | https://news.ycombinator.com/item?id=49620327 https://news.ycombinator.com/item?id=49620327 | 3 comments 09 Sep 2026 07:04:58 UTC | Sam Altman's statement on the Navier-Stokes dispute | http://twitter.com/sama/status/2097385167002415140 http://twitter.com/sama/status/2097385167002415140 | https://news.ycombinator.com/item?id=49622377 https://news.ycombinator.com/item?id=49622377 | 8 comments 09 Sep 2026 13:08:45 UTC | The Navier-Stokes solution for the legal profession | http://lexifina.com/blog/navier-stokes-solution-for-the-legal-profession http://lexifina.com/blog/navier-stokes-solution-for-the-lega... | https://news.ycombinator.com/item?id=49625957 https://news.ycombinator.com/item?id=49625957 | 0 comments 09 Sep 2026 13:59:20 UTC | Navier stokes- Problem solution and the math for absolute dumbfucks | http://x.com/kingofknowwhere/article/18 http://x.com/kingofknowwhere/article/18 Jun 2036 22:40:17 UTC640886376 | https://news.ycombinator.com/item?id=49626706 https://news.ycombinator.com/item?id=49626706 | 0 comments 09 Sep 2026 14:39:38 UTC | OpenAI's 165-page Navier-Stokes proof failed a basic physics test | item?id=49627395 | https://news.ycombinator.com/item?id=49627395 https://news.ycombinator.com/item?id=49627395 | 0 comments 09 Sep 2026 16:28:57 UTC | To Serve Man: AI, Math, and NavierStokes | http://ml5885.github.io/writing/navier-stokes.html http://ml5885.github.io/writing/navier-stokes.html | https://news.ycombinator.com/item?id=49629132 https://news.ycombinator.com/item?id=49629132 | 2 comments 09 Sep 2026 17:33:47 UTC | Lean certificates accompanying Navier-Stokes and Euler results | http://github.com/openai/NavierStokesAndEuler/tree/main http://github.com/openai/NavierStokesAndEuler/tree/main | https://news.ycombinator.com/item?id=49630159 https://news.ycombinator.com/item?id=49630159 | 0 comments 09 Sep 2026 18:54:55 UTC | NavierStokesAndEuler | http://github.com/openai/NavierStokesAndEuler http://github.com/openai/NavierStokesAndEuler | https://news.ycombinator.com/item?id=49632068 https://news.ycombinator.com/item?id=49632068 | 0 comments
marcus_cc 6d ago
[flagged]
tosh 8d ago
> My two favourite hypothetical questions regarding this used to be: > If I'm running Codex and one of my API keys accidentally gets consumed in the context, what are the chances that someone else might ask for an API key in the future and get mine back? (I asked someone at OpenAI once and they called this the "regurgitation" problem and assured me that they take great pains to prevent that... but wouldn't describe how.) > If I brainstorm with ChatGPT about potential new directions for my company, what's the chance that information might be exposed to a competitor in six months' time who asks "what might company X plan to do next"? > My new preferred hypothetical for this is: > If I use ChatGPT to help me partially solve a Millennium Prize problem, what are the chances that my work will influence training such that a later model helps someone else solve it first?
- weinzierl 8d ago
  Maybe just a rumor of a high value target having their API keys accidentally consumed in the context...
- feverzsj 8d ago
  LLM can't be trained that easily. More like actual human are checking your logs and stealing valuable things from you.
  - grey-area 8d ago
    Or searching anonymised logs for mentions of this problem and using that as part of the context or training. This would work just as well and have plausible deniability.
    - rakejake 8d ago
      Exactly! This is the real Occam's Razor explanation.
  - rzzzt 8d ago
    They wouldn't appear in weights but could be added to the context. My conversations regularly go "regarding your Java problem"... which was a separate item in the history from earlier. As long as I only see these (and nobody else sees mine), it can be helpful.
shellfishgene 8d ago
What's missing from the story I think is the part about "...then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear...". If only the two of them were working on the problem in secret, how did their breakthrough become a rumor?
- dboreham 8d ago
  They weren't working in secret?
- tyre 8d ago
  People talk. If you have a breakthrough solving one of the most famous problems outstanding, you're going to tell people. You'll say, "Don't tell anyone", which they will ignore because they get a rush and perceived status by sharing it. So then they tell someone, along with "Don't tell anyone", etc. It's a small enough world (both in academic math, one at Anthropic) that you get to OAI in very few hops.
  - dguest 8d ago
    The reality is also that most of your colleagues have no interest in stealing your work: they have their own work to do anyway, and having a colleague effervescing about whatever they are working on is kind of the norm in pure research. Just because they are making progress it doesn't mean they are about to do anything interesting. Also it's not like you're looking for a lost pair of car keys: just getting to the level where you can understand a problem well enough to "steal" it takes a huge amount of work. People are going to know if you're at the level where you could be a competitor. So in general it's pretty safe to talk generally about whatever you're doing.
  - 20k 8d ago
    "The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag." We know that OpenAI trained on their prompts, plagiarism is incredibly likely. The only thing we don't know is whether or not it was deliberate plagiarism yet
caughtinthought 8d ago
Basically no new info here, not really sure why this post needed to be written tbh.
- iso1337 8d ago
  [flagged]
  - jdlshore 8d ago
    There’s no shilling here. The person who posted the link isn’t the person who wrote the blog.
    - sk4rekr0w 8d ago
      He is in the HN ingroup of whenever he posts a blog, a prominent HN mod or poster with 1 billion karma will inevitably post it, and so it goes. It's sort of like the music industry.
      - neuroticnews25 8d ago
        Does poster karma boost the post in any way?
        sk4rekr0w 8d ago
        I don't believe HN boosts their algo but I think people recognize posters like celebs. I recognize tosh, simonw, etc. Also it's an easy way to farm karma. The pelican guy posted a pelican, let's upvote it? It's at least a bit of psychosis / mass effect in this. For what it's worth, I like the pelicans but just making an observation
        retsibsi 8d ago
        > It's at least a bit of psychosis I know semantic shift is inevitable, but can we put the brakes on this one at least a little? This doesn't even connect to the original meaning.
tyre 8d ago
Yeah, this was pretty shitty by OpenAI. Not surprising, sadly. Them being assholes, trying to exclude an author just because he worked at Anthropic, shows the kind of culture within (that part of) their organization. The focus wasn't on supporting academics or expanding research. It was on getting great marketing. If they had to burn millions of dollars solving a problem _that they thought was already being solved_ to do so, they'd do it.
deleted 8d ago
[deleted]
dboreham 8d ago
The concept that "knowing something has been done" allows others to find the solution to an previously unsolvable problem is an old proven one. For example when Germany launched a rocket (V2 prototype) the British knew its rough trajectory and from spying it's rough size. Although they had previously believed that ballistic missiles weren't possible because no engine could provide the necessary thrust to weight ratio, given the obvious German launching of one, they went through all the known chemical compounds to arrive at the combination (Ethanol and LOX) used. [Story from RV Jones "Most Secret War"].
octocop 8d ago
Is there a good tldr on this topic?
- emil-lp 8d ago
  This article is the tldr.
nicce 8d ago
Can’t wait to see the human verifying the results and then figure out that the AI model actually cheated and the results are not correct.
- imjonse 8d ago
  the proofs were verified in Lean, so unlikely.
  - nicce 8d ago
    As long as the proofs itself are correct. How long they were this time? Edit: at least ~600,000 lines https://stanfordtechreview.com/articles/openai-buckmaster-navier-stokes-lean-proofs https://stanfordtechreview.com/articles/openai-buckmaster-na...
    - latent-person 8d ago
      To claim something verified in Lean is wrong, you need to either argue that the theorem was stated incorrectly, or that there is a bug in Lean (assuming no `sorry` etc, which is checked by comparator). The number of lines needed to prove it is irrelevant (other than checking for a bug in Lean gets harder).
      - nicce 8d ago
        That is the point. Someone must verify that the Lean matches the actual theorem, precisely as it should be interpreted.
        latent-person 8d ago
        Which has nothing to do with the total number of lines, it's just the theorem statement you need to check. Here is what they showed, which is under 300 lines with comments https://github.com/openai/NavierStokesAndEuler/blob/main/ComparatorChallenges/NavierStokes.lean https://github.com/openai/NavierStokesAndEuler/blob/main/Com...
avs733 8d ago
I’ll go back to the point about authorship. I’m Not a mathematician but I am in academia. if you are fucking around with authorship you are immediately suspect. That aspect alone would/should be unthinkable to any serious academic. Authorship reflects who did the work and changing it for business competition reasons should be a red flag for multiple different reasons. They include, the sheer tactlessness of treating a major theoretical advancement as a competitive posturing first, the norms of academia second, and all the misunderstandings of the culture of the disciplines culture that people will now suspect are hiding beneath the visible surface (insert topography joke). Math as a field is fairly unique even in how they list authorship. It was long the norm that authorship to be alphabetical because the idea of first, second, senior etc authorship is harder to define than many other fields. “The stated rationale for alphabetical order is that it treats co-authorship as intellectually joint work: every listed author’s name carries equal weight, and no one has to negotiate, or be seen to negotiate, over billing. That is a genuine advantage over position-coded conventions, where disputes over who is “first author” are one of the most common sources of authorship conflict in fields that use them” [0] That norm is changing, slowly, but one option people are pursuing is notable: randomized author order. Their is a perception that alphabetical is too biased…that’s the world OpenAI is stepping into when they make that offer of authorship to one scholar with a demand that he exclude his partner. I can’t speak to the facts of anything else in this, but if a grad student came to me and said someone made them that offer, I would tell them to run and if they were brave report it. [0] a to the point lay description of the history of math authorship can be found here: https://casrai.org/guides/mathematics-alphabetical-authorship-tradition https://casrai.org/guides/mathematics-alphabetical-authorshi...
- emil-lp 8d ago
  Yes, there is no doubt about scientific misconduct. I think the entire math community agree on that.
- sobellian 8d ago
