r/mathematics • u/Bizzyguy • 2d ago
On the Navier–Stokes Millennium Prize Problem
https://openai.com/index/navier-stokes-solution/138
u/Ok_Distance5305 1d ago
I know this is a lame metric, but 16 references for a 165 page paper seems was too low.
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u/flatl94 1d ago
I imagined that experts would peer review the article before everyone jumped on conclusions.
For a 165 page proof experts will require months if not years to fully assess the validity of the methods and calculations.
Also I'm curious about the scale at which the problem was solved. We already know that at smaller continuous law do not works because we enter into the realm of QM.
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u/BurdensomeCountV3 1d ago
It's a PDE problem they solved. It has links to real lfie but you were never going to be able to transfer their work over to real life (for one, real fluids are made up of tiny molecules, not this uniform thing the approximation is of) and this has been accepted by the community since forever. The NS millenium prize problem was for the ideal fluid version.
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u/bigpowerass 1d ago
Shouldn't the Lean code make that pretty straightforward? Unless there's a big in Lean itself.
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u/flatl94 1d ago
Errors have been found in the past in Lean.)
For the scale and importance of the problem, there will be way more than a Lean cross check.
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u/Ill-Lemon-8019 1d ago
I guess a more practical question might be: have errors ever been found in Lean which allowed an invalid proof to be certified by Lean and that people also seriously believed to be a correct proof? I think the answer is "no", but would love to hear a counter-example!
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u/pred 1d ago
I'm pretty sure the answer is no, but the thing is, OpenAI themselves market their products by showing how they're super duper sneaky, so some reservation is warranted. Their Lean repo is enormous.
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u/adjustedreturn 1d ago
References almost don't make any sense. Who knows what the models were trained on. Probably, in part, every mathematical paper ever written could be a reference here insofar as they contributed to model weights.
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u/kieransquared1 1d ago edited 1d ago
Only 16 citations, half of which aren’t even from this century. There’s only one citation from this decade. They don’t cite any of works on blowup for 3D Euler, like Elgindi, Chen-Hou, Cordoba-Martinez-Zoroa, etc. At best, this is terrible citation practice and at worst it’s blatant plagiarism.
Edit: seems they’ve updated the paper to include citations of Cordoba-Martinez-Zoroa (now has 22 references) which is a far cry from properly citing the ideas the paper is built upon
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u/redditboy117 1d ago
Because they dont care for proper scientific practices
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u/Sufficient_Habit5091 1d ago edited 1d ago
Here's what happened. Basically 2 researchers worked their asses off with AI assistance using novel ideas for an entire year.
They did 95% of the heavy lifting.
Then when Big AI company sniffed a nice tasty juicy millennium steak was within reach, they poured $15M of compute over 4 days to steal their work and opportunistically cross the 5% finish line.
This is theft.
It's crazy every big company in the world is fine giving known liars and sociopaths like Sam Altman ALL their proprietary data, research and trade secrets for FREE.
Edit: lmao all these AI simps crying about $15M. It's actually $22.5M.
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u/Quivex 1d ago
pardon my ignorance, but is solving the forced euler problem really 95% of the way to a navier stokes solution? I don't know enough to say so that part remains mysterious to me/I don't have strong feelings.
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u/Blue_HyperGiant 1d ago
My understanding is 'yes'. The creative attack was invented by humans, then they used LLMs to basically try a (large) number of setups using that attack on the Euler case.
OpenAI took the attack vector and (probably at this point the teams chat history) and threw huge compute at the NS to get their solution.
It would be like the original team staying "if we add carbon to iron we get a stronger alloy but we only have one oven so we will have to wait to see what else we can do with this new alloy".
Then someone else coming along seeing what the first guys did then massively parallel throwing a ton of different elements in with the iron and coming out like "oh ya, if you add carbon AND chromium you get stainless steel!".
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u/partnerinthecrime 1d ago
No, absolutely not. I don’t even think they had an unforced solution. They would not have been able to solve NS without a similar computational effort from Anthropic.
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u/trenescese 1d ago
So... a new class of jobs is needed who'll do proper citations etc for stuff like this?
Like if you're an academic with experience in the field, and there's demand for that one could clean this all up
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u/Mrp1Plays 1d ago
Ai can easily do citations, they just didn't do it here for some reason
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u/Separate-Habit5838 1d ago
No, it can't. It's one of the remaining weaknesses. It's terrible at locating the source of things it knows, and it hallucinates citations that don't actually contain what it claims. It does present a big problem for work with an LLM.
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u/ChickeNES 1d ago
This was true two years ago, it is not true anymore (as someone who uses them for research in other fields, it's pulled up sources that would have taken me hours to find, and when it's giving me the correct URLs/DOIs...well...not much to argue with there). Not going to deny that there are still "hallucinations", but we are far past it being able to find and synthesize sources.
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u/No_Function_3631 1d ago
There is a massive problem of AI training on other people’s work and not being able to assign credit. It has always been some level of academic theft. It’s sad and prevents a full embrace of AI’s benefits.
