> ... 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.
I have a similar story, but perhaps even stranger.
I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick.
The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters.
There are always a few competitive guys who spend the entire conference taking turns to play it. And every single time, the same thing happens.
Say the current high score is around 200m. Everybody fails somewhere around that number: 190m, 186m... Maybe someone manages 210m. And the high score moves up at a snail's pace.
Then, a new guy shows up and gets something like 500m on his third try. From their next turn on, everybody easily does 450 or more, even though they were struggling to get past 200 just one turn ago.
What makes it stranger is that the game is dead simple. It's not like the new guy discovered a move that unlocked this capability. And it wasn't a lack of motivation either - they'd all been playing for an hour already. They just started performing better after seeing it was possible. There has to be a name for this phenomenon.
Reminds me of amateur table tennis. There is a strange dynamic where you down regulate your performance unconsciously when the opponent is playing worse and vice versa.
I think the difference is that, in the table tennis example, it happens unconsciously and you can't help it. But you're right, it likely happens in most sports.
The mixed boys/girls classes example is, as you said, deliberate. And I too remember holding back on purpose in such situations when I was a kid.
With the arcade, no one was deliberately holding back. I'm sure of it.
Is it that you’re holding back against weaker opponents, or that you’re more excited and engaged when you’re playing against someone that forces you closer to the edge of your ability?
I like to leverage that when brainstorming solutions to hard problems. Instead of contemplating small percentage improvements, try to think about what's in the way of improvements that are orders of magnitude better (e.g., don't take time to run a big task from 100s to 90s, take it to milliseconds). Sometimes it unlocks big ideas.
There's little reason to aim for a score a lot higher than the current best; and when getting close to the score you're aiming for, it's easy to get agitated and make a mistake.
And if you do beat the high score, you're likely to loosen your attention right after that, and it's even annoying to keep going for much more.
Reference-dependent effort ("bunching" around a target) [1] is probably
the closest thing. The existing high score was acting as everyone's reference
point. Anchoring [2] is the more general cognitive version.
> 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.
Maybe that shows how scientific discoveries come to be. It's not a genius sitting alone in their chamber for a decade and then suddenly they emerge with this huge thing. That's Hollywood fiction. Scientific progress is the colaborative effort of countless researchers over long periods of time, communicating, exchanging ideas, many of them wrong, tweaking, trying, thinking, arguing. When a breakthrough happens then it's the tip of a mountain of work that came before it. If two individuals stand on that mountain and feel there is something somewhere then it's not too strange that they take the last step at roughly the same time because conditions were right. The preconditions were in place at that time, the results required for this were available and the focus was on this specific thing.
I'd say it illustrates well that this last piece, the person celebrated for the achievement, is disproportionally overvalued and the rest of the work they are standing on is disproportionally ignored.
I always like to bring up how many decades of research, how many hundreds of years of entire PhD-theses, how many sleepless nights were used up to generate all the protein structure data that made up the corpus of Protein Data Bank - that was then hovered up by the AlphaFold team, and guess who got the Nobel Prize...
Just like all non-AI related nobel prizes before them.
Every laureate stands on the shoulder of giants which is their field as a generations-spanning body of researchers. They did the last step and get recognized. The good ones acknowledge that in their acceptance speeches.
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.
You see this in many things. Look at climbing for instance, or running. Once the first v17 had been done, suddenly many people did them. Or running with a sub 2 hour marathon.
Not the hope, but telling them that an answer does exist. This ofcourse means now we are going to go into an even more darker cave next time we are looking for some gold and pathbreaking discoveries will become even more rare. Add to that, the fear of people not winning against ai and having fewer rewards, then fewer people even enter those fields or attempt problems over the next generation.
AI erodes skills not at individual but at civilisational level.
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.
If you believe the totality of the document, there was more shadiness in how OpenAI acted than just timing. Save other things they are accused of, the progression from rumors to replication would attract much less scrutiny. With those in mind timing begins to look suspicious at best.
Would anyone be surprised if major model companies had tagged the accounts of competitor employees for extra tracking? Given the concerns about distillation and bench marking it hardly seems irrational, but how it is used matters quite a lot.
That's the other thing. Even if it somehow magically turns out that they didn't plagiarize Buckmaster and Alpöge, that an independent audit goes through all their processes and finds that they could not possibly have stolen anything, and ignoring their outrageous attempts to force a coauthor off the author list, and ignoring that their employees act like small children on social media, this is a company whose culture is “we heard of a breakthrough being possible, let's scoop it”.
Normally, when you tell a coworker that you're wrapping up a result, unless they're some kind of sociopath, their natural inclination would not be to try to steal it from you.
>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."
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.
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.
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.
The only way it would be able to tell you the ending is if it was somehow given more importance in pretraining, loaded into context, or represented in multiple sets of training samples. I have a blog that I make very LLM friendly and usually load posts up into context when I’m working on something relevant. I’ve also opted to improve models for everyone. Despite this, the model can’t recognize my site or any of my posts when I ask it to recall without internet usage (I also turn memory off btw).
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.
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".]
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.
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.
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?
I understood the rumors (as described by OpenAI) to be that “one of” the prizes was solvable. If they heard NS specifically was solvable and aren’t saying that, they’re intentionally obfuscating that.
"On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."
No, sorry I was reading it correctly but they addressed the issue in the post itself. They make it clear they were aiming at all 7 problems looking for the "two" that were rumored to be solved. But they didn't go hog on NS until they made progress. See sibling comments. I misread it the first time to be a claim that they "heard one of 7 human intractable problems are solved and spent 15 million on the right one".