  OAI's side of the story is that they discovered the approaches (and indeed solved problems - Euler equations vs NS equations) differed. They then offered Buckmaster lead authorship of OAI's proof, without Alpöge. But they never demanded that Alpöge be stripped of coauthorship on resolving the regularity of the Euler equations. At least that's the claim. https://xcancel.com/SebastienBubeck/status/2097379411691516310 https://xcancel.com/SebastienBubeck/status/20973794116915163...
sdcfgy 8d ago
My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no. I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.
- junofan 8d ago
  Their privacy policy for normie subscribers says in plain English they use your Personal Data for research. I think it’s pretty unreasonable to use the service and expect otherwise.
  - ZeWaka 8d ago
    >implying most users read them
  - andersmurphy 8d ago
    You'd think theft would still be illegal regardless of what a privacy policy says.
    - georgemcbay 8d ago
      > You'd think theft would still be illegal regardless of what a privacy policy says. I wish that were true, but I live in the United States and it is 2026. The President of the United States rug-pulls memecoin crypto and regularly pardons people like Paul Walczak (who was convicted of massive payroll fraud) in exchange for large donations. I wouldn't make any assumptions about what is considered theft anymore, at least not when it is being committed by people who have enough money to be above the law.
      - andersmurphy 8d ago
        I mean the fact that comments like this get downvoted is wild.
  - 8d ago
civvv 8d ago
LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence», I wonder if we will see similar examples by LLM’s soon. It seems to me currently impossible that LLM’s can replace human mathematicians, because of their (assumption) likely dependence on human input in the sense of enormous amounts of pre-existing attempts/data. If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt an LLM would be useful at all on their own. Is this the «ultimate ASI test»?
- krona 8d ago
  Extreme temperature levels (>2.0) can push a GPT of its manifold, essentially producing predictions barely distinguishable from random noise (it flattens the probability distribution of the next token). In theory this could predict anything including the next field of mathematics (infinite monkey theorem) but realistically that would never happen. However, how to we know the next field of mathematics isn't a novel combinations of several other sub-fields? That level of mathematics would be indistinguishable from magic to most people and so in their eyes the GPT did something truly inventive.
- eru 8d ago
  A lot of what humans do is combining old ideas. And an LLM could in theory also stumble upon entirely new ideas: there's randomness in how they generate their reasoning and answers after all. I suspect that we are seeing a lot of advances coming from the combination of existing but somewhat obscure knowledge coming from LLMs at the moment, because LLMs are really good at this. At least compared to humans. Even before our AI friends became good, they were already known for having read approximately every paper and every textbook published in any language. You only need to increase intelligence a fairly small amount from there to get to something like the 'convex hull' of human knowledge. Compare https://slatestarcodex.com/2016/11/17/the-alzheimer-photo/ https://slatestarcodex.com/2016/11/17/the-alzheimer-photo/ The gist is that basically whenever anyone comes up with a new method you get a big burst of activity of picking up all the now lower hanging fruit, that was previously out of reach.
kdavis 8d ago
All your datum are belong to us!
aadyachinubhai 8d ago
LLMs can't contribute good code to some of the good OSS math libraries, How is it even solving these problems?
- matrix2596 8d ago
  search, verifiability and compute
- emil-lp 8d ago
  That's a good question. It is able to contribute code, but maybe not good code. It's the same in math: it's able to solve problems, but not necessarily in a good way with a human readable code. Math papers are a lot like software: - theorems are like API - lemmata like internal/private function API - definitions are like types - the proofs are the implementation The proofs of ChatGPT are not necessarily readable or maintainable.
- linkgoron 8d ago
  You don't need a GOOD proof, just A proof.
- feverzsj 8d ago
  No one knows if it's actually LLM doing the heavy weight. It could be just human written brute force algorithm running on their massive computer cluster.
- vbarrielle 8d ago
  Math problems are often stated in a way that makes it possible to automatically verify if a solution is correct. Which means a loop that speculates an approach (LLM and/or prompts), implements it (LLM), then checks (automated) can work. You still need to have a very good LLM, and probably very good prompts with interesting research directions otherwise you can probably loop forever.
- recursivecaveat 8d ago
  Notably all the major announcements so far are counterexamples or formalizations of existing results to my knowledge. Not necessarily something you can just brute force, but areas with high return on elbow grease.
rao-v 8d ago
It’s reasonable to wonder about what chat usage data gets into models (to be honest probably quite little - carefully curating training data and creating higher quality synth data seems to be the current approach) and the implied risk to privacy and creativity (every new patent filed this year probably touched a model before filing). What I cannot reconcile is the timeline and the concern in this specific case. I don’t think training pipelines are anything close to the level of continuous training needed to incorporate Aug 15th ideas into a model that generates a breakthrough early Sept. Either OpenAI nakedly had someone with mathematical understanding dig into a specific user’s chats (a massive red flag) or this really is poor handling of a more classic parallel discovery situation (with one party clearly having worked on it longer)
- KeplerBoy 8d ago
  I would assume a lot of codex data goes back into training. A well steered session is extremely valuable data.
- simonw 7d ago
  The breakthrough was on August 15th, but Tristan and Levent had been working towards it (with the help of various models) for the best part of a year. I personally doubt that their work influenced the OpenAI result - OpenAI themselves say "While unlikely, we cannot rule out that..." - but that "we cannot rule out" is exactly the problem. If even OpenAI "cannot rule out" the influence of their usage of ChatGPT on this layer result then my discomfort at not understanding how my own usage of ChatGPT affects its training is magnified.
josalhor 8d ago
I think this drama was blown up a bit out of proportion. The entire discourse I am seeing online seems to revolve around this: > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models I mean... yeah? What do you expect? What else can they say? How could you prove a negative in this case? I do not want to comment on specific OAI employee chat messages, but on the actual OAI discovery here.
- emil-lp 8d ago
  If they have zero-retention, then it is not possible. So what they are saying is that they don't have zero retention.
  - josalhor 8d ago
    But why is this news? This is clearly described in their ToS and in the Settings to improve their models.
- Fordec 8d ago
  A very simple "these two pipelines don't connect up in our architecture, here's our internal high level network diagram combined with our data ingestion opt-out feature flag that we will stand by in court" as opposed to "yeah, we don't even entirely know how our own customer facing systems are connected to our training pipeline, but it probably didn't happen".
  - josalhor 8d ago
    Have the other researchers opted out? On all their accounts? Through the entire time? And did they discuss this with anyone else? And did those people ask ChatGPT stuff? And did they disable it? If I was OpenAI, I would be very careful about my wording here when making claims of "we have never trained on any of their ideas directly or indirectly".
    - Fordec 8d ago
bob1029 8d ago
> ... we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors ... I've observed this exact effect last week. I made a discovery regarding a stepwise performance improvement in a codebase. I shared the benchmark results with a peer and within 12 hours they replicated the same. We had both been looking for this for years. I think giving someone hope that an answer exists might as well be the same thing as giving them the answer these days. Competition is a hell of a drug, and frontier LLMs aggressively compound that energy.
- adg33 8d ago
  It's something that happened before LLMs - multiple discovery. Calculus is a classic example.
  - jansport123 8d ago
    Yes but in this case, the allegation is Leibniz literally looked into newtons notebooks
    - adg33 8d ago
      Yep - it's a different case. But the idea that without LLMs, it's unlikely the same idea would be discovered independently is not true - it does happen.
- skylurk 8d ago
  > I think giving someone hope that an answer exists might as well be the same thing as giving them the answer these days. If you read the history of major scientific discoveries, this has been the case for a long time. There are many things that were independently discovered by different people at nearly the same time. Once people know something is solved or solvable, it gets a relentless amount of focus.
  - eru 8d ago
    This seems to be the norm rather than the exception. On a tangent, the genius of people like eg Einstein is not so much that he came up with all these things: other people were close, but that he was a singular individual that did all of these discoveries, instead of five different guys all making some breakthrough here or there.
l5870uoo9y 8d ago
I run a small SaaS[1], like so many others, that uses AI to generate and optimize SQL. Getting this to perform optimally has been a lot of work and now I wonder if OpenAI is outright stealing this knowledge, which without a doubt is highly valuable to them. [1]: https://www.sqlai.ai https://www.sqlai.ai
- KeplerBoy 8d ago
  SQL is so ubiquitous and the use case so obvious, there's no way they have not already been tracking performance and benchmaxxing on SQL queries for years. But I don't think openai will bother to release a competitor, the real threat is that anyone with a decent LLM and a harness to try a few queries will land at the same or a better query within minutes.
- biorach 8d ago
  It's extremely unlikely that there is anything interesting or novel in the optimisation of a small SaaS SQL
  - krapp 7d ago
    But what if they added "be interesting and novel" to their prompt? Did you consider that?
    - biorach 7d ago
      I did not. Having spent considerable amounts of time undoing the effects of overconfident junior programmers who decided to be interesting and novel on small business code bases, I guess if we're going to replace juniors with AI we may as well ask for the full experience.
- paxys 7d ago