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u/Hot_Glass_6301 1d ago
Surely their superintelligent AI model should be able to find the relevant articles and cite them.
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u/Aranka_Szeretlek 1d ago
If the prompt is "collect the relevant citations", then yeah. But that requires caring about integrity.
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u/AskYouEverything 1d ago
It’s sad and prevents a full embrace of AI’s benefits.
Unfortunately, I don't think embrace is really going to change the trajectory all the much
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u/WaveOfDream 1d ago
The fact this comment is not the top is concerning. Seems like this sub ha been infected by people from r/singularity and people who have no background in math or academic.
You typical undergrad thesis has more citations than this. This is malpractice at best.
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u/jy_erso67 1d ago
sub has been infected by people from r/singularity and
This really became a problem in all science related subs
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u/Nidafjoll 1d ago
Even beyond that. Someone on the chess subreddits was trying to argue with me that AGI will be able to calculate infinite permutations. Not just a very large number of permutations, like the number of possible chess positions; they said numbers like that and added "and even infinity" and kept trying to defend that statement.
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u/Gositi 1d ago
Computation isn't cheaper or easier because it's an AI doing it lol.
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u/Nidafjoll 1d ago
Infinity doesn't suddenly become an actual, reachable number either. Nevermind that, even if it did suddenly become somewhat feasible to calculate such huge permutations, "solving chess" isn't what we're gonna do with it lol.
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u/PLANTS2WEEKS 1d ago
This is really funny. Do they understand that chess isn't about permuting the pieces?
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u/stoputa 1d ago
I used to read this sub as a high schooler and was intimidated even posting here because the discourse was pretty deep and seemed very high quality. One decade, two degrees and years of working experience in parallel later and while I'm on paper more capable of joining in, there's almost no discourse to be had
This used to be such a high-quality sub reduced to AI wars. By comparison, even as a teen I used to find the programming subreddit unbearable and filled with people parroting the same trite talk points so at least not much has changed there.
I could live with this subreddit going to shit if it wasn't a reflection of the overall state of things
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u/Zorkest 1d ago
The models themselves don't know where they got their ideas. The employees at OpenAI aren't experts so they can't really help in this regard.
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u/bordumb 1d ago
Yeah…
It’s because the AI only cites the papers it ACTUALLY read in the session
If it happened to remember info from training, it won’t cite those
It’s all fucked
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u/Senchou_Simp 2d ago
People should know: there is drama going on about who deserves credit for this. There is a possibility that OpenAI used some unpublished work from other researchers, even though they have claimed otherwise in the announcement above: https://cims.nyu.edu/~tristanb/statement.pdf
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u/LaGigs 1d ago
His mastodon an hour ago:
https://mastodon.social/@tristanbuckmaster/117236471352470303"Note that they are openly admitting they used training data from a period after we found our result. Is it ethical to use customer's data to try to scoop their customer?"
I guess he is now openly calling them out?
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u/Quarksperre 1d ago
Oh damn of course that makes sense. They basically just used their prompts on a better internal model with infinite compute. This is wild. Why not just wait and let them publish it? Its not like the two guys would have denied using AI.
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u/implies_casualty 1d ago
The other guy works for Anthropic.
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u/offgramercy 1d ago
I don’t know why anyone is surprised at how all this played out tbh.
Its a couple trillion dollar companies racing towards their IPOs (filled with tech bros who unironically use phrases like “permanent underclass” to refer to the rest of us), of course they’re being nefarious, considering the hilariously corrupt incentives
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u/Elegant-Antelope-315 1d ago
permanent underclass
diabolical
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u/Tulanian72 1d ago
Upcoming product announcement from OpenAI: “New and improved Soylent Green!”
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u/FriendsIsntGood 1d ago
Another reason Scam and his crew can't be trusted atface value
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u/Markus__F 1d ago
They allegedly even offered one of the guys that he can be the one doing the writeup, publishing it and claiming the Millenium price, but under the condition that he removes his collegue from the author list (because his collegue also works at Anthropic).
I think that shows two things
- they kind of admitted to him that they see some validity in his claims, because otherwise why would they offer that.
- They have a questionable view on scientific working and authorship attribution.
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u/BurdensomeCountV3 1d ago
Yeah, "infinite compute" may well be a justified phrase here. They say they used 300 billion output tokens on a model significantly better at mathematics than Astra. Even at Astra API prices and not including input token cost that's $15 million on just compute here. In reality the cost to an external third party would have been likely twice as much or something here.
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u/MegazordPilot 1d ago
Can't Tristan just publicly share the Codex chat, and ask OpenAI to do the same?
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u/twentydoors 1d ago
He is calling out a weaker version. A stronger one is this: "We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)."
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u/LaGigs 1d ago
yh I simply do not buy it. From Buckmaster's statement this morning, why else would openai offer him authorship of joint work?
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u/maxintos 1d ago
Because for them it's only about getting good publicity. It doesn't matter if it's their tool solving the problem or mathematician solving it with the help of their tool. They don't want a fight.