Didn't they say that they launched an effort to evaluate their model on all open Millennium Prize problems, and then narrowed down to Navier-Stokes as the most promising after seeing results on simplified versions of the problems?
Yes, you're right. It seems like they claim to have started broadly and narrowed it down based on some progress. That leads to different questions but does answer my initial "fishy" point.
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»?
This is also what I've been thinking. The result itself is amazing but it's not like this was completely unexpected. There has been a huge amount of progress on the problem in the last 10 years without which it seems unlikely today's full resolution would have been possible. It is not clear what strategy was taken but it sounds like it borrowed heavily from the two spanish mathematicians. Experts will scrutinize the proof and it will be interesting to see if anything truly original or unexpected was done, outside of known techniques, a move 37.
The kind of humans who invent entire fields of science on their own come by a few times a generation. It’s fine to say AI isn’t anywhere as close to them in intelligence, but instead is comparable to the “average” mathematician who is building on the work done by others and taking it a bit further.
Yeah, thats likely true to some extent. But my point is perhaps a "counter-thought" to the idea that this is ASI level intelligence and that math is now a computer task and not a human one. If it is incapable of moving maths forwards into the "unknown" it simply can not replace humans, and this might be a hard structural block for LLM's.
If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt a human mathematician would be useful at all on their own.
How have we got to the place we are today then? Someone must have made the first steps onto uncharted territory, otherwise we would be in a homogeneous state frozen in time.
I am not saying that LLM intelligence can not be the same, that they are uncapable of dicovering new fields/problems that they have no training on. I am just pointing out that historically it kind of "must" be true that humans are capalbe of this, but we have yet to see an LLM do something like this, something radically "new" in a sense. All of these breakthroughs appear to me (not a mathematician) to be more a case of "digging" through millions of existing attempts/work, patching it together into a result.
This would already make LLM's one of the greatest tool mankind has ever made, but it has yet to display what I would consider a necessity for human level intelligence, which is this ability to discover entirely "new" things.
Would an LLM, given enough time and only the currently available trainingdata with no further input from humans, be able to solve something that was discovered tomorrow?
For humans my answer would be: maybe, probably, because this has been done historically.
For LLM's I would not be comfortable in claiming that they could. I think they would not be any better at this than traditional computational bruteforce.
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.
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.
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.
> 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?
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.
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?
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.
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.
"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
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.
> one should not use LLM services for confidential or proprietary information
That’s obvious, isn’t it? Just like you wouldn’t upload your confidential documents to an online spellchecker, or your proprietary code to an online compiler?
I worked in a EU company that was developing a product competing with one of Microsoft offerings. All the code was hosted on GitHub, we used Azure for hosting and all the internal communications were in Microsoft Teams.
To me it looked absurd. But I was almost the smallest cog in the corporate structure, so I never asked what were the reasons for all these decisions.
It's either that, not use an LLM, or local-host an LLM. If you can local-host one then great, this is a compelling reason to do that too. A lot of people aren't in that position.
Everyone is in a position not to use an LLM. They may not want to inconvenience themselves on someone else’s desires though. I think at that point you should evaluate your working relationship.
I don’t use them. I have evaluated them and the trade off is too detrimental to me and society in the long term.
That they do it is just concerning to me in that it says that home-ran models just aren't good enough. Surely researchers like this have the processing power to run them at home, they just don't have the processing power to train models of comparable level.
This is something I feared would happen and where open source would be left behind. Maybe they can do something with crowd-sourcing computational power from volunteirs. They were after all able to get Leela Chess Zero to be comparable to AlphaZero by training from volunteer processing power but it seems to me we live in a world now where the best models keep their stuff closed.
In imagine generation too. I'm not sure how well Stable Diffusion can compete in following instructions with all those advanced models that are kept secret.
Yes people have to service the use case of a single person. All sorts of models exist that are designed to be ran at home. Yes, you need a relatively beefy graphics card for it but if your machine can handle the latest video games at good graphics it can handle these local models. How well they compare against these things remains to be seen but apparently OpenAI released gpt-oss-20b which is comparable to o3-mini apparently in terms of reasoning power. There's also oss-120b which does require at least a company server to run but this should well be within the budget of a university.
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.
My doctor's privacy policy is a bit more abusive than OpenAI's. It exists mostly because of a $%^&&* legal framework rather than malice, and I've grown accustomed to "if I don't want to die then I sign away these rights." Despite my having theoretically signed my soul away, my doctor isn't selling personal information to my exes or to life insurance companies (though they could in the US; that extremely personal information is no longer mine). OpenAI is engaging in the "technically legal maybe we'll see but obviously unintended" side of this transaction, and maybe that works out for them, but I wouldn't personally choose to be a shill for "it's unreasonble to expect somebody with 'legal' permission to do something other than the maximum 'legally' permitted" if I were in your shoes.
Depends on your profession? I sometimes work on open source code as part of my professional duties. Nothing that goes on there is necessary to keep private.
Aren't business consulting firms even worse? They are explicitly for business and there are known cases where they shared confidential information of one of their customers with another one.
I have the setting turned on in Gemini Pro even though I work on proprietary code because 1. the setting allows for some (very limited) "memory", and 2. I consider my source code almost public even when it's not open source because I don't work on programs that involve extremely high level of know how or proprietary algorithms. It's mostly CRUD that can be copied in a myriad of ways, whether people use my methods or other methods.
If Gemini can improve based on my code and sessions (maybe doubtful but who knows) and others can benefit from it, that would be a welcome side-effect.