  No one wants to “steal” your vibe coded crap. Your prompts aren’t as unique or valuable as you think.
feverzsj 8d ago
It could be much worse. OpenAI can easily identify these outstanding human behind their accounts. Human in OpenAI constantly check their logs for breakthrough. When they find something interesting, they brute force the result using their massive computing power. No LLM is even needed.
- grey-area 8d ago
  Or, using anonymised data, search for anyone seriously trying to tackle this problem - probably about 10 people in the entire world and use their ideas as a starting point. They wouldn’t even need to be watching specific accounts or using de-anonymised data if they know what they’re looking for.
cs_throwaway 8d ago
Maybe someone on the NYU team forgot to opt out of “improve the model for everyone”.
burrish 8d ago
>While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. What do you mean, as OpenAI employee, you cannot tell that his work has entered the training data ? But also correct me if I'm wrong, if the two mathematician were really close to finish this problem, and their conversation were used by OpenAI, shouldn't the Agent have succeeded way faster/efficiently instead of using "4.9 million messages and used about 300 billion output tokens."
- feverzsj 8d ago
  It's almost as if it was actually found by manually written brute-force algorithm running on OpenAI's massive computer cluster.
- jansport123 8d ago
  I’m not a mathematician so take this with a grain of salt. Apparently terry tao commented that the approach used for the Euler paper can “probably” be used for solving NS but it’s still technically challenging and can probably be done with an LLM with a lot of compute. To me the crux of the issue is whether the insight were stolen so that the problem becomes something that is in the domain of LLMs. This is much different than LLMs coming up with the insight. OpenAI wants everyone to think the LLM came up with the insight and solved the thing by itself even though they have perhaps an army of researchers.
- CSMastermind 8d ago
  Having the chat logs enter the training data and having them have a meaningful influence on the ultimate result the model produces are very different things. The text for all the Goosebumps books are certainly in the training data and to some small amount influenced the solve. But their contribution was so vanishingly small it would seem absurd to say R L Stein should have recourse for contibuting to the solve.
  - pbmonster 8d ago
    But this is different, right? The equivalent would be taking a (fully offline) LLM and asking it about the ending of one specific Goosebumps book, and it revealing the twist. And although that specific book was (probably) only once in the training data, a high parameter LLM can usually "remember" the twist.
sk4rekr0w 8d ago
Time to repeat the same angry mob style discussion again. Great job to the mods.
protoman3000 8d ago
If they wanted to solve a Millenium prize problem so much, why did they not try to solve P-NP instead? It boggles the mind.
- cammikebrown 8d ago
  That one is way more difficult.
- eru 8d ago
  What makes you think they didn't try?
- throw-qqqqq 8d ago
  Are you kidding/trolling? The P=NP problem is FAR more fundamental, and if proven true, would basically be a proof that e.g. public key crypto can be broken (NOT a description of how to though). Basically, it would be a proof that all the REALLY hard (combinatorial) problems out there, have a much simpler solution, if we were able to find it. EDIT: NS is used daily in engineering and gas/fluid modeling. We sort of “know it works”. The smoothness proof is “just” formalizing what practitioners assume is true (very coarsely said, no intention to diminish the result!) It’s a bit like the Collatz function IMO, empirical evidence isn’t proof, but we’ve got a huge amount of evidence for the behavior we’re trying to prove. I believe P vs NP is a different beast entirely. We don’t even know which way the answer should go.
  - eru 7d ago
    > The P=NP problem is FAR more fundamental, Yes. > and if proven true, would basically be a proof that e.g. public key crypto can be broken (NOT a description of how to though). Well, only if the answer is that P=NP. > I believe P vs NP is a different beast entirely. We don’t even know which way the answer should go. Most people expect P < NP, and then crypto wouldn't be broken. P=NP would also break pseudo-random number generators, for pretty much the same reason as the rest of crypto. However Don Knuth is one example of an expert who thinks P = NP is plausible. Btw, we do know quite a lot about how a proof of P vs NP will _not_ look like. That is we are in the curious situation where we can prove that certain proof techniques won't work on this problem. Weirdly enough, we already have the optimal algorithm, we just can't prove its runtime. Ie we have an algorithm that runs in polynomial time on all NP hard problems, if P=NP. (But the constant factors are crazy.)
jwr 8d ago
I always thought it was enough to switch off the "Improve the model for everyone" setting on chatgpt.com: "Allow your content to be used to train our models, which makes ChatGPT better for you and everyone who uses it. We take steps to protect your privacy." But apparently there is also an entire completely different route "Do not train on my data"? Does this mean that before I submitted the "Do not train on my data" request, my data was used for training in spite of "Improve the model for everyone" being turned off? We are getting to facebook/meta-levels of privacy settings obfuscation.
- teiferer 8d ago
  That's because what people enter into LLMs is the last gold there is out there. Everything else is already scraped or ensloppified. Maybe next step is to filter your input client side through an unknown number of obfuscators where you ask LLMs to rephrase your question (onion router idea) such that no single provider can be certain that this is human input and not some slop feedback loop.
- jsw97 8d ago
  The last time I checked there was a loophole — if you provide feedback in-session (responding to “how are we doing” or “which prompt is better”) then they can use that feedback + relevant context. Relevant context for chatgpt might include memories / other sessions. That may not be the only loophole. That in itself is a dark, dark pattern. There should at the very least be explicit warnings for users who have checked “do not train”; or they should not be presented with such dialogs.
krapcys 8d ago
[dead]
caidan 8d ago
I mean this is just the logical end game. The company/ies that control the uber mind will devour ALL useful or valuable work. Unlimited intelligence at unlimited scale means the value of humans for knowledge work goes to zero. We will eventually not have meaningful access to the uberminds because we will be pointless. At which point our Silicon Valley luminaries will really have no choice but to extinguish as many of us as possible for the greater good. After all if we are all pointless then that has to be weighed against are cost to Mother Earth. Clearly the only moral solution is to cull or allow to be culled some 98% or so down to a more sustainable, manageable population of curiosities. The end game of ai is the remnants of humanity in a zoo, and that’s if humans control the outcome… the machine minds might be more charitable as they would be less afraid…
- eru 8d ago
  Fortunately, there's plenty of competition between AI labs. Not all of them are even in Silicon Valley.
geraneum 8d ago
Having in mind the allegations by Apple against OpenAI, I don't find it unthinkable that there could've been some form of misconduct happening there.
Simran-B 8d ago
I don't get the sales pitch, spend 15 million dollars to win a 1 million dollar price? Showing of the model's capabilities - okay, but it's not like it solved the problem on its own, and apparently not particularly efficient. Are there practical applications that justify the investment?
- grey-area 8d ago
  The answer to this is obvious: the effect on the multi-billion dollar valuation in the imminent IPO.
- teiferer 8d ago
  How is that any different from any other academic research? Every PhD candidate solves problems essentially nobody cares about. They don't even get $1M, they get nothing. There are two benefits though. One is recognition. Cred. The PhD candidate gets to put a ", Ph.D." behind their name, opening doors to future academic employment or other endeavors where people value titles. The AI lab gets to say their tech solved sth that humanity wanted bad for a long time. Both cases with substantial financial upside (higher income for Mr. PhD and higher company valuation for the AI lab). The other one is that this is how scientific progress works. $1M or not. That number was just a PR campaign by the math community to point to some goals. It's clear that it would cost more than $1M to get there.
keremk 8d ago
Occam's Razor says: "They heard this problem is solved or about to be solved amongst the rest of the other problems. They prioritized this and put substantial compute with their newest model and solved it." I know everyone loves juicy rumors, theories etc. but honestly that is the simplest and most plausible explanation given the state of AI improvement now. Obviously spending 15 million on a problem is not a slam dunk decision even for a company like OpenAI but if it has a significantly high chance of solving it and their competitor will be claiming they solved it, then it raises the stakes and they go after it. In fact this is the most rational and also curiosity-driven thing to do and totally what I would have expected from any frontier lab. Of course if one wants to prove their confirmation biases that they train on sessions or be able to identify individual users, the non-zero chance of that being also another explanation is attractive enough to wet their appetites.
- l5870uoo9y 8d ago
  Given that the solution took a somewhat “unusual” approach, I find it even more unlikely that an AI model would have come up with this on its own.
  - pietz 8d ago
    Isn't that *exactly* the type of solution you'd expect from AI? Move 37 comes to mind.
    - iLoveOncall 8d ago
      Only if you understand nothing about the difference between LLMs and AlphaGo.
- npiano 8d ago
  Why is that simple or plausible? Why is simpler or more plausible than lifting an almost-finished solution from a researcher's account?
  - ghshephard 8d ago
throwaway63467 8d ago
Well OpenAI wants to maintain its edge and solving a Millennium problem is of course fantastic PR, and given that Anthropic seems to be working on that it’s not hard to imagine they wanted to be first. I don’t get how people buy into that whole “oh we heard models can solve Millennium prize problems now so we thought why not give it a go…” story - it’s a bit funny. This whole AI bubble is about hype and solving such problems is probably one of the best ways to keep this hype up so you can safely assume both OpenAI and Anthropic are using significant resources on these areas.
tu26muwu 8d ago
> The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster [...] I think you should not say that. Buckmaster did only state his version of events and was very clear on that he did not make any accusations at all. To quote from his statement pdf: > I am not accusing anyone of anything.