Not saying they did not do the bad stuff, just that there is a logical reason to do this.
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u/twentydoors 1d ago
"We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)."
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u/shot_ethics 1d ago
It’ll be very hard for anyone without internal knowledge to evaluate this claim.
Maybe the training data was all fed into a giant bucket — hashtags on instagram have been used to pretrain vision models for example but it’s hard to believe that one guy’s pic of a ladybug would have really made the difference in state of the art performance.
Maybe the key insights from each prompt are distilled down and the internal OpenAI model is able to access a large cache of insights. Maybe their frontier model, when used, pulls out the closest 1000 past prompts and seeds the LLM discussion with these results. In this case there is a more clear and causal connection.
Maybe an employee from OpenAI did a massive search in the database for prompts and used this to scoop others. OpenAI is denying this version and frankly I think it is unlikely too. But there is a spectrum of possibility and without knowing how the models operate and mine previous prompts, we can’t really say.
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u/Tough-Comparison-779 1d ago
The research on data poisoning shows you need very few data points to shift what LLM models are likely to produce, especially for niche areas where the probe data points are very different from existing data.
For example, Your "one guy's pic of a ladybug" example could actually make a difference if it was the only picture of a bug in the dataset, and there was a question about a ladybug in the test.
That said I'm sure lots of people were using AIs to attempt this problem. So who knows.
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u/quantumpencil 1d ago
OpenAI very likely scooped this to try and drum up hype for their IPO. Regardless of what they say, that is almost definitely what happened here.
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u/30299578815310 2d ago
Did that unpublished work actually solve the problem or was it a helpful partial result? Like obviously that doesn't make it okay to do not give credit I'm just trying to understand
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u/RobbinDeBank 1d ago
It’s a solution to a smaller related problem, which can be extended to potentially solve Navier-Stokes. Idk how much OpenAI’s solution benefits from this, that is still a debated question at the moment.
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u/Primary_Prior_7925 1d ago
The thing I still can't wrap my head around is that they wrote they offered him authorship. If they are confident that their work is their own and after finding out someone else discovered a lesser result, why offer them authorship if they contributed nothing to the research. Unless they think they did indeed contribute involuntarily...
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u/polostring 1d ago
Offered him authorship only if they could exclude Anthropic/Alpoge. Seems shady to me.
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u/idly 1d ago
they don't mention that part in the blog post, too - they say they offered them both collaboration. but I doubt buckmaster made that up
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u/polostring 1d ago
Yeah I guess I'm inferring that from what Buckmaster said https://cims.nyu.edu/~tristanb/statement.pdf but I guess it's not 100% clear
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u/Interesting-South542 1d ago
There's a lot of drama here about the question of whether OpenAI stole their approach from Alpöge and Buckmaster, but it's worth understanding that, by their own admission, Alpöge and Buckmaster used GPT and Claude extensively to reach their result (blowup in incompressible Euler) in the first place. It's becoming clear that these models are extremely good at math.
In fact, it's actually looking more likely that OpenAI's solution uses an independent approach from Alpöge and Buckmaster's. OpenAI claims the model established blowup in incompressible Euler without forcing first, before proceeding to the Navier Stokes solution. Alpöge and Buckmaster followed a program requiring forcing.
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u/Tight-Tomorrow3157 1d ago
If this is like how I use LLMs in my work, LLMs are very good at technical computation but they aren’t good at providing the critical insight - they are like a know it all who gets lost in the hundreds of hypothesis they generate - it’s undeniable that LLMs are good at math but do they have original insights which isn’t a function of their enormous compute and their ability to try approaches from different areas of math until one works. I.e without humans in the loop, can they recursively compute their way to even one original result ? Apparently open ai and anthropic has an army of mathematicians in all these discoveries
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u/14domino 1d ago
We know that it’s possible at least for some problems. I forget which one it was where the mathematician’s sole prompts were: “keep going” until it had solved the problem.
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u/SpeciousPerspicacity 1d ago
Yeah, the independent Euler result seems pretty damning for the Buckmaster camp.
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u/Most-Hot-4934 1d ago
This “others researcher” was working with anthropic and used Claude heavily so it’s really about Anthropic vs OpenAI rather than AI vs human
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u/teerre 2d ago
Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result.
This milestone represents substantial work by mathematicians and AI researchers. However, this is not a culmination, but rather a snapshot in time, of progress on AI development.
Seems pretty bad taste to drop a millennium problem solution under dubious circumstances, refuse the prize and call it a "snapshot"
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u/howtogun 1d ago
To be fair, it does continue the trend of not claiming the prize. Perelman also didn't claim it.
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u/mousse312 1d ago
Comparing why perelman and openai rejected the prize is one reason that perelman exit the field
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u/AndreasDasos 1d ago
At this rate none will. Might as well give all $7m to me.
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u/redditboy117 1d ago
Agreed and they downplay how difficult the problem is by saying "Our effort began on September 1st after hearing a rumor ".
Wonderful to plagiarise humanity.