> 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.
> Wait until you learn how many other SaaS and web 2.0 and cloud based things are also run by assholes.
Though it's not the real acronym, Larry Ellison himself has stated that Oracle stands for One Real Asshole Called Larry Ellison. He famously prides himself on it.
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.
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.
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.
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.
Isn't it also a simple idea that a model designed to recall relevant information from its training data, which is also known to have been trained on data from user transcripts, would, in fact, reproduce directly relevant work by leading experts in the field? Seems like Occam's razor would apply to that situation as well.
We know that LLMs are trained to recall relevant info. We know AI vendors are using user transcripts to train models. Two plus two equals four, right? I mean, an LLM that failed to recall the transcripts of those researchers would be a bad model.
Funny how they did not solve any of the other problems, just the one where there was already solutions to the NS with some restrictions in their chats, and their solution seems to derive from those.
So instead of dictating research to unsolved, or largely unsolved, problems, we are now as "a society" directing compute power towards sniping research outcomes.
I thought this was an ebay thing for people with too much free money, but it seems a bit larger.
Because it is not finished. Their follow up claim is that OpenAI’s approach looks like another proof they had been working on the side, but hasn’t published yet
OpenAI have admitted their new model they used was trained on prompts at around the time that researcher was working on it, so it seems self evident that it was used as part of the millennium solution
1) Because AI models are 1000x better about following a problem to its conclusion than coming up with a genuinely new idea.
2) Because if we accept the facts ChatGPT only came up with its "new" idea after being told exactly what the new idea was by a mathematician (OpenAI doesn't dispute this btw). And OpenAIs story comes down to the usual "We didn't look at it, trust me bro", which is made more hard to believe because OpenAI only started their efforts after receiving news of what the researcher was doing.
Oh and OpenAI emphasizes that part of the researcher's progress was made ... on OpenAI.
3) And, probably, the researchers were likely stopped by token limits, and that's the only reason they were slower than OpenAI themselves, which is very, very unfair.
4) OpenAI's story "smells" (like so many AI stories lately). Supposedly the company's team asked ChatGPT about solving millennium problems, and out of all millennium problems it just happens to pick the one where a solution can be found in its chat logs?
5) Yet again it would be in good taste for these AI companies to just give this to the researchers (no shortage of difficult unsolved math problems, so if AI can solve them all, just find another one). But instead, yet again they're fighting about it.
6) OpenAI admits they only went after this problem, with a team, no less, after finding out which researcher went after what problem, because of how they thought it would affect ChatGPT's PR. They are demonstrating, in other words, their willingness to destroy human researcher's reputation for PR wins.
That's getting close to big tobacco level morals right there.
7) If anyone wants to verify how much OpenAI cares about the truth, just ask on ChatGPT about the copyright lawsuit outcome and how it applies to OpenAI.
You'll get EXACTLY the sort of responses you get from Qwen about Tiananmen ("we didn't do it, you have no data, everyone's lying and if we did do it, it was perfectly reasonable because " style argument. Try it)
I don’t know much about NS problem or Euler problem anyway. Can’t tell how significant it is to go from Tristan approach to OpenAI’s results.
It is 10k agents after all with a model that is 2x-3x more powerful than Astra. So claims some intuition is his alone and the model can’t find it independently is Tristan’s belief not the reality, which I don’t find particularly convincing.
I do think that Levent guy isn’t independent and indeed does have an enormous amount of tokens to spend and also on an internal model from Anthropic.
All things considered, I think OpenAI people are competitive, even aggressive. But I don’t think they steal anything. Ultimately, the model’s capability is the real surprise factor here, the fact they could get a solution after all in 3 days, that is the cause of drama, if it is 3 months, then it is a nothing burger, because by then the original results had already been published.
> Ultimately, the model’s capability is the real surprise factor here, the fact they could get a solution after all in 3 days, that is the cause of drama ...
And there we go, a beside-the-point answer that tries to bring it back to the PR claim. And of course, an unsupported PR claim: if the initial insight really did come from a human, that would indicate the model's capability either isn't there or didn't matter.
And sorry to say, but competitive adversarial rewards for humans + access to the answer always ends in peeking. In kindergarten. In universities. In Engineering firms. In Finance. No difference other than the justification afterwards. Humans peek in competitive settings. They just do. The fix is not "trust me bro", the fix is making sure they have no ability to do it in the first place.
And OpenAI's answer to the "did you peek at the answer?" is trust me, bro ... as per usual.
If OpenAI indeed played fair, then this is a serious "dick move", and not at all how academia is supposed to work. AND if they played fair OpenAI effectively attacked one of their customers here.
If OpenAI didn't play fair then this is stealing from their customers. Which at a different level is their whole business model (get training data from customers, who even pay for that, train better model with that data, charge more, repeat).
There's also an elephant here in this room: Quite "coincidental" one of the coauthors worked for the competition. Of course GPT would know this fact. And OAI has every incentive to particularly monitor those accounts.-
That 100x step up from using 100 agents for Euler to 100_000 agents for Navier-Stokes, in a single day seems a bit sus.
I also think this is not ethical behavior. This is at least academic dishonesty, kind of a plagiarism or intellectual theft.
That’s why they wanted to credit Tristan and to give $1M award to him. But again, they acted unethically in that process as well. They wanted him to remove Levent (Anthropic affiliation) as co-author and threatened Tristan to “end his career”. Their behavior is actually telling, their work was not completely independent from Tristan&Levent’s unpublished work.
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)
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.
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.
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.
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.
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.
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.