- Aeolun 8d ago
  But we all know that is code for 'something wonky happened, and it wasn't me'.
- paxys 7d ago
  Oh please. This whole “I’m not accusing them of anything, but this sure seems suspicious” doesn’t work past the 6th grade. He knew exactly what he was doing.
_bobm 8d ago
Hah, what is the infrastructure which takes user sessions (chats with API keys, directions, navier-stokes math/progress) and regurgitates this into pre-training, RL, fine-tuning data? Or better, in-context data? People talk about the "compute" but what about the "storage"? Is storage exponentially greater, or soon to be, than the compute? Is the storage going to slow down growing to some constant rate, i.e. all people on earth using chatgpt, or no, on the contrary, it will keep growing? If there were any shady business, I do not condone it, but technologically we are not there yet for said shady business to happen.
- awestroke 8d ago
  AI companies use heuristics to filter sessions, then llms to further filter, then use various techniques too anonymize the session, then process it and add it to various datasets for further selection and refinement. they don't need huge storage for this.
  - _bobm 8d ago
    what is behind "process" it and "further selection" and "refinement" and how big are these "datasets"? These companies ship the encrypted session to you not because they want to. I agree that they have pipelines for what you are describing but how effective they are at scale and at focusing is the question.
Palmik 8d ago
Duplicate of primary links / sources
karmasimida 8d ago
Use Bedrock or any kind of big tech hosted version of the frontier labs can be a solution. I think if secrecy is of utmost importance to you, then do not send data to first parties
maciejzj 8d ago
I know that this may be somewhat dramatised and even infantile, but my reflection is that in the world run by these reckless AI companies everyone looses. Navier-Stokes is solved but it feels like no one has won anything, controversy prevails, there is no glory in the math breakthrough. There is hardly anything to cherish, and even the guys at the top of it in OA who sit on the (supposedly) superhuman intelligence come across as massive losers and frauds.
zshn 8d ago
I really should get up to speed with LEAN, I know AI can probably write it better than me but I'd like to grasp it better still...
- HEX4AGON 7d ago
  If you’ve done functional programming and is familiar with mathematical proofs it should be quite intuitive to read the language
pietz 8d ago
I find the claims from OpenAI somehow more relatable and reasonable. - They threw compute on a problem another team/company was rumored to have solved to see what their secret model could do. - The texts I read do make it seem like OpenAI wanted to talk and share credit generously. - Imagine working on a frontier math problem with someone at Anthropic and not only do you use Codex but also through a non-business account that allows training on your data. - Timeline-wise, if they mainly used GPT 5.6 it's unlikely any meaningful data made it into an model that's being internally validated right now.
- piker 8d ago
  It’s fishy though that they heard one of seven problems was about to be solved and threw perhaps 15 million bucks at the right one. [Edit: they said "two of": "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. .. we launched an effort ... on all open Millennium Prize problems".]
  - pietz 8d ago
    Why in the world is that fishy? Isn't that exactly what almost everyone would do given that they wanted to see how capable their model is and the tense competition they have with Anthropic right now? Stealing impressive headlines from your competitor is pure gold.
    - piker 8d ago
      If they were willing to spend 105 million it, perhaps. But that would be surprising. It’s fishy because they spent something like 15 million on the right one.
      - aswegs8 8d ago
        Again, that is the point. There is rumours that this one thing would be solvable, so they focus on this, spending 15m on one specific thing, instead of 105m on many. How is that fishy?
iLoveOncall 8d ago
The main thing to take away from this whole story is that frontier labs have hired teams of mathematicians with the sole purpose of solving open problems. If this doesn't show you that the fantastical claims of their LLM's ability to solve problems on their own are bullshit, I don't know what will. It's pretty clear all of this is a marketing effort only, and they pass human results as LLM findings. We already know that the supposedly industry-changing Mythos and Fable results were actually complete BS and they're just your run of the mill model. There's nothing at all to suggest this is any different, and once we get this "unreleased model" (aka bob from the math department), we'll see it was all lies again.
lucfranken 8d ago
Outside of this discussion about what is fair and not. This is so highly interesting to think through. The amount of millions available to do those kind of research cases is practically unlimited. There are an unlimited amount of cases to work on. What a huge development would this give to both humans and the world in general. Because in the end better understanding gives new options. It's deeply interesting that those things now get a concrete economical price which seems to be viable to extrapolate. The enormous additional "production" of knowledge will inherently increase the speed of all pieces of research and development. Taken into account that it's used wisely, the risks with a strong force are always huge as well.
ohoho 8d ago
[flagged]
_bobm 8d ago
People are focused on the drama but the problem showing is the data. This is the elephant in the room and I am surprised that openai can be that stupid with it. How can openai do this, what is being claimed, at the scale of their entire userbase? If they do this only for particular sessions then how do they sieve through sessions for the good stuff? How are sessions stored, how are they processed, how much storage and how much compute is used in these pipelines, how economical is it, how fast are the requirements on the storage on the compute growing as userbase grows and generated data grows. All these questions are far more pertinent than the navier-stokes, but i can only imagine all at openai doubling down on this "very important" mathematical milestone.
- jonathanstrange 8d ago
  It seems completely trivial to feed sessions to their own LLM and ask it to look for various things in them, from detecting problematic use cases to finding interesting mathematical work.
  - _bobm 8d ago
    let's say that they ask a single question for each session they get. they are immediately doubling the compute they need in processing and then post-processing the same session twice. nothing trivial about it. not saying they cannot feed "their own LLM" saying it isn't trivial especially at scale. if you do not trust me try it without the "at scale" part.
    - jonathanstrange 7d ago
      It's trivial and a solved issue for the companies developing frontier AI models. Obviously, you don't even need AI for searching every prompt every user has ever written to find interesting topics, but you can create automated summaries and use AI on them if you want. There is no "scaling issue" here for companies who are used to processing almost everything that has ever been written anyway. I didn't want to insinuate that it's trivial for small companies or individuals to do big data mining at that scale, sorry if I made that impression.
TrackerFF 8d ago
IMO the drama surrounding this case somewhat overshadows some more important facts: A) That we're at the point where SOTA models can, on their own or guided, be used to solve such monumental problems B) That EVEN if they exist, they're still so cost prohibitive that they are completely out of range for pretty much everyone. Yes, yes, if the costs drop like a stone the hoi polloi can access this power in a year or two - but fundamentally it will divide cutting edge resource into two groups: Those with money, and those without. That sort of latency, in turn, could lead to some feedback loop where research centers / groups that break barriers get more resources, and those who do not, are starved of resources. This sort of stratification can seriously lead to more centralized research. Do we want a future where only the chosen few get to make progress? For no other reason than that they are the ones with enough resources to spend on the required compute.
- choudharism 8d ago
  This has ~never not been the case for any research in any modern sense.
vb-8448 8d ago
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models AKA everything you send to them (and I bet it's the same for any other lab) will be used, no matter what are the TOS, the law or what they publicly say.
- unified101 8d ago
  Put down the pitchfork. It's a toggle in their settings.
  - vb-8448 7d ago
    If you trust a "toggle" I have a bridge to sell. Users data is just too precious to ignore.
    - unified101 7d ago
      Which bridge? Do share the contract.
      - vb-8448 7d ago
        Tower Bridge suits you? But hurry up, there are a lot of pretenders.
yieldcrv 8d ago
Sorry math proof savants, the narcissism dream part of your career is dead OpenAI even wanted to respect that part but now you’re too focused on them being able to leverage the treasure map at the same time instead of the treasure for humanity being found at all, a completely different treasure where you both have to deal with getting paid by the bounty provider anyway Goofy
intended 8d ago
The more I see of frontier lab economics, the less it seems like the earlier predictions on how they will grow hold. This imbroglio looks like a point in the journey for a firm that is realizing it is not going to make money selling shovels during a gold rush, and that it has more to gain from just… being vertically integrated across an industry. Open models have definitely hampered the ability to sell tokens at a premium, so mass market adoption is impossible. But then take someone like Jane Street, for example. They self report making $30bn leveraging LLMs. It’s a defensible assumption that they are making profit on it. Perhaps it’s more profitable for OpenAI/Anthropic to build their own funds. They have the capital, compute, they can afford to recruit teams and buy any IP/Data required. This isn’t a fully fleshed out argument, but it is the first time it feels like the winds are changing.
RhysU 8d ago
I keep looking for a technical article to appear on HN discussing literally anything about the mathematical result--- Not fluff, not marketing, actual content. Instead, all I read on HN about N.-S. is human soap opera, told from every possible angle. In 100 years we won't care about the soap opera. The N.-S. result itself will still matter. Someone, anyone, please, submit articles on the result itself.
- paxys 7d ago
  If you want a level headed technical discussion instead of pitchforks and drama you have come to the wrong forum.
stn_za 7d ago
Isn't this comparable to mathematicians building on eachothers work, however incomplete or disproven prior work was?