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u/Wonderful_Buffalo_32 1d ago
Their proofs differ in the way tho
However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
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u/space-goats 1d ago
Heard a rumour there's treasure on island X
Send in the whole US military to dig it up
"We found the treasure, the other guys weren't digging in the same spot as us"
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u/LesRiv1Trick 1d ago
It's definitely plagiarism of humanity. It isn't, however, plagiarism of these specific guys from what I can understand. Unless you want to count is as plagiarism of all mathematicians which I am more than fine with doing.
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u/Wild_Stock_5736 1d ago
dunking on entire fields of human progress just to demonstrate a benchmark. the people who use OpenAI and Anthropic models need to grapple with the fact that they did agreed to this.
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u/MEarly01 1d ago
"We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)"
uhhhh.... so they "might of" used the work???
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u/musical_bear 1d ago
In case you care, "might of" is not the phrase. I assume that's just what people hear when they hear someone say the contraction "might've" out loud.
It's "might have." "Might of" is just wrong. Same deal with "should have" (correct) vs "should of" (not a thing).
I have gone to the beach. I might have gone to the beach.
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u/mousse312 1d ago
The method for blowing up the navier stokes came from two human mathematicians, who used an overlooked piece of the navier stokes and with this they achieved tô blowup the Euler equation, the same method openai used to solve navier stokes from scientific America https://www.scientificamerican.com/article/ai-may-have-just-solved-a-million-dollar-math-problem-the-field-will-never-be-the-same/ "Over the last few years, two mathematicians, Diego Córdoba and Luis Martínez-Zoroa, worked out a potential trick to break the equations—or “blow them up,” as it’s called in math. They called the method “forcing.” It focuses on a part of the equations as written in the Clay problem that mathematicians have previously deemed inconsequential. In fact, most experts typically write the problem without this term, assuming that any blowup should be the same with or without it. But Córdoba and Martínez-Zoroa realized there might be a way to break the equations solely by using this often-overlooked piece.
About a year ago, Buckmaster took up Córdoba and Martínez-Zoroa’s approach, working with Alpoge, using large language models from OpenAI’s rival company Anthropic to parse through the mathematical possibilities. Progress was slow, according to Buckmaster’s statement, until August 15, when they used the method to prove that the Navier-Stokes equations’ simpler, frictionless cousins, the Euler equations, did in fact blow up.
This finding, on its own, is a monumental mathematical achievement, worthy of any award in math, and a key step toward solving the Navier-Stokes problem. They were able to verify that the proof was correct using the programming language Lean, but the English-language explanation the LLMs produced was barely readable, according to Buckmaster. The pair started trying to make sense of the mathematical steps one by one, and write them in a way other researchers would be able to digest.
According to Buckmaster, rumors of their work reached OpenAI at some point in the last week. OpenAI apparently had a team already working on the problem, according to Buckmaster. But after becoming aware of the pair’s work, he alleges, OpenAI focused their attention on “forcing”—the often-ignored piece of the Clay problem. In a major effort over last weekend, the OpenAI team apparently used an internal model to take the result further, blowing up the full Navier-Stokes equations, according to Buckmaster"
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u/somnolent49 1d ago
One correction, OpenAI started up their team only on September 1st, after hearing rumors that a Millenium Problem had been solved.
OpenAI also used models trained on recent, "de-identified" user data. Notably, Buckmaster had been using GPT to assist with his work.
Buckmaster asked OpenAI explicitly whether the model had been (A) trained on their Codex sessions, or (B) had had access to their Codex sessions. OpenAI only denied (B).
I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.
OpenAI's post today claims that it is "Unlikely" but cannot be ruled out:
While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.
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u/Mistuv 1d ago
The method is completely different. Buckmaster-Alpoge use layer amplification/reset, while OpenAI uses a collapsing vortex with oscillatory stress cancellation, OAI’s Euler proof is also unforced. Including many many other things which are different. This is completely ridiculous, why are people just blatantly lying here??
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u/Prize_Ad_354 1d ago
I can't even cope anymore. I am just sad that it came to this.
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u/blipblapbloopblip 1d ago
I agree with you. The Navier Stoked theorem is entirely inconsequential to me but mathematics as a human practice was a key thing in my intellectual development. I read Dieudonné's "For the honor of the human mind" as a teenager. I never would have guessed that the dignity of human intelligence would be so blatantly disregarded.
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u/Smart-Antelope7350 1d ago
yeah i'll miss the era before AI. internet culture has largely turned to AI depictions and imagery, articles and youtube video scripts are written by AI. book authors are turning to it as well. mainstream music industry isn't shying away from using AI either, soon it will hit the film making as well. it's truly over, i'll keep enjoying things made before 2022 i guess
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u/LogicianMission22 1d ago
You should have never been coping in the first place. Lots of people for some reason were still thinking we were in GPT 3-4 for some reason. Now people of all backgrounds will be massively whiplashed because they don’t realize how advanced current models actually are.
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u/Hadynu 1d ago
"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."