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.
> 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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
I can give you some context.
1. Terence Tao's mastodon explains the way this problem was solved does not in itself contribute much. LLMs (and in this case) produce massive, often unintelligible proofs that do not further understanding. It is often that in pursuit of solving these problems, many other discoveries are made.
2. There is a more serious question about scooping. If OAI is using chat data from researchers to make discoveries, essentially every researcher who chats with an LLM can get scooped. You could be 80% of your way to solving a problem, and LLM could solve the remaining 20%, and get all the credit. Years of your work could be scooped in an instant. If you're a PhD student, this is even worse. Here it's a world famous problem. But imagine you're a PhD student, working on your small but extremely career/progression critical problem, and you get scooped by an AI you talk to. No one is even going to care.
1. I know, but that is somewhat irrelevant to my question
2. I am indeed a CS PhD student (well, I am finishing now)
> If OAI is using chat data from researchers to make discoveries, essentially every researcher who chats with an LLM can get scooped
But they make very clear that they do train on this if you do not disable the setting. We can comment on the fact that this is opt out instead of opt in, but this discourse of OAI sniping the solution out of some researchers hands seems to be running on the best case speculation of the researchers having perfectly handled all their chats and discussions with other researchers and the worse case of OAI not having full pipeline control and I think that is an unfair assumption.
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".
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".
All very good questions that could end up in a court of law with a Millenium Prize on the line. In a competent world, these are very answerable from logs and considering the news cycle this is creating, should be able to be pulled up and made into a public postmortem in short order. You know, if it's all been above board that is. And if the researchers don't wish for that information to be public knowledge, it can be shared with the researchers promptly for a retraction of their statements lest some libel gets litigated.
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…
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).
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.
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.
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.
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.
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.
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?
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.
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.
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.
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.
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"].
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.
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.
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.
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.
Kind of a tangent, but in some fields authorship is actually more of a formal rank: once you're in the group you appear on every paper. A good fraction of the "authors" won't even know that a paper is being published in their name, and the vast majority haven't read a word of it.
In these fields it can be quite a challenge to not appear on a paper.
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
> ... 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.
I have a similar story, but perhaps even stranger.
I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick.
The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters.
There are always a few competitive guys who spend the entire conference taking turns to play it. And every single time, the same thing happens.
Say the current high score is around 200m. Everybody fails somewhere around that number: 190m, 186m... Maybe someone manages 210m. And the high score moves up at a snail's pace.
Then, a new guy shows up and gets something like 500m on his third try. From their next turn on, everybody easily does 450 or more, even though they were struggling to get past 200 just one turn ago.
What makes it stranger is that the game is dead simple. It's not like the new guy discovered a move that unlocked this capability. And it wasn't a lack of motivation either - they'd all been playing for an hour already. They just started performing better after seeing it was possible. There has to be a name for this phenomenon.
Reminds me of amateur table tennis. There is a strange dynamic where you down regulate your performance unconsciously when the opponent is playing worse and vice versa.
Could be described as some physical form of this effect: https://en.wikipedia.org/wiki/Asch_conformity_experiments
The term would be conformity / normative social influence.
Surely this has nothing to do with specifically table tennis, nor that it's amateur.
A better example would be mixed boys/girls sports classes in school, where the boys deliberately hold back as to not injure/scare the girls.
It's a pretty obvious and human thing not to go out and completely destroy a much weaker opponent. We're social animals after all.
There also may be an element of energy conservation, there's objectively no need to put in any more effort than necessary. Inefficient.
I think the difference is that, in the table tennis example, it happens unconsciously and you can't help it. But you're right, it likely happens in most sports.
The mixed boys/girls classes example is, as you said, deliberate. And I too remember holding back on purpose in such situations when I was a kid.
With the arcade, no one was deliberately holding back. I'm sure of it.
Is it that you’re holding back against weaker opponents, or that you’re more excited and engaged when you’re playing against someone that forces you closer to the edge of your ability?
I like to leverage that when brainstorming solutions to hard problems. Instead of contemplating small percentage improvements, try to think about what's in the way of improvements that are orders of magnitude better (e.g., don't take time to run a big task from 100s to 90s, take it to milliseconds). Sometimes it unlocks big ideas.
I wonder if it's the same with the sub 2 hour marathon which was broken this year (it certainly was with the 4 minute mile).
Achieving a high score requires focus and effort.
There's little reason to aim for a score a lot higher than the current best; and when getting close to the score you're aiming for, it's easy to get agitated and make a mistake.
And if you do beat the high score, you're likely to loosen your attention right after that, and it's even annoying to keep going for much more.
Reference-dependent effort ("bunching" around a target) [1] is probably the closest thing. The existing high score was acting as everyone's reference point. Anchoring [2] is the more general cognitive version.
[1] https://www.nber.org/system/files/working_papers/w20343/w203... [2] https://en.wikipedia.org/wiki/Anchoring_effect
> 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.
Maybe that shows how scientific discoveries come to be. It's not a genius sitting alone in their chamber for a decade and then suddenly they emerge with this huge thing. That's Hollywood fiction. Scientific progress is the colaborative effort of countless researchers over long periods of time, communicating, exchanging ideas, many of them wrong, tweaking, trying, thinking, arguing. When a breakthrough happens then it's the tip of a mountain of work that came before it. If two individuals stand on that mountain and feel there is something somewhere then it's not too strange that they take the last step at roughly the same time because conditions were right. The preconditions were in place at that time, the results required for this were available and the focus was on this specific thing.