233 points by tosh 8d ago

If you'd like to explore what the Navier–Stokes blow-up construction looks like visually, I vibe-coded an interactive 3D visualization based on the published result for fun :) Demo: https://minfx.ai/navier-stokes/ https://minfx.ai/navier-stokes/ Source code: https://github.com/minfx-ai/navier-stokes-blowup https://github.com/minfx-ai/navier-stokes-blowup

1vuio0pswjnm7 7d ago

08 Sep 2026 05:42:28 UTC | Navier-Stokes Tristan Buckmaster [pdf] | http://cims.nyu.edu/~tristanb/statement.pdf http://cims.nyu.edu/~tristanb/statement.pdf | https://news.ycombinator.com/item?id=49605915 https://news.ycombinator.com/item?id=49605915 | 823 comments 08 Sep 2026 07:50:24 UTC | I talked to deep buddy about AI solving Navier Stokes rumors | http://www.echohive.ai/deep-talk-buddy/navier-stokes http://www.echohive.ai/deep-talk-buddy/navier-stokes | https://news.ycombinator.com/item?id=49606955 https://news.ycombinator.com/item?id=49606955 | 0 comments 08 Sep 2026 14:40:37 UTC | Major breakthrough made on Navier-Stokes Problem | http://www.newscientist.com/article/2588115-major-breakthrough-made-on-famous-millennium-maths-problem/ http://www.newscientist.com/article/2588115-major-breakthrou... | https://news.ycombinator.com/item?id=49610993 https://news.ycombinator.com/item?id=49610993 | 3 comments 08 Sep 2026 15:02:35 UTC | Has OpenAI model solved 80-year-old Navier-Stokes problem? | http://www.firstpost.com/tech/has-openai-model-solved-80-year-old-navier-stokes-problem-mathematician-raises-questions-14044080.html http://www.firstpost.com/tech/has-openai-model-solved-80-yea... | https://news.ycombinator.com/item?id=49611362 https://news.ycombinator.com/item?id=49611362 | 3 comments 08 Sep 2026 17:13:21 UTC | On the NavierStokes Millennium Prize Problem | http://openai.com/index/navier-stokes-solution/ http://openai.com/index/navier-stokes-solution/ | https://news.ycombinator.com/item?id=49613262 https://news.ycombinator.com/item?id=49613262 | 1129 comments 08 Sep 2026 17:26:44 UTC | Navier-Stokes and the Future AI Acceleration in Science | http://blog.valency.io/posts/navier-stokes-ai-science http://blog.valency.io/posts/navier-stokes-ai-science | https://news.ycombinator.com/item?id=49613469 https://news.ycombinator.com/item?id=49613469 | 0 comments 08 Sep 2026 18:41:41 UTC | We're Sharing a Solution to the Navier-Stokes Millennium Prize Problem | http://twitter.com/OpenAI/status/2097374640582668336 http://twitter.com/OpenAI/status/2097374640582668336 | https://news.ycombinator.com/item?id=49614788 https://news.ycombinator.com/item?id=49614788 | 1 comment 08 Sep 2026 19:35:46 UTC | Improve the model for everyone: OpenAI and the NavierStokes problem | http://twitter.com/danimberman/status/2097379292367802672 http://twitter.com/danimberman/status/2097379292367802672 | https://news.ycombinator.com/item?id=49615732 https://news.ycombinator.com/item?id=49615732 | 1 comment 08 Sep 2026 20:28:33 UTC | Show HN: Browser viz of OpenAI's "spaghetti" NavierStokes vortex (illustration) | http://3d-retro.com/experiments/vortex http://3d-retro.com/experiments/vortex | https://news.ycombinator.com/item?id=49616564 https://news.ycombinator.com/item?id=49616564 | 1 comment 08 Sep 2026 21:31:38 UTC | Global regularity problem for the incompressible three-dimensional Navier-Stokes | http://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/ http://terrytao.wordpress.com/2026/09/07/finite-time-blowup-... | https://news.ycombinator.com/item?id=49617372 https://news.ycombinator.com/item?id=49617372 | 0 comments 08 Sep 2026 22:56:30 UTC | Navier-Stokes Proof | http://medium.com/@m.alfaro.007/open-sourcing-the-universes-code-navier-stokes-eight-pages-and-the-speed-of-light-cbbf4ee84464 http://medium.com/@m.alfaro.007/open-sourcing-the-universes-... | https://news.ycombinator.com/item?id=49618321 https://news.ycombinator.com/item?id=49618321 | 0 comments

1vuio0pswjnm7 7d ago

09 Sep 2026 02:11:50 UTC | Statement from AMS Leadership on Navier-Stokes Problem | http://www.ams.org/news?news_id=7686 http://www.ams.org/news?news_id=7686 | https://news.ycombinator.com/item?id=49619946 https://news.ycombinator.com/item?id=49619946 | 1 comment 09 Sep 2026 03:02:22 UTC | Navier-Stokes Sebastien Bubeck | http://twitter.com/SebastienBubeck/status/2097379411691516310 http://twitter.com/SebastienBubeck/status/209737941169151631... | https://news.ycombinator.com/item?id=49620327 https://news.ycombinator.com/item?id=49620327 | 3 comments 09 Sep 2026 07:04:58 UTC | Sam Altman's statement on the Navier-Stokes dispute | http://twitter.com/sama/status/2097385167002415140 http://twitter.com/sama/status/2097385167002415140 | https://news.ycombinator.com/item?id=49622377 https://news.ycombinator.com/item?id=49622377 | 8 comments 09 Sep 2026 13:08:45 UTC | The Navier-Stokes solution for the legal profession | http://lexifina.com/blog/navier-stokes-solution-for-the-legal-profession http://lexifina.com/blog/navier-stokes-solution-for-the-lega... | https://news.ycombinator.com/item?id=49625957 https://news.ycombinator.com/item?id=49625957 | 0 comments 09 Sep 2026 13:59:20 UTC | Navier stokes- Problem solution and the math for absolute dumbfucks | http://x.com/kingofknowwhere/article/18 http://x.com/kingofknowwhere/article/18 Jun 2036 22:40:17 UTC640886376 | https://news.ycombinator.com/item?id=49626706 https://news.ycombinator.com/item?id=49626706 | 0 comments 09 Sep 2026 14:39:38 UTC | OpenAI's 165-page Navier-Stokes proof failed a basic physics test | item?id=49627395 | https://news.ycombinator.com/item?id=49627395 https://news.ycombinator.com/item?id=49627395 | 0 comments 09 Sep 2026 16:28:57 UTC | To Serve Man: AI, Math, and NavierStokes | http://ml5885.github.io/writing/navier-stokes.html http://ml5885.github.io/writing/navier-stokes.html | https://news.ycombinator.com/item?id=49629132 https://news.ycombinator.com/item?id=49629132 | 2 comments 09 Sep 2026 17:33:47 UTC | Lean certificates accompanying Navier-Stokes and Euler results | http://github.com/openai/NavierStokesAndEuler/tree/main http://github.com/openai/NavierStokesAndEuler/tree/main | https://news.ycombinator.com/item?id=49630159 https://news.ycombinator.com/item?id=49630159 | 0 comments 09 Sep 2026 18:54:55 UTC | NavierStokesAndEuler | http://github.com/openai/NavierStokesAndEuler http://github.com/openai/NavierStokesAndEuler | https://news.ycombinator.com/item?id=49632068 https://news.ycombinator.com/item?id=49632068 | 0 comments

marcus_cc 6d ago

[flagged]

tosh 8d ago

> My two favourite hypothetical questions regarding this used to be: > If I'm running Codex and one of my API keys accidentally gets consumed in the context, what are the chances that someone else might ask for an API key in the future and get mine back? (I asked someone at OpenAI once and they called this the "regurgitation" problem and assured me that they take great pains to prevent that... but wouldn't describe how.) > If I brainstorm with ChatGPT about potential new directions for my company, what's the chance that information might be exposed to a competitor in six months' time who asks "what might company X plan to do next"? > My new preferred hypothetical for this is: > If I use ChatGPT to help me partially solve a Millennium Prize problem, what are the chances that my work will influence training such that a later model helps someone else solve it first?

weinzierl 8d ago
Maybe just a rumor of a high value target having their API keys accidentally consumed in the context...
feverzsj 8d ago
LLM can't be trained that easily. More like actual human are checking your logs and stealing valuable things from you.
- grey-area 8d ago
  Or searching anonymised logs for mentions of this problem and using that as part of the context or training. This would work just as well and have plausible deniability.
  - rakejake 8d ago
    Exactly! This is the real Occam's Razor explanation.
- rzzzt 8d ago
  They wouldn't appear in weights but could be added to the context. My conversations regularly go "regarding your Java problem"... which was a separate item in the history from earlier. As long as I only see these (and nobody else sees mine), it can be helpful.

shellfishgene 8d ago

What's missing from the story I think is the part about "...then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear...". If only the two of them were working on the problem in secret, how did their breakthrough become a rumor?

dboreham 8d ago
They weren't working in secret?
tyre 8d ago
People talk. If you have a breakthrough solving one of the most famous problems outstanding, you're going to tell people. You'll say, "Don't tell anyone", which they will ignore because they get a rush and perceived status by sharing it. So then they tell someone, along with "Don't tell anyone", etc. It's a small enough world (both in academic math, one at Anthropic) that you get to OAI in very few hops.
- dguest 8d ago
  The reality is also that most of your colleagues have no interest in stealing your work: they have their own work to do anyway, and having a colleague effervescing about whatever they are working on is kind of the norm in pure research. Just because they are making progress it doesn't mean they are about to do anything interesting. Also it's not like you're looking for a lost pair of car keys: just getting to the level where you can understand a problem well enough to "steal" it takes a huge amount of work. People are going to know if you're at the level where you could be a competitor. So in general it's pretty safe to talk generally about whatever you're doing.
- 20k 8d ago
  "The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag." We know that OpenAI trained on their prompts, plagiarism is incredibly likely. The only thing we don't know is whether or not it was deliberate plagiarism yet

caughtinthought 8d ago

Basically no new info here, not really sure why this post needed to be written tbh.

iso1337 8d ago
[flagged]
- jdlshore 8d ago
  There’s no shilling here. The person who posted the link isn’t the person who wrote the blog.
  - sk4rekr0w 8d ago
    He is in the HN ingroup of whenever he posts a blog, a prominent HN mod or poster with 1 billion karma will inevitably post it, and so it goes. It's sort of like the music industry.
    - neuroticnews25 8d ago
      Does poster karma boost the post in any way?
      - sk4rekr0w 8d ago
        I don't believe HN boosts their algo but I think people recognize posters like celebs. I recognize tosh, simonw, etc. Also it's an easy way to farm karma. The pelican guy posted a pelican, let's upvote it? It's at least a bit of psychosis / mass effect in this. For what it's worth, I like the pelicans but just making an observation
        retsibsi 8d ago
        > It's at least a bit of psychosis I know semantic shift is inevitable, but can we put the brakes on this one at least a little? This doesn't even connect to the original meaning.

tyre 8d ago

Yeah, this was pretty shitty by OpenAI. Not surprising, sadly. Them being assholes, trying to exclude an author just because he worked at Anthropic, shows the kind of culture within (that part of) their organization. The focus wasn't on supporting academics or expanding research. It was on getting great marketing. If they had to burn millions of dollars solving a problem _that they thought was already being solved_ to do so, they'd do it.

deleted 8d ago

[deleted]

dboreham 8d ago

The concept that "knowing something has been done" allows others to find the solution to an previously unsolvable problem is an old proven one. For example when Germany launched a rocket (V2 prototype) the British knew its rough trajectory and from spying it's rough size. Although they had previously believed that ballistic missiles weren't possible because no engine could provide the necessary thrust to weight ratio, given the obvious German launching of one, they went through all the known chemical compounds to arrive at the combination (Ethanol and LOX) used. [Story from RV Jones "Most Secret War"].

octocop 8d ago

Is there a good tldr on this topic?

emil-lp 8d ago
This article is the tldr.

nicce 8d ago

Can’t wait to see the human verifying the results and then figure out that the AI model actually cheated and the results are not correct.