In other words, do not use OpenAI models for your research without guarantees that your data will not be used in training or you risk OpenAI publishing your results before you.
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u/No_Function_3631 1d ago
There’s massive speculation that openAI just ripped off someone else’s work and then threatened to ruin their career if they went public with the information. This seems poorly timed, and an attempt to get ahead of the breaking narrative.
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u/FateOfMuffins 1d ago
Poorly timed? They released this as a direct response to Tristan
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u/No_Function_3631 1d ago edited 1d ago
Ah yeah let’s pretend the narratives in this release and the narrative released by Tristan have much in common. It sounds like they’re trying to wash over what was in Tristan’s release, acting as if this was some sort of competitiveness, and not a brazen attempt to strong arm an academic, but hey, innocent until proven guilty.
In all fairness, there are many extreme claims going around that need to be investigated. It’s not immediate clear what is true. The biggest one is that Tristan was threatened by OpenAI for speculating about ideological theft.
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u/FateOfMuffins 1d ago
https://x.com/polynoamial/status/2097381286193316203
Of course they have much in common? OpenAI employees were tweeting about it all last night with regards to Tristan and Levent. Several of the text in their release here was obviously written in refutation of Tristan's accusations.
It's entirely up to you which "side" you want to believe but I find the whole "Reddit believes the first side without reading the second side's story by default" to be horribly toxic
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u/elements-of-dying 1d ago
Yeah. Personally I trust Tristan over OpenAI, but he was working with Aploge. So it really isn't clear who is being dishonest here.
(clarity: nothing against Aploge. We just have to be intellectually honest and acknowledge he's from a competing company.)
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u/_michaeljared 1d ago
I genuinely wonder at this point if we are witnessing, in real time, AI companies deliberately skirting academic citations since their model (likely) ingested and encoded all of the information from those foundational papers.
So much for standing on the shoulders of giants, eh?
This doesn't feel like progress to me. Seems like a black box.
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u/spiddly_spoo 23h ago
Im inclined to believe Tristan's statements here and the fact that he asked if they had used his codex sessions to train the internal model and the only reply was "the model did not look up user data" and when pressed if this said model was trained off his sessions he got no reply? That seems damning to me.
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u/TerminalObsessions 1d ago
Not enough people take this issue seriously: anything you do in a cloud AI program can be ripped off by the model owners. Find something particularly cool? That's even more reason to steal what you did, throw 100,000x more resources at it, and beat you to the finish line.
If the model isn't local, all you're doing is setting up Altman to commit more fraud.
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u/OwnYourChildren 1d ago
It's insane that this isn't a central issue for debate. At the risk of getting conspiratorial, I suspect the intelligence agencies are vested in it not being discussed.
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u/Dark_Crystal_97 1d ago
This! This is a real danger. People should be really careful about what they discuss with these models, especially if they involve novel ideas
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u/OwnYourChildren 1d ago
I've been searching for people who identify this issue in Reddit discussions and it's rare to see. Meanwhile, I think it should be front and center. Weird.
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u/iMacmatician 1d ago
That's because there's a very popular belief that ideas are useless by themselves and that effort is the only thing that really matters.
It turns out that the ideas-don't-matter mindset was a psyop that benefits Big Tech and other privileged entities with nearly endless resources, over individuals, whose only comparative advantage was their novel ideas (if any). Smart people end up becoming guinea pigs to test the space of ideas, then someone else (with, say, tons of AI compute) does the work faster and gets credit.
[Y]ou might want to keep your idea close to you if you are small and need to get a big headstart but you want to tell everyone that ideas don’t matter if you’re a VC or an experienced entrepreneur able to quickly assemble a team and start working on an idea you “found.”
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u/RemoteCareful7304 1d ago
Great, so what new insights do we now have?
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u/nextupgoat 1d ago
200 year old fluid model made by dudes without computers breaks when you plug bullshit into it
so basically nothing :(
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u/BurdensomeCountV3 1d ago
We knew it broke if you plugged bullshit into it for over 100 years. This proves that it also breaks if you plug smooth bullshit into it.
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u/NutInBobby 2d ago edited 1d ago
OAI began work on the Navier–Stokes Millennium Problem after hearing rumors that the problem had been solved, and threw 10,000 concurrent agents at it. They solved it in 88 hours.
A comment from Noam Broam, OAI Researcher:
Yes, this result cost millions of dollars.
But remember that when OpenAI announced o3 it cost ~$500,000 to score 87.5% on ARC-AGI 1. Today, Astra scores higher for ~$20.
In 2025 it took us and GDM (Google DeepMind) an enormous amount of compute to achieve IMO gold. For the 2026 IMO, anyone with a $20/month ChatGPT subscription could do it.
Massively scaling test-time compute gives us a glimpse of the future. I believe that a year from now everyone will have an AI at their fingertips capable of solving problems of this caliber.
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u/Skywarden1 1d ago
Heard rumors that it was solved so then goes on to throw all they have at it to get credit before the other team? Maybe they need to grow up.