I'd say it illustrates well that this last piece, the person celebrated for the achievement, is disproportionally overvalued and the rest of the work they are standing on is disproportionally ignored.
This ties back into AI, too, right?
I always like to bring up how many decades of research, how many hundreds of years of entire PhD-theses, how many sleepless nights were used up to generate all the protein structure data that made up the corpus of Protein Data Bank - that was then hovered up by the AlphaFold team, and guess who got the Nobel Prize...
Just like all non-AI related nobel prizes before them.
Every laureate stands on the shoulder of giants which is their field as a generations-spanning body of researchers. They did the last step and get recognized. The good ones acknowledge that in their acceptance speeches.
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.
You see this in many things. Look at climbing for instance, or running. Once the first v17 had been done, suddenly many people did them. Or running with a sub 2 hour marathon.
Not the hope, but telling them that an answer does exist. This ofcourse means now we are going to go into an even more darker cave next time we are looking for some gold and pathbreaking discoveries will become even more rare. Add to that, the fear of people not winning against ai and having fewer rewards, then fewer people even enter those fields or attempt problems over the next generation. AI erodes skills not at individual but at civilisational level.
It's something that happened before LLMs - multiple discovery. Calculus is a classic example.
Yes but in this case, the allegation is Leibniz literally looked into newtons notebooks
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.
If you believe the totality of the document, there was more shadiness in how OpenAI acted than just timing. Save other things they are accused of, the progression from rumors to replication would attract much less scrutiny. With those in mind timing begins to look suspicious at best.
Would anyone be surprised if major model companies had tagged the accounts of competitor employees for extra tracking? Given the concerns about distillation and bench marking it hardly seems irrational, but how it is used matters quite a lot.
That's the other thing. Even if it somehow magically turns out that they didn't plagiarize Buckmaster and Alpöge, that an independent audit goes through all their processes and finds that they could not possibly have stolen anything, and ignoring their outrageous attempts to force a coauthor off the author list, and ignoring that their employees act like small children on social media, this is a company whose culture is “we heard of a breakthrough being possible, let's scoop it”.
Normally, when you tell a coworker that you're wrapping up a result, unless they're some kind of sociopath, their natural inclination would not be to try to steal it from you.
>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."
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.
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.
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.
The only way it would be able to tell you the ending is if it was somehow given more importance in pretraining, loaded into context, or represented in multiple sets of training samples. I have a blog that I make very LLM friendly and usually load posts up into context when I’m working on something relevant. I’ve also opted to improve models for everyone. Despite this, the model can’t recognize my site or any of my posts when I ask it to recall without internet usage (I also turn memory off btw).
It's almost as if it was actually found by manually written brute-force algorithm running on OpenAI's massive computer cluster.
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.
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".]
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.
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.
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?
I understood the rumors (as described by OpenAI) to be that “one of” the prizes was solvable. If they heard NS specifically was solvable and aren’t saying that, they’re intentionally obfuscating that.
Because that’s the one Anthropic was rumored to have solved.
"On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."
That doesn't reject my claim. They just didn't name them in this post. It feels like, you're going through great lengths reading something into this.
No, sorry I was reading it correctly but they addressed the issue in the post itself. They make it clear they were aiming at all 7 problems looking for the "two" that were rumored to be solved. But they didn't go hog on NS until they made progress. See sibling comments. I misread it the first time to be a claim that they "heard one of 7 human intractable problems are solved and spent 15 million on the right one".
Didn't they say that they launched an effort to evaluate their model on all open Millennium Prize problems, and then narrowed down to Navier-Stokes as the most promising after seeing results on simplified versions of the problems?
Yes, you're right. It seems like they claim to have started broadly and narrowed it down based on some progress. That leads to different questions but does answer my initial "fishy" point.
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»?
This is also what I've been thinking. The result itself is amazing but it's not like this was completely unexpected. There has been a huge amount of progress on the problem in the last 10 years without which it seems unlikely today's full resolution would have been possible. It is not clear what strategy was taken but it sounds like it borrowed heavily from the two spanish mathematicians. Experts will scrutinize the proof and it will be interesting to see if anything truly original or unexpected was done, outside of known techniques, a move 37.
The kind of humans who invent entire fields of science on their own come by a few times a generation. It’s fine to say AI isn’t anywhere as close to them in intelligence, but instead is comparable to the “average” mathematician who is building on the work done by others and taking it a bit further.
Yeah, thats likely true to some extent. But my point is perhaps a "counter-thought" to the idea that this is ASI level intelligence and that math is now a computer task and not a human one. If it is incapable of moving maths forwards into the "unknown" it simply can not replace humans, and this might be a hard structural block for LLM's.
If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt a human mathematician would be useful at all on their own.
How have we got to the place we are today then? Someone must have made the first steps onto uncharted territory, otherwise we would be in a homogeneous state frozen in time.
I am not saying that LLM intelligence can not be the same, that they are uncapable of dicovering new fields/problems that they have no training on. I am just pointing out that historically it kind of "must" be true that humans are capalbe of this, but we have yet to see an LLM do something like this, something radically "new" in a sense. All of these breakthroughs appear to me (not a mathematician) to be more a case of "digging" through millions of existing attempts/work, patching it together into a result.
This would already make LLM's one of the greatest tool mankind has ever made, but it has yet to display what I would consider a necessity for human level intelligence, which is this ability to discover entirely "new" things.
Would an LLM, given enough time and only the currently available trainingdata with no further input from humans, be able to solve something that was discovered tomorrow?
For humans my answer would be: maybe, probably, because this has been done historically.