imjonse 8d ago
the proofs were verified in Lean, so unlikely.
- nicce 8d ago
  As long as the proofs itself are correct. How long they were this time? Edit: at least ~600,000 lines https://stanfordtechreview.com/articles/openai-buckmaster-navier-stokes-lean-proofs https://stanfordtechreview.com/articles/openai-buckmaster-na...
  - latent-person 8d ago
    To claim something verified in Lean is wrong, you need to either argue that the theorem was stated incorrectly, or that there is a bug in Lean (assuming no `sorry` etc, which is checked by comparator). The number of lines needed to prove it is irrelevant (other than checking for a bug in Lean gets harder).
    - nicce 8d ago
      That is the point. Someone must verify that the Lean matches the actual theorem, precisely as it should be interpreted.
      - latent-person 8d ago
        Which has nothing to do with the total number of lines, it's just the theorem statement you need to check. Here is what they showed, which is under 300 lines with comments https://github.com/openai/NavierStokesAndEuler/blob/main/ComparatorChallenges/NavierStokes.lean https://github.com/openai/NavierStokesAndEuler/blob/main/Com...

avs733 8d ago

I’ll go back to the point about authorship. I’m Not a mathematician but I am in academia. if you are fucking around with authorship you are immediately suspect. That aspect alone would/should be unthinkable to any serious academic. Authorship reflects who did the work and changing it for business competition reasons should be a red flag for multiple different reasons. They include, the sheer tactlessness of treating a major theoretical advancement as a competitive posturing first, the norms of academia second, and all the misunderstandings of the culture of the disciplines culture that people will now suspect are hiding beneath the visible surface (insert topography joke). Math as a field is fairly unique even in how they list authorship. It was long the norm that authorship to be alphabetical because the idea of first, second, senior etc authorship is harder to define than many other fields. “The stated rationale for alphabetical order is that it treats co-authorship as intellectually joint work: every listed author’s name carries equal weight, and no one has to negotiate, or be seen to negotiate, over billing. That is a genuine advantage over position-coded conventions, where disputes over who is “first author” are one of the most common sources of authorship conflict in fields that use them” [0] That norm is changing, slowly, but one option people are pursuing is notable: randomized author order. Their is a perception that alphabetical is too biased…that’s the world OpenAI is stepping into when they make that offer of authorship to one scholar with a demand that he exclude his partner. I can’t speak to the facts of anything else in this, but if a grad student came to me and said someone made them that offer, I would tell them to run and if they were brave report it. [0] a to the point lay description of the history of math authorship can be found here: https://casrai.org/guides/mathematics-alphabetical-authorship-tradition https://casrai.org/guides/mathematics-alphabetical-authorshi...

emil-lp 8d ago
Yes, there is no doubt about scientific misconduct. I think the entire math community agree on that.
sobellian 8d ago
OAI's side of the story is that they discovered the approaches (and indeed solved problems - Euler equations vs NS equations) differed. They then offered Buckmaster lead authorship of OAI's proof, without Alpöge. But they never demanded that Alpöge be stripped of coauthorship on resolving the regularity of the Euler equations. At least that's the claim. https://xcancel.com/SebastienBubeck/status/2097379411691516310 https://xcancel.com/SebastienBubeck/status/20973794116915163...

sdcfgy 8d ago

My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no. I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

junofan 8d ago
Their privacy policy for normie subscribers says in plain English they use your Personal Data for research. I think it’s pretty unreasonable to use the service and expect otherwise.
- ZeWaka 8d ago
  >implying most users read them
- andersmurphy 8d ago
  You'd think theft would still be illegal regardless of what a privacy policy says.
  - georgemcbay 8d ago
    > You'd think theft would still be illegal regardless of what a privacy policy says. I wish that were true, but I live in the United States and it is 2026. The President of the United States rug-pulls memecoin crypto and regularly pardons people like Paul Walczak (who was convicted of massive payroll fraud) in exchange for large donations. I wouldn't make any assumptions about what is considered theft anymore, at least not when it is being committed by people who have enough money to be above the law.
    - andersmurphy 8d ago
      I mean the fact that comments like this get downvoted is wild.
- 8d ago

civvv 8d ago

LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence», I wonder if we will see similar examples by LLM’s soon. It seems to me currently impossible that LLM’s can replace human mathematicians, because of their (assumption) likely dependence on human input in the sense of enormous amounts of pre-existing attempts/data. If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt an LLM would be useful at all on their own. Is this the «ultimate ASI test»?

krona 8d ago
Extreme temperature levels (>2.0) can push a GPT of its manifold, essentially producing predictions barely distinguishable from random noise (it flattens the probability distribution of the next token). In theory this could predict anything including the next field of mathematics (infinite monkey theorem) but realistically that would never happen. However, how to we know the next field of mathematics isn't a novel combinations of several other sub-fields? That level of mathematics would be indistinguishable from magic to most people and so in their eyes the GPT did something truly inventive.
eru 8d ago
A lot of what humans do is combining old ideas. And an LLM could in theory also stumble upon entirely new ideas: there's randomness in how they generate their reasoning and answers after all. I suspect that we are seeing a lot of advances coming from the combination of existing but somewhat obscure knowledge coming from LLMs at the moment, because LLMs are really good at this. At least compared to humans. Even before our AI friends became good, they were already known for having read approximately every paper and every textbook published in any language. You only need to increase intelligence a fairly small amount from there to get to something like the 'convex hull' of human knowledge. Compare https://slatestarcodex.com/2016/11/17/the-alzheimer-photo/ https://slatestarcodex.com/2016/11/17/the-alzheimer-photo/ The gist is that basically whenever anyone comes up with a new method you get a big burst of activity of picking up all the now lower hanging fruit, that was previously out of reach.

kdavis 8d ago

All your datum are belong to us!

aadyachinubhai 8d ago

LLMs can't contribute good code to some of the good OSS math libraries, How is it even solving these problems?

matrix2596 8d ago
search, verifiability and compute
emil-lp 8d ago
That's a good question. It is able to contribute code, but maybe not good code. It's the same in math: it's able to solve problems, but not necessarily in a good way with a human readable code. Math papers are a lot like software: - theorems are like API - lemmata like internal/private function API - definitions are like types - the proofs are the implementation The proofs of ChatGPT are not necessarily readable or maintainable.
linkgoron 8d ago
You don't need a GOOD proof, just A proof.
feverzsj 8d ago
No one knows if it's actually LLM doing the heavy weight. It could be just human written brute force algorithm running on their massive computer cluster.
vbarrielle 8d ago
Math problems are often stated in a way that makes it possible to automatically verify if a solution is correct. Which means a loop that speculates an approach (LLM and/or prompts), implements it (LLM), then checks (automated) can work. You still need to have a very good LLM, and probably very good prompts with interesting research directions otherwise you can probably loop forever.
recursivecaveat 8d ago
Notably all the major announcements so far are counterexamples or formalizations of existing results to my knowledge. Not necessarily something you can just brute force, but areas with high return on elbow grease.

rao-v 8d ago

It’s reasonable to wonder about what chat usage data gets into models (to be honest probably quite little - carefully curating training data and creating higher quality synth data seems to be the current approach) and the implied risk to privacy and creativity (every new patent filed this year probably touched a model before filing). What I cannot reconcile is the timeline and the concern in this specific case. I don’t think training pipelines are anything close to the level of continuous training needed to incorporate Aug 15th ideas into a model that generates a breakthrough early Sept. Either OpenAI nakedly had someone with mathematical understanding dig into a specific user’s chats (a massive red flag) or this really is poor handling of a more classic parallel discovery situation (with one party clearly having worked on it longer)

KeplerBoy 8d ago
I would assume a lot of codex data goes back into training. A well steered session is extremely valuable data.
simonw 7d ago
The breakthrough was on August 15th, but Tristan and Levent had been working towards it (with the help of various models) for the best part of a year. I personally doubt that their work influenced the OpenAI result - OpenAI themselves say "While unlikely, we cannot rule out that..." - but that "we cannot rule out" is exactly the problem. If even OpenAI "cannot rule out" the influence of their usage of ChatGPT on this layer result then my discomfort at not understanding how my own usage of ChatGPT affects its training is magnified.

josalhor 8d ago

I think this drama was blown up a bit out of proportion. The entire discourse I am seeing online seems to revolve around this: > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models I mean... yeah? What do you expect? What else can they say? How could you prove a negative in this case? I do not want to comment on specific OAI employee chat messages, but on the actual OAI discovery here.

emil-lp 8d ago
If they have zero-retention, then it is not possible. So what they are saying is that they don't have zero retention.
- josalhor 8d ago
  But why is this news? This is clearly described in their ToS and in the Settings to improve their models.
Fordec 8d ago
A very simple "these two pipelines don't connect up in our architecture, here's our internal high level network diagram combined with our data ingestion opt-out feature flag that we will stand by in court" as opposed to "yeah, we don't even entirely know how our own customer facing systems are connected to our training pipeline, but it probably didn't happen".
- josalhor 8d ago
  Have the other researchers opted out? On all their accounts? Through the entire time? And did they discuss this with anyone else? And did those people ask ChatGPT stuff? And did they disable it? If I was OpenAI, I would be very careful about my wording here when making claims of "we have never trained on any of their ideas directly or indirectly".
  - Fordec 8d ago

bob1029 8d ago

> ... we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors ... I've observed this exact effect last week. I made a discovery regarding a stepwise performance improvement in a codebase. I shared the benchmark results with a peer and within 12 hours they replicated the same. We had both been looking for this for years. I think giving someone hope that an answer exists might as well be the same thing as giving them the answer these days. Competition is a hell of a drug, and frontier LLMs aggressively compound that energy.