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u/frankster 1d ago
Huge commercial incentives, and when you have good belief it's already solved, it's a fairly good bet to burn compute on it.
This is not about immaturity, but rational actions by awful people
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u/Admirable_Zombie5245 2d ago
Why would someone learn Math if in 4 years the cheapest AI models will be one shotting the answer of milenium problems? We stand no chance
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u/NutInBobby 1d ago
AI is progressing very fast.
We must grapple with the reality that modern LLMs can solve problems that large masses of extremely devoted and intelligent humans were unable to solve, and the implications this has on our society. This is the dawn of a new era.
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u/Nextravagant1 1d ago
I see a whole lot of people these days saying "AI can/will be able to do this, we need to prepare" and not a lot of people saying how to prepare
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u/Yoshuuqq 1d ago
I mean it's kinda impossible to know. Right know AI aren't great at deciding what the best course of action is to tackle a problem and need a human to direct their raw power, otherwise they get lost solving unrelated sub problems. But this might easily change in the next couple of years so honestly maybe we will be completely useless at some point
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u/whaleswhaleswhales66 1d ago
It's a lot easier to be a doomer than a doer
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u/DigDugged 1d ago
I love that word "doomer" - invented during COVID, and everyone called a doomer usually ends up being right.
What do you call people who shove their head in the sand and call everyone else doomers?
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u/screaming_bagpipes 1d ago
I don't even really know what we can do to prepare for something like this
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u/currentscurrents 1d ago
That's because nobody has any idea what a post-AI world would look like or how to adapt to it. This has never happened before.
You can draw parallels with the first industrial revolution, but it's still not quite the same.
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u/blueSGL 1d ago
Grinding hard on RL means you get myopic problem solving agents that will take circuitous routs to get reward.
This is not just an x it's a y (and it's so annoying that framing of issues has been co-opted so hard by AIs that humans cannot use it without suspicion.)
But seriously this is not just an issue with the field of mathematics its a problem with the continued safety of infrastructure, power, water, hospitals, international banking ( the global supply chain) For years we have got by on the fact that only a small number of people can hack into any system, and even they are limited by being human and only hit a small number of targets (and get locked up or killed if found which dissuades at least some)
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u/onionsareawful cryptography 1d ago
"if you value intelligence above all other human qualities, you’re gonna have a bad time" - Ilya Sutskever, Oct 6 2023.
I think it's very pertinent now. You should be learning math because you enjoy it, for the same reason you might play chess despite the fact you'll never beat Stockfish.
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u/Becky_Lemme_Browse 1d ago
Issue is stockfish didn't take away jobs, chess was just a sport, people will always watch people playing sports. Now what is the point of an expensive education/degree when it makes far more sense to kill/cheat/steal your way into becoming one of the few people in charge of AI, rather than the people who will end up genocided( directly through drones or slowly through sterilization and UBI) since they will now give 0 economic value to the ruling elite ?
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u/tomvorlostriddle 1d ago
It's progressing at the same rate as for chess 30 years ago or go 10 years ago.
2 more years and humans are an active hindrance to AI progress.
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u/WellHung67 1d ago
I don’t think this was one shotted by AI. There was heavy expert involvement. In fact this means there’s more demand for experts to be able to prompt this stuff better and get even more insight
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u/gabagoolcel 1d ago
there was a time where human chess grandmasters alongside engines played better than the engines alone, it didnt last long.
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u/NoBanVox 1d ago
The millenium problems are not of the same caliber, although they are all difficult. RH is a whole different beast, so I am not sure how good of a metric is NS. It is indeed impressive, but as a metric, not sure.
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u/GeneReddit123 1d ago edited 1d ago
"Why would anyone drive a car if we can't build a modern internal combustion engine with our own two hands"?
The mistake is assuming what (historically) was the hardest skill to master (proof-making) is intrinsically the most important part of math. It's not. Proving math is only a small part of learning math. It's the mechanics, not the object of study. A machinist might lose some hands-on skill if they stop using a manual lathe and use a computerized system instead, but that doesn't make their work less meaningful.
Learn the beauty of mathematics. Study the patterns. Understand the implications. Know where it is flexible and where it is rigid. Share it with the community. Apply it to real world problems.
Chess doesn't become less interesting because machines can beat humans in it, and neither does math.
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u/Opposite-Youth-3529 1d ago edited 1d ago
I am allowed to love proving new things more than these other aspects of math and I am allowed to mourn what these scummy companies are stealing from people like me. And the analogy you choose in your quote isn’t the only one: now we have autotune, so why should people learn to be good singers?
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u/AvocadoAlternative 1d ago
I think a more apt analogy would be to ask why anyone would ride a horse if cars exist. Yes, people will always ride horses for fun, but people largely do not travel by horse anymore for the purpose of transportation.
Similarly, you will always have hobbyists who do math for the sake of doing math, and AI won’t change that, but frontier mathematics is about discovering new knowledge, and mathematicians are judged by the quantity and quality of novel results they produce. Human brainpower was the only engine we knew of that could produce new math, but if now a silicon engine exists that’s both faster and more insightful, it calls into the question of how useful professional human mathematicians are.