For LLM's I would not be comfortable in claiming that they could. I think they would not be any better at this than traditional computational bruteforce.
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.
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/
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.
> 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?
LLM can't be trained that easily. More like actual human are checking your logs and stealing valuable things from you.
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.
Exactly! This is the real Occam's Razor explanation.
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.
LLMs can learn from one sample.
Maybe just a rumor of a high value target having their API keys accidentally consumed in the context...
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.
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?
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.
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.
"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
And deliberate or not it is still plagiarism by the sound of it.
They weren't working in secret?
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.
> one should not use LLM services for confidential or proprietary information
That’s obvious, isn’t it? Just like you wouldn’t upload your confidential documents to an online spellchecker, or your proprietary code to an online compiler?
Everyone, including the security services in my country, uses OneDrive and O365.
I don’t get it.
I worked in a EU company that was developing a product competing with one of Microsoft offerings. All the code was hosted on GitHub, we used Azure for hosting and all the internal communications were in Microsoft Teams.
To me it looked absurd. But I was almost the smallest cog in the corporate structure, so I never asked what were the reasons for all these decisions.
Or you wouldn't write confidential emails in Outlook and have confidential conversations in Teams. Obviously. Right? Right?
Or if you're going to trust one of them, maybe it shouldn't be OpenAI
Why would I trust any of them?
It's either that, not use an LLM, or local-host an LLM. If you can local-host one then great, this is a compelling reason to do that too. A lot of people aren't in that position.
Everyone is in a position not to use an LLM. They may not want to inconvenience themselves on someone else’s desires though. I think at that point you should evaluate your working relationship.
I don’t use them. I have evaluated them and the trade off is too detrimental to me and society in the long term.
Or use Lumo from Proton. Are there any other privacy first companies offering LLMs?
Chutes.ai models are served from a Trusted Execution Environment, so the GPU owners can't see your prompts.
Lumo seems the most reputable. There's confer.to, duck.ai, and nanogpt.
That they do it is just concerning to me in that it says that home-ran models just aren't good enough. Surely researchers like this have the processing power to run them at home, they just don't have the processing power to train models of comparable level.
This is something I feared would happen and where open source would be left behind. Maybe they can do something with crowd-sourcing computational power from volunteirs. They were after all able to get Leela Chess Zero to be comparable to AlphaZero by training from volunteer processing power but it seems to me we live in a world now where the best models keep their stuff closed.
In imagine generation too. I'm not sure how well Stable Diffusion can compete in following instructions with all those advanced models that are kept secret.
> Surely researchers like this have the processing power to run them at home,
Nobody has that power. Certainly not mathematicians.
Yes people have to service the use case of a single person. All sorts of models exist that are designed to be ran at home. Yes, you need a relatively beefy graphics card for it but if your machine can handle the latest video games at good graphics it can handle these local models. How well they compare against these things remains to be seen but apparently OpenAI released gpt-oss-20b which is comparable to o3-mini apparently in terms of reasoning power. There's also oss-120b which does require at least a company server to run but this should well be within the budget of a university.
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.
My doctor's privacy policy is a bit more abusive than OpenAI's. It exists mostly because of a $%^&&* legal framework rather than malice, and I've grown accustomed to "if I don't want to die then I sign away these rights." Despite my having theoretically signed my soul away, my doctor isn't selling personal information to my exes or to life insurance companies (though they could in the US; that extremely personal information is no longer mine). OpenAI is engaging in the "technically legal maybe we'll see but obviously unintended" side of this transaction, and maybe that works out for them, but I wouldn't personally choose to be a shill for "it's unreasonble to expect somebody with 'legal' permission to do something other than the maximum 'legally' permitted" if I were in your shoes.
I think those are pretty unreasonable terms and it’s sad that you’re defending them.
Does google docs own the content of docs you make with it? Does Apple claim ownership of discoveries made using their tools?
>implying most users read them
If that is the case, why on earth would you use it in any professional setting?
Depends on your profession? I sometimes work on open source code as part of my professional duties. Nothing that goes on there is necessary to keep private.
Vulnerabilities, responsible disclosure etc?
You can use 'Daybreak Blue' from OpenAI for that, if you want to.
Because it's cheap and easy. Hold for many such questions...
Why is all of the world dependent on tech an ever more hostile US? Same answer.
Aren't business consulting firms even worse? They are explicitly for business and there are known cases where they shared confidential information of one of their customers with another one.
I have the setting turned on in Gemini Pro even though I work on proprietary code because 1. the setting allows for some (very limited) "memory", and 2. I consider my source code almost public even when it's not open source because I don't work on programs that involve extremely high level of know how or proprietary algorithms. It's mostly CRUD that can be copied in a myriad of ways, whether people use my methods or other methods.
If Gemini can improve based on my code and sessions (maybe doubtful but who knows) and others can benefit from it, that would be a welcome side-effect.
You'd think theft would still be illegal regardless of what a privacy policy says.
> 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.
I mean the fact that comments like this get downvoted is wild.
I think it’s pretty unreasonable to use the service.
There’s an opt out so I’m blade for now.
> as they all seem to be run by assholes.
Wait until you learn how many other SaaS and web 2.0 and cloud based things are also run by assholes.
You know this metaphor? https://en.wikipedia.org/wiki/Turtles_all_the_way_down
But instead of turtles, it's assholes.
But more seriously, no, none of what I wrote above is an attempt to excuse or play down the specific role of assholes in large AI companies.
Of course. I work for assholes. The thing is they’re getting out assholed by several orders of magnitude here.