adg33 8d ago
It's something that happened before LLMs - multiple discovery. Calculus is a classic example.
- jansport123 8d ago
  Yes but in this case, the allegation is Leibniz literally looked into newtons notebooks
  - adg33 8d ago
    Yep - it's a different case. But the idea that without LLMs, it's unlikely the same idea would be discovered independently is not true - it does happen.
skylurk 8d ago
> I think giving someone hope that an answer exists might as well be the same thing as giving them the answer these days. If you read the history of major scientific discoveries, this has been the case for a long time. There are many things that were independently discovered by different people at nearly the same time. Once people know something is solved or solvable, it gets a relentless amount of focus.
- eru 8d ago
  This seems to be the norm rather than the exception. On a tangent, the genius of people like eg Einstein is not so much that he came up with all these things: other people were close, but that he was a singular individual that did all of these discoveries, instead of five different guys all making some breakthrough here or there.

l5870uoo9y 8d ago

I run a small SaaS[1], like so many others, that uses AI to generate and optimize SQL. Getting this to perform optimally has been a lot of work and now I wonder if OpenAI is outright stealing this knowledge, which without a doubt is highly valuable to them. [1]: https://www.sqlai.ai https://www.sqlai.ai

KeplerBoy 8d ago
SQL is so ubiquitous and the use case so obvious, there's no way they have not already been tracking performance and benchmaxxing on SQL queries for years. But I don't think openai will bother to release a competitor, the real threat is that anyone with a decent LLM and a harness to try a few queries will land at the same or a better query within minutes.
biorach 8d ago
It's extremely unlikely that there is anything interesting or novel in the optimisation of a small SaaS SQL
- krapp 7d ago
  But what if they added "be interesting and novel" to their prompt? Did you consider that?
  - biorach 7d ago
    I did not. Having spent considerable amounts of time undoing the effects of overconfident junior programmers who decided to be interesting and novel on small business code bases, I guess if we're going to replace juniors with AI we may as well ask for the full experience.
paxys 7d ago
No one wants to “steal” your vibe coded crap. Your prompts aren’t as unique or valuable as you think.

feverzsj 8d ago

It could be much worse. OpenAI can easily identify these outstanding human behind their accounts. Human in OpenAI constantly check their logs for breakthrough. When they find something interesting, they brute force the result using their massive computing power. No LLM is even needed.

grey-area 8d ago
Or, using anonymised data, search for anyone seriously trying to tackle this problem - probably about 10 people in the entire world and use their ideas as a starting point. They wouldn’t even need to be watching specific accounts or using de-anonymised data if they know what they’re looking for.

cs_throwaway 8d ago

Maybe someone on the NYU team forgot to opt out of “improve the model for everyone”.

burrish 8d ago

>While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. What do you mean, as OpenAI employee, you cannot tell that his work has entered the training data ? But also correct me if I'm wrong, if the two mathematician were really close to finish this problem, and their conversation were used by OpenAI, shouldn't the Agent have succeeded way faster/efficiently instead of using "4.9 million messages and used about 300 billion output tokens."

feverzsj 8d ago
It's almost as if it was actually found by manually written brute-force algorithm running on OpenAI's massive computer cluster.
jansport123 8d ago
I’m not a mathematician so take this with a grain of salt. Apparently terry tao commented that the approach used for the Euler paper can “probably” be used for solving NS but it’s still technically challenging and can probably be done with an LLM with a lot of compute. To me the crux of the issue is whether the insight were stolen so that the problem becomes something that is in the domain of LLMs. This is much different than LLMs coming up with the insight. OpenAI wants everyone to think the LLM came up with the insight and solved the thing by itself even though they have perhaps an army of researchers.
CSMastermind 8d ago
Having the chat logs enter the training data and having them have a meaningful influence on the ultimate result the model produces are very different things. The text for all the Goosebumps books are certainly in the training data and to some small amount influenced the solve. But their contribution was so vanishingly small it would seem absurd to say R L Stein should have recourse for contibuting to the solve.
- pbmonster 8d ago
  But this is different, right? The equivalent would be taking a (fully offline) LLM and asking it about the ending of one specific Goosebumps book, and it revealing the twist. And although that specific book was (probably) only once in the training data, a high parameter LLM can usually "remember" the twist.

sk4rekr0w 8d ago

Time to repeat the same angry mob style discussion again. Great job to the mods.

protoman3000 8d ago

If they wanted to solve a Millenium prize problem so much, why did they not try to solve P-NP instead? It boggles the mind.

cammikebrown 8d ago
That one is way more difficult.
eru 8d ago
What makes you think they didn't try?
throw-qqqqq 8d ago
Are you kidding/trolling? The P=NP problem is FAR more fundamental, and if proven true, would basically be a proof that e.g. public key crypto can be broken (NOT a description of how to though). Basically, it would be a proof that all the REALLY hard (combinatorial) problems out there, have a much simpler solution, if we were able to find it. EDIT: NS is used daily in engineering and gas/fluid modeling. We sort of “know it works”. The smoothness proof is “just” formalizing what practitioners assume is true (very coarsely said, no intention to diminish the result!) It’s a bit like the Collatz function IMO, empirical evidence isn’t proof, but we’ve got a huge amount of evidence for the behavior we’re trying to prove. I believe P vs NP is a different beast entirely. We don’t even know which way the answer should go.
- eru 7d ago
  > The P=NP problem is FAR more fundamental, Yes. > and if proven true, would basically be a proof that e.g. public key crypto can be broken (NOT a description of how to though). Well, only if the answer is that P=NP. > I believe P vs NP is a different beast entirely. We don’t even know which way the answer should go. Most people expect P < NP, and then crypto wouldn't be broken. P=NP would also break pseudo-random number generators, for pretty much the same reason as the rest of crypto. However Don Knuth is one example of an expert who thinks P = NP is plausible. Btw, we do know quite a lot about how a proof of P vs NP will _not_ look like. That is we are in the curious situation where we can prove that certain proof techniques won't work on this problem. Weirdly enough, we already have the optimal algorithm, we just can't prove its runtime. Ie we have an algorithm that runs in polynomial time on all NP hard problems, if P=NP. (But the constant factors are crazy.)

jwr 8d ago

I always thought it was enough to switch off the "Improve the model for everyone" setting on chatgpt.com: "Allow your content to be used to train our models, which makes ChatGPT better for you and everyone who uses it. We take steps to protect your privacy." But apparently there is also an entire completely different route "Do not train on my data"? Does this mean that before I submitted the "Do not train on my data" request, my data was used for training in spite of "Improve the model for everyone" being turned off? We are getting to facebook/meta-levels of privacy settings obfuscation.

teiferer 8d ago
That's because what people enter into LLMs is the last gold there is out there. Everything else is already scraped or ensloppified. Maybe next step is to filter your input client side through an unknown number of obfuscators where you ask LLMs to rephrase your question (onion router idea) such that no single provider can be certain that this is human input and not some slop feedback loop.
jsw97 8d ago
The last time I checked there was a loophole — if you provide feedback in-session (responding to “how are we doing” or “which prompt is better”) then they can use that feedback + relevant context. Relevant context for chatgpt might include memories / other sessions. That may not be the only loophole. That in itself is a dark, dark pattern. There should at the very least be explicit warnings for users who have checked “do not train”; or they should not be presented with such dialogs.

krapcys 8d ago

[dead]

caidan 8d ago

I mean this is just the logical end game. The company/ies that control the uber mind will devour ALL useful or valuable work. Unlimited intelligence at unlimited scale means the value of humans for knowledge work goes to zero. We will eventually not have meaningful access to the uberminds because we will be pointless. At which point our Silicon Valley luminaries will really have no choice but to extinguish as many of us as possible for the greater good. After all if we are all pointless then that has to be weighed against are cost to Mother Earth. Clearly the only moral solution is to cull or allow to be culled some 98% or so down to a more sustainable, manageable population of curiosities. The end game of ai is the remnants of humanity in a zoo, and that’s if humans control the outcome… the machine minds might be more charitable as they would be less afraid…

eru 8d ago
Fortunately, there's plenty of competition between AI labs. Not all of them are even in Silicon Valley.

geraneum 8d ago

Having in mind the allegations by Apple against OpenAI, I don't find it unthinkable that there could've been some form of misconduct happening there.

Simran-B 8d ago

I don't get the sales pitch, spend 15 million dollars to win a 1 million dollar price? Showing of the model's capabilities - okay, but it's not like it solved the problem on its own, and apparently not particularly efficient. Are there practical applications that justify the investment?

grey-area 8d ago
The answer to this is obvious: the effect on the multi-billion dollar valuation in the imminent IPO.
teiferer 8d ago
How is that any different from any other academic research? Every PhD candidate solves problems essentially nobody cares about. They don't even get $1M, they get nothing. There are two benefits though. One is recognition. Cred. The PhD candidate gets to put a ", Ph.D." behind their name, opening doors to future academic employment or other endeavors where people value titles. The AI lab gets to say their tech solved sth that humanity wanted bad for a long time. Both cases with substantial financial upside (higher income for Mr. PhD and higher company valuation for the AI lab). The other one is that this is how scientific progress works. $1M or not. That number was just a PR campaign by the math community to point to some goals. It's clear that it would cost more than $1M to get there.

keremk 8d ago

Occam's Razor says: "They heard this problem is solved or about to be solved amongst the rest of the other problems. They prioritized this and put substantial compute with their newest model and solved it." I know everyone loves juicy rumors, theories etc. but honestly that is the simplest and most plausible explanation given the state of AI improvement now. Obviously spending 15 million on a problem is not a slam dunk decision even for a company like OpenAI but if it has a significantly high chance of solving it and their competitor will be claiming they solved it, then it raises the stakes and they go after it. In fact this is the most rational and also curiosity-driven thing to do and totally what I would have expected from any frontier lab. Of course if one wants to prove their confirmation biases that they train on sessions or be able to identify individual users, the non-zero chance of that being also another explanation is attractive enough to wet their appetites.

l5870uoo9y 8d ago
Given that the solution took a somewhat “unusual” approach, I find it even more unlikely that an AI model would have come up with this on its own.
- pietz 8d ago
  Isn't that *exactly* the type of solution you'd expect from AI? Move 37 comes to mind.
  - iLoveOncall 8d ago
    Only if you understand nothing about the difference between LLMs and AlphaGo.
npiano 8d ago
Why is that simple or plausible? Why is simpler or more plausible than lifting an almost-finished solution from a researcher's account?
- ghshephard 8d ago

throwaway63467 8d ago

Well OpenAI wants to maintain its edge and solving a Millennium problem is of course fantastic PR, and given that Anthropic seems to be working on that it’s not hard to imagine they wanted to be first. I don’t get how people buy into that whole “oh we heard models can solve Millennium prize problems now so we thought why not give it a go…” story - it’s a bit funny. This whole AI bubble is about hype and solving such problems is probably one of the best ways to keep this hype up so you can safely assume both OpenAI and Anthropic are using significant resources on these areas.

tu26muwu 8d ago

> The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster [...] I think you should not say that. Buckmaster did only state his version of events and was very clear on that he did not make any accusations at all. To quote from his statement pdf: > I am not accusing anyone of anything.