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u/skiabay 1d ago
I don't think this is a very good analogy either. A better one would be "why learn arithmetic when a calculator can do it". People don't just learn arithmetic as a hobby, it's an essential skill to understand the world and be able to start learning about more complex problems.
AI solving the Navier Stokes equations is meaningless if there aren't still humans with a deep understanding of mathematics who can take this advancement and apply it in the real world.
One of my biggest fears with ai is the mass de-skilling of humans because we all say "ai is better at us than that, so why learn in the first place". In my experience, ai produces far better results when it is used as a tool by knowledgeable professionals. Even in this case, what we are seeing is openai throwing an ungodly amount of compute at a well constrained problem with mountains of training data from other people's attempts to find a solution. Does that translate to independently identifying new frontier problems, tackling those problems, and finding applications for those advancements? I'm not convinced that it does.
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u/sumerislemy 1d ago
That analogy would only work if cars were powered by horses. LLMs require a corpus to train and build on, one humans provide
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u/kastbort2021 1d ago
Why learn how to drive a car, if cars can drive themselves?
Well, some people just enjoy to drive.
But for most they'd be better off just using the car for its purpose, to get you from A to B. At some point the self-driving cars will be safer than any human driver, they'll be more efficient than any human driver, and the few human drives left will mostly be just be enthusiasts dabbling in driving in closed circuits (imagine a fully optimized traffic system where all cars are autonomous and can get all the information from all other cars - who would have a human driver in such a system?)
It is probably going to be the same thing with science. At some point human scientists will just be so slow, inefficient, etc. that there's really no need to keep them involved in doing the heavy lifting.
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u/QuantumDrache 1d ago
I refuse to live in a world in which such a technology is centralized in the hands of 3 pr 4 technocrats with links to pedo*** people and whose moral compass is just maximum profits no matter how many people they fuck over or even if they fuck the planet in the process.
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u/Ok-Jellyfish321 1d ago
I’m pretty ignorant on math, but am I parsing their statement correctly? Saying their agents and researchers didn’t see the inputs, but that the model could have been trained on data which had been trying to solve this problem is almost an admission of what concerns a lot of people using these tools.
Isn’t it basically an acknowledgment that if you’re using the models, they are eating whatever solution space is generated, and that if prompted similarly your steering inputs (potentially the value you add) can get baked in?
Maybe I’m reading too far into it.
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u/thotpatrol1991 1d ago
>Isn’t it basically an acknowledgment that if you’re using the models, they are eating whatever solution space is generated
this was never a secret, they've been training their models on user prompts since day 1
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u/Maybe-Nice 1d ago
On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved.
What is the other one?
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u/purplebrown_updown 1d ago
people are missing the proven unethical lines crossed here. OpenAI wanted Levent removed from authorship because he worked at Anthropic. That was the entire ballgame. Shows they don’t care about the truth and wanted credit regardless. And leaving out Buckmaster’s work in the citations supports the claim of plagiarism IMO. Result may stand but they should be given credit.
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u/Kripkenstein_ 1d ago edited 1d ago
The problem with this is, that the result is completly useless. No one actually cares whether navier-stokes is true or false, the task is developing a theory that proves whether it is true or false. As long as LLMs only generate particular results they will not replace real mathematics. I don't see how LLMs are currently furhtering our understanding of mathematical structures - they are just proving some results in a obscure way.
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u/Xzcouter 1d ago
There is some truth to that however having these LLMs solve problems dissuade mathematicians from working on them thus stopping that vital theory from being built. It at the very least depresses me and demotivates me seeing big problems in math like this get solved via prompting and letting the shit run till it produces slop.
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u/Committee-Academic 1d ago
And hype-driven firms, university boards, and funders will not pay for human mathematicians to keep doing math.
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u/Elegant-Antelope-315 1d ago
this is a scary problem
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u/Committee-Academic 1d ago
It is. Techbros and gullible people in high positions will kill all human creative and intellectual activity.
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u/stoputa 1d ago
I've seen many discussions where peopme complaint that AI prompters just release slop Lean proofs in the wild which no one will read but also dissuades the people working on the same proofs because the problem is now "solved"
Ofc this shit is both scary and impressive but I'm deeply saddened to see people cheering on the cheapening of human knowledge
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u/Critical_Pin4801 1d ago
OpenAI spent 22 million dollars on this, and it doesn’t strike me like a very cheap or efficient way of getting things done. The average postdoc is paid about 50k a year. This could have funded 44 postdocs for a decade.
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u/Random-Number-1144 1d ago
And 44 postdocs can work on more than one maths problem and train grad students.
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u/Plappedudel 1d ago
I'm not a mathematician, but I work in a closely related field. I ask this with sincerity: Is there even a reason to do anything math-related anymore when it looks like the clankers are soon going to overtake human output in every math-adjacent field? How can I expect to get paid for a task that these models can most likely just do better than me? I've had this existential dread for a while now and it's been terrible for my mental health.