LLMs can't contribute good code to some of the good OSS math libraries, How is it even solving these problems?
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.
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.
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.
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.
You don't need a GOOD proof, just A proof.
search, verifiability and compute
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.
Isn't it also a simple idea that a model designed to recall relevant information from its training data, which is also known to have been trained on data from user transcripts, would, in fact, reproduce directly relevant work by leading experts in the field? Seems like Occam's razor would apply to that situation as well.
We know that LLMs are trained to recall relevant info. We know AI vendors are using user transcripts to train models. Two plus two equals four, right? I mean, an LLM that failed to recall the transcripts of those researchers would be a bad model.
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.
Isn't that *exactly* the type of solution you'd expect from AI?
Move 37 comes to mind.
Only if you understand nothing about the difference between LLMs and AlphaGo.
Funny how they did not solve any of the other problems, just the one where there was already solutions to the NS with some restrictions in their chats, and their solution seems to derive from those.
They explain in the article that they eventually redirected all their resources towards NS.
So instead of dictating research to unsolved, or largely unsolved, problems, we are now as "a society" directing compute power towards sniping research outcomes.
I thought this was an ebay thing for people with too much free money, but it seems a bit larger.
Considering how language models work, you'd expect two distinct conversations on the same mathematical problem to have enormous crossover.
Why is that simple or plausible? Why is simpler or more plausible than lifting an almost-finished solution from a researcher's account?
Because they solved different problems, and where there was overlap, the solutions look different?
Because it is not finished. Their follow up claim is that OpenAI’s approach looks like another proof they had been working on the side, but hasn’t published yet
OpenAI have admitted their new model they used was trained on prompts at around the time that researcher was working on it, so it seems self evident that it was used as part of the millennium solution
1) Because AI models are 1000x better about following a problem to its conclusion than coming up with a genuinely new idea.
2) Because if we accept the facts ChatGPT only came up with its "new" idea after being told exactly what the new idea was by a mathematician (OpenAI doesn't dispute this btw). And OpenAIs story comes down to the usual "We didn't look at it, trust me bro", which is made more hard to believe because OpenAI only started their efforts after receiving news of what the researcher was doing.
Oh and OpenAI emphasizes that part of the researcher's progress was made ... on OpenAI.
3) And, probably, the researchers were likely stopped by token limits, and that's the only reason they were slower than OpenAI themselves, which is very, very unfair.
4) OpenAI's story "smells" (like so many AI stories lately). Supposedly the company's team asked ChatGPT about solving millennium problems, and out of all millennium problems it just happens to pick the one where a solution can be found in its chat logs?
5) Yet again it would be in good taste for these AI companies to just give this to the researchers (no shortage of difficult unsolved math problems, so if AI can solve them all, just find another one). But instead, yet again they're fighting about it.
6) OpenAI admits they only went after this problem, with a team, no less, after finding out which researcher went after what problem, because of how they thought it would affect ChatGPT's PR. They are demonstrating, in other words, their willingness to destroy human researcher's reputation for PR wins.
That's getting close to big tobacco level morals right there.
7) If anyone wants to verify how much OpenAI cares about the truth, just ask on ChatGPT about the copyright lawsuit outcome and how it applies to OpenAI.
You'll get EXACTLY the sort of responses you get from Qwen about Tiananmen ("we didn't do it, you have no data, everyone's lying and if we did do it, it was perfectly reasonable because " style argument. Try it)
I don’t know much about NS problem or Euler problem anyway. Can’t tell how significant it is to go from Tristan approach to OpenAI’s results.
It is 10k agents after all with a model that is 2x-3x more powerful than Astra. So claims some intuition is his alone and the model can’t find it independently is Tristan’s belief not the reality, which I don’t find particularly convincing.
I do think that Levent guy isn’t independent and indeed does have an enormous amount of tokens to spend and also on an internal model from Anthropic.
All things considered, I think OpenAI people are competitive, even aggressive. But I don’t think they steal anything. Ultimately, the model’s capability is the real surprise factor here, the fact they could get a solution after all in 3 days, that is the cause of drama, if it is 3 months, then it is a nothing burger, because by then the original results had already been published.
> Ultimately, the model’s capability is the real surprise factor here, the fact they could get a solution after all in 3 days, that is the cause of drama ...
And there we go, a beside-the-point answer that tries to bring it back to the PR claim. And of course, an unsupported PR claim: if the initial insight really did come from a human, that would indicate the model's capability either isn't there or didn't matter.
And sorry to say, but competitive adversarial rewards for humans + access to the answer always ends in peeking. In kindergarten. In universities. In Engineering firms. In Finance. No difference other than the justification afterwards. Humans peek in competitive settings. They just do. The fix is not "trust me bro", the fix is making sure they have no ability to do it in the first place.
And OpenAI's answer to the "did you peek at the answer?" is trust me, bro ... as per usual.
If OpenAI indeed played fair, then this is a serious "dick move", and not at all how academia is supposed to work. AND if they played fair OpenAI effectively attacked one of their customers here.
If OpenAI didn't play fair then this is stealing from their customers. Which at a different level is their whole business model (get training data from customers, who even pay for that, train better model with that data, charge more, repeat).
There's also an elephant here in this room: Quite "coincidental" one of the coauthors worked for the competition. Of course GPT would know this fact. And OAI has every incentive to particularly monitor those accounts.-
I agree with Occam.
That 100x step up from using 100 agents for Euler to 100_000 agents for Navier-Stokes, in a single day seems a bit sus.
I also think this is not ethical behavior. This is at least academic dishonesty, kind of a plagiarism or intellectual theft.