Aeolun 8d ago
But we all know that is code for 'something wonky happened, and it wasn't me'.
paxys 7d ago
Oh please. This whole “I’m not accusing them of anything, but this sure seems suspicious” doesn’t work past the 6th grade. He knew exactly what he was doing.

_bobm 8d ago

Hah, what is the infrastructure which takes user sessions (chats with API keys, directions, navier-stokes math/progress) and regurgitates this into pre-training, RL, fine-tuning data? Or better, in-context data? People talk about the "compute" but what about the "storage"? Is storage exponentially greater, or soon to be, than the compute? Is the storage going to slow down growing to some constant rate, i.e. all people on earth using chatgpt, or no, on the contrary, it will keep growing? If there were any shady business, I do not condone it, but technologically we are not there yet for said shady business to happen.

awestroke 8d ago
AI companies use heuristics to filter sessions, then llms to further filter, then use various techniques too anonymize the session, then process it and add it to various datasets for further selection and refinement. they don't need huge storage for this.
- _bobm 8d ago
  what is behind "process" it and "further selection" and "refinement" and how big are these "datasets"? These companies ship the encrypted session to you not because they want to. I agree that they have pipelines for what you are describing but how effective they are at scale and at focusing is the question.

Palmik 8d ago

Duplicate of primary links / sources

karmasimida 8d ago

Use Bedrock or any kind of big tech hosted version of the frontier labs can be a solution. I think if secrecy is of utmost importance to you, then do not send data to first parties

maciejzj 8d ago

I know that this may be somewhat dramatised and even infantile, but my reflection is that in the world run by these reckless AI companies everyone looses. Navier-Stokes is solved but it feels like no one has won anything, controversy prevails, there is no glory in the math breakthrough. There is hardly anything to cherish, and even the guys at the top of it in OA who sit on the (supposedly) superhuman intelligence come across as massive losers and frauds.

zshn 8d ago

I really should get up to speed with LEAN, I know AI can probably write it better than me but I'd like to grasp it better still...

HEX4AGON 7d ago
If you’ve done functional programming and is familiar with mathematical proofs it should be quite intuitive to read the language

pietz 8d ago

I find the claims from OpenAI somehow more relatable and reasonable. - They threw compute on a problem another team/company was rumored to have solved to see what their secret model could do. - The texts I read do make it seem like OpenAI wanted to talk and share credit generously. - Imagine working on a frontier math problem with someone at Anthropic and not only do you use Codex but also through a non-business account that allows training on your data. - Timeline-wise, if they mainly used GPT 5.6 it's unlikely any meaningful data made it into an model that's being internally validated right now.

piker 8d ago
It’s fishy though that they heard one of seven problems was about to be solved and threw perhaps 15 million bucks at the right one. [Edit: they said "two of": "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. .. we launched an effort ... on all open Millennium Prize problems".]
- pietz 8d ago
  Why in the world is that fishy? Isn't that exactly what almost everyone would do given that they wanted to see how capable their model is and the tense competition they have with Anthropic right now? Stealing impressive headlines from your competitor is pure gold.
  - piker 8d ago
    If they were willing to spend 105 million it, perhaps. But that would be surprising. It’s fishy because they spent something like 15 million on the right one.
    - aswegs8 8d ago
      Again, that is the point. There is rumours that this one thing would be solvable, so they focus on this, spending 15m on one specific thing, instead of 105m on many. How is that fishy?

iLoveOncall 8d ago

The main thing to take away from this whole story is that frontier labs have hired teams of mathematicians with the sole purpose of solving open problems. If this doesn't show you that the fantastical claims of their LLM's ability to solve problems on their own are bullshit, I don't know what will. It's pretty clear all of this is a marketing effort only, and they pass human results as LLM findings. We already know that the supposedly industry-changing Mythos and Fable results were actually complete BS and they're just your run of the mill model. There's nothing at all to suggest this is any different, and once we get this "unreleased model" (aka bob from the math department), we'll see it was all lies again.

lucfranken 8d ago

Outside of this discussion about what is fair and not. This is so highly interesting to think through. The amount of millions available to do those kind of research cases is practically unlimited. There are an unlimited amount of cases to work on. What a huge development would this give to both humans and the world in general. Because in the end better understanding gives new options. It's deeply interesting that those things now get a concrete economical price which seems to be viable to extrapolate. The enormous additional "production" of knowledge will inherently increase the speed of all pieces of research and development. Taken into account that it's used wisely, the risks with a strong force are always huge as well.

ohoho 8d ago

[flagged]

_bobm 8d ago

People are focused on the drama but the problem showing is the data. This is the elephant in the room and I am surprised that openai can be that stupid with it. How can openai do this, what is being claimed, at the scale of their entire userbase? If they do this only for particular sessions then how do they sieve through sessions for the good stuff? How are sessions stored, how are they processed, how much storage and how much compute is used in these pipelines, how economical is it, how fast are the requirements on the storage on the compute growing as userbase grows and generated data grows. All these questions are far more pertinent than the navier-stokes, but i can only imagine all at openai doubling down on this "very important" mathematical milestone.

jonathanstrange 8d ago
It seems completely trivial to feed sessions to their own LLM and ask it to look for various things in them, from detecting problematic use cases to finding interesting mathematical work.
- _bobm 8d ago
  let's say that they ask a single question for each session they get. they are immediately doubling the compute they need in processing and then post-processing the same session twice. nothing trivial about it. not saying they cannot feed "their own LLM" saying it isn't trivial especially at scale. if you do not trust me try it without the "at scale" part.
  - jonathanstrange 7d ago
    It's trivial and a solved issue for the companies developing frontier AI models. Obviously, you don't even need AI for searching every prompt every user has ever written to find interesting topics, but you can create automated summaries and use AI on them if you want. There is no "scaling issue" here for companies who are used to processing almost everything that has ever been written anyway. I didn't want to insinuate that it's trivial for small companies or individuals to do big data mining at that scale, sorry if I made that impression.

TrackerFF 8d ago

IMO the drama surrounding this case somewhat overshadows some more important facts: A) That we're at the point where SOTA models can, on their own or guided, be used to solve such monumental problems B) That EVEN if they exist, they're still so cost prohibitive that they are completely out of range for pretty much everyone. Yes, yes, if the costs drop like a stone the hoi polloi can access this power in a year or two - but fundamentally it will divide cutting edge resource into two groups: Those with money, and those without. That sort of latency, in turn, could lead to some feedback loop where research centers / groups that break barriers get more resources, and those who do not, are starved of resources. This sort of stratification can seriously lead to more centralized research. Do we want a future where only the chosen few get to make progress? For no other reason than that they are the ones with enough resources to spend on the required compute.

choudharism 8d ago
This has ~never not been the case for any research in any modern sense.

vb-8448 8d ago

> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models AKA everything you send to them (and I bet it's the same for any other lab) will be used, no matter what are the TOS, the law or what they publicly say.

unified101 8d ago
Put down the pitchfork. It's a toggle in their settings.
- vb-8448 7d ago
  If you trust a "toggle" I have a bridge to sell. Users data is just too precious to ignore.
  - unified101 7d ago
    Which bridge? Do share the contract.
    - vb-8448 7d ago
      Tower Bridge suits you? But hurry up, there are a lot of pretenders.

yieldcrv 8d ago

Sorry math proof savants, the narcissism dream part of your career is dead OpenAI even wanted to respect that part but now you’re too focused on them being able to leverage the treasure map at the same time instead of the treasure for humanity being found at all, a completely different treasure where you both have to deal with getting paid by the bounty provider anyway Goofy

intended 8d ago

The more I see of frontier lab economics, the less it seems like the earlier predictions on how they will grow hold. This imbroglio looks like a point in the journey for a firm that is realizing it is not going to make money selling shovels during a gold rush, and that it has more to gain from just… being vertically integrated across an industry. Open models have definitely hampered the ability to sell tokens at a premium, so mass market adoption is impossible. But then take someone like Jane Street, for example. They self report making $30bn leveraging LLMs. It’s a defensible assumption that they are making profit on it. Perhaps it’s more profitable for OpenAI/Anthropic to build their own funds. They have the capital, compute, they can afford to recruit teams and buy any IP/Data required. This isn’t a fully fleshed out argument, but it is the first time it feels like the winds are changing.

RhysU 8d ago

I keep looking for a technical article to appear on HN discussing literally anything about the mathematical result--- Not fluff, not marketing, actual content. Instead, all I read on HN about N.-S. is human soap opera, told from every possible angle. In 100 years we won't care about the soap opera. The N.-S. result itself will still matter. Someone, anyone, please, submit articles on the result itself.

paxys 7d ago
If you want a level headed technical discussion instead of pitchforks and drama you have come to the wrong forum.

stn_za 7d ago

Isn't this comparable to mathematicians building on eachothers work, however incomplete or disproven prior work was?