That’s why they wanted to credit Tristan and to give $1M award to him. But again, they acted unethically in that process as well. They wanted him to remove Levent (Anthropic affiliation) as co-author and threatened Tristan to “end his career”. Their behavior is actually telling, their work was not completely independent from Tristan&Levent’s unpublished work.
This is not the simplest explanation.
The most direct line from problem to proof is OpenAI building off of conversations the mathematicians had with their AI.
Basically no new info here, not really sure why this post needed to be written tbh.
On the contrary, a level-headed summary that gathers information from all the different sources is necessary.
Sounds like a great use case for an LLM
It's got 'max' and 'ultra' but I don't see a setting for level-headed.
They are busy generating pelicans on bicycles. The summary therefore needs to be written by a human.
(This was a joke. I value Simon's role in the community.)
Yes, you have ability to get information very quickly, but not everyone does.
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)
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.
I would assume a lot of codex data goes back into training. A well steered session is extremely valuable data.
Isn't this comparable to mathematicians building on eachothers work, however incomplete or disproven prior work was?
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.
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.
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.
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.
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.
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.
> 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.
Put down the pitchfork. It's a toggle in their settings.
If you trust a "toggle" I have a bridge to sell.
Users data is just too precious to ignore.
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.
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.
What makes you think they didn't try?
That one is way more difficult.
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.
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.
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.
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.
I not only think it is not trivial, I know it is not solved.
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.
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.
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.
Maybe someone on the NYU team forgot to opt out of “improve the model for everyone”.
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
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.
They could explain how they use data from their users "to improve our models".
In the absence of that, how can we make informed decisions about how to use their tools?
(And "you can opt out" is a weak answer IMO, because I can't guarantee that everyone I email about something has also opted out.)
I can give you some context. 1. Terence Tao's mastodon explains the way this problem was solved does not in itself contribute much. LLMs (and in this case) produce massive, often unintelligible proofs that do not further understanding. It is often that in pursuit of solving these problems, many other discoveries are made. 2. There is a more serious question about scooping. If OAI is using chat data from researchers to make discoveries, essentially every researcher who chats with an LLM can get scooped. You could be 80% of your way to solving a problem, and LLM could solve the remaining 20%, and get all the credit. Years of your work could be scooped in an instant. If you're a PhD student, this is even worse. Here it's a world famous problem. But imagine you're a PhD student, working on your small but extremely career/progression critical problem, and you get scooped by an AI you talk to. No one is even going to care.
1. I know, but that is somewhat irrelevant to my question 2. I am indeed a CS PhD student (well, I am finishing now)
> If OAI is using chat data from researchers to make discoveries, essentially every researcher who chats with an LLM can get scooped
But they make very clear that they do train on this if you do not disable the setting. We can comment on the fact that this is opt out instead of opt in, but this discourse of OAI sniping the solution out of some researchers hands seems to be running on the best case speculation of the researchers having perfectly handled all their chats and discussions with other researchers and the worse case of OAI not having full pipeline control and I think that is an unfair assumption.
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".
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".
All very good questions that could end up in a court of law with a Millenium Prize on the line. In a competent world, these are very answerable from logs and considering the news cycle this is creating, should be able to be pulled up and made into a public postmortem in short order. You know, if it's all been above board that is. And if the researchers don't wish for that information to be public knowledge, it can be shared with the researchers promptly for a retraction of their statements lest some libel gets litigated.
If they have zero-retention, then it is not possible.
So what they are saying is that they don't have zero retention.
But why is this news? This is clearly described in their ToS and in the Settings to improve their models.
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...
If you’ve done functional programming and is familiar with mathematical proofs it should be quite intuitive to read the language
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…
Fortunately, there's plenty of competition between AI labs. Not all of them are even in Silicon Valley.
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.
the proofs were verified in Lean, so unlikely.
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-na...
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).
That is the point. Someone must verify that the Lean matches the actual theorem, precisely as it should be interpreted.
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/Com...
That seems to be indeed true. I guess it gets validated quite soon.
But still possible [1].
[1] https://leodemoura.github.io/blog/2026-8-1-postmortem-for-ke...
> 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.
But we all know that is code for 'something wonky happened, and it wasn't me'.
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.
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.
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
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.
No one wants to “steal” your vibe coded crap. Your prompts aren’t as unique or valuable as you think.
It's extremely unlikely that there is anything interesting or novel in the optimisation of a small SaaS SQL
But what if they added "be interesting and novel" to their prompt? Did you consider that?
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.
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?
The answer to this is obvious: the effect on the multi-billion dollar valuation in the imminent IPO.
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.
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.
This has ~never not been the case for any research in any modern sense.
Duplicate of primary links / sources
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.
If you want a level headed technical discussion instead of pitchforks and drama you have come to the wrong forum.
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.
All your datum are belong to us!
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"].
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.
So, Simon or what's your name, you think your opinion on this has weight since you are a "blogger" or something, and sit on a pack of green paper?
Time to repeat the same angry mob style discussion again. Great job to the mods.
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.
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-authorshi...
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/20973794116915163...
Authorship is weird.
Kind of a tangent, but in some fields authorship is actually more of a formal rank: once you're in the group you appear on every paper. A good fraction of the "authors" won't even know that a paper is being published in their name, and the vast majority haven't read a word of it.
In these fields it can be quite a challenge to not appear on a paper.
Yes, there is no doubt about scientific misconduct. I think the entire math community agree on that.
Is there a good tldr on this topic?
This article is the tldr.
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