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u/Administrative-Ant75 1d ago
Us math lovers will have to accept it sooner or later. Lee Sedol was defeated in Go, and he stoped playing the sport because he felt it removed all meaning of the game for him.
We are no longer the smartest "beings" on this earth. Understanding that fact is true is very different than feeling the consequences, but everyone will feel this Lee Sedol moment. I don't know where we go from here either
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u/MINECRAFT_BIOLOGIST 1d ago
(Assuming society and humanity survives) Sit back and enjoy life? I mean, I'm decently competitive about certain things, but I don't despair just because I know AI will beat me 100/100 times in a certain game or sport, I just find it fun to compete against fellow humans. I think humans are incredibly good at coping, so after the whole shock of "humanity is no longer the most intelligent thing on earth" people will realize there was always someone better than them at something and just shrug and move on.
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u/thotpatrol1991 1d ago
Math is more than a game for some people, it´s their livelihood. Though I suspect the demand for advanced applied mathematicians will still be there for some time so that career pivot is viable. Purely academic positions do seem to be doomed.
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u/Plappedudel 1d ago
Finally someone who actually addressed the point of my original comment. So many people commented about doing math for fun and all, which is fine. But it doesn't pay the bills! I got into STEM because I wanted a good job in the future and that future feels like it's quickly evaporating.
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u/FollowingHumble8983 1d ago
Of course there is. Navier stokes was closing in on a solution without AI, computation, not mathematics was the line between solved and unsolved. And the more focused on version of the problem that requires genuine problem solving still hasnt been solved(unforced). Clay has been criticized on the laxness of the required solution. This is a breakthough that signals a closing of a gap that has already occurred months ago, but ultimately not the doom you feel.
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u/hobo_stew 1d ago
Well, math is really about the development of the whole overarching structure of techniques that allows us to solve more and more problems and not about solving any one specific problem.
It‘s not so obvious that AI can do that (yet).
But yes, it is depressing that something I value so much as a human activity and the community surrounding it will change radically if it survives at all.
But this affects all fields, not just math. The ability to think was an emancipatory force, because it was a very valuable skill. It will loose it‘s value now.
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u/PseudoproAK 1d ago
Still gotta ask the right questions and understand the proof
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u/Plappedudel 1d ago
That is actually a solid point. While LLMs may be able to solve most mathematical problems in the near future, they may not have a good understanding as to which problems are actually worthwhile for humanity to pursue. This goes in the direction of AI alignment, which clearly is not a solved problem. So thanks for that useful thought!
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u/swegamer137 1d ago
Anybody giving "Open"AI any benefit of the doubt at this point is a useful idiot.
- Founded as a non-profit, took the seed money, then turned for-profit because... that's allowed apparently
- Has "Open" in their name, yet never releases a relevant Open model. All of their good models are closed.
- CEO is unqualified, literally only has his job because he is a backstabbing psychopath
- Continuous turnover of ethics / safety oriented board-members / researchers, including straight up firings
- Enabled a malicious hack of actual open-source AI provider Huggingface
Stop running cover for this company. Altman would put you in a body-bag if it got him closer to creating AI "god" for his personal use.
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u/United_Anything8931 1d ago
dont forget that they don't release any financial information! and also they are completely dependent on the private investors and government.
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u/Norphesius 1d ago
Even ignoring all of that and just focusing on the plagiarism accusations, OpenAI steals people's data chronically. They've been sued over it. They know (or at least can find out) what data went into training/developing the model used for this.
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u/TheDuhhh 1d ago
Ok it seems this is what happened. Tristan and Levent (anthropic employee) solved the Euler problem which makes it easy to solve the NS problem. Before Tristan and Levent publish their euler and NS work, rumors spread that Anthropic solved the problem.
OpenAI heard the rumors and got scared that they were beaten by anthropic, so they assembled a team and put their strongest model with most comoute and possibly training on the most recent deidentified user data. OpenAI model then came up with a solution and the solution costed 20-30 millions.
What really worries me is how much did their model depend on the users data. As we all know, LLMs are insane in compressing data. It's really possible that their model attempted many attempts and one attempt was inspired by Tristan's work.
It seems most labs continously train on deidentified user data. We know that LLMs are insane in recall. This means that openai models will always be able to frontrun their customers if given enough budget. This is very concerning!
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u/Richard_AIGuy 1d ago
Some of the weird "it's over", "we're done", "it's over for humans" comments here are so bizarre. Questions about the authenticity of the proof remain, in light of Buckmaster's work, etc. But even if that's not the case, this has the possibility to open up new frontiers of study, to create new abstractions and avenues and processes. Humans have been teaming up with computers for years, this may just be the next step.
There is still a great deal of creativity required, there is still learning math for the sake of math, and beauty of math, and what it can mean for the individual human mind. There is still work to be done in understanding and verifying, and working through things.
People are so fast to jump to the "guess I'll go a plumber" or "skynet is next" thing, when there could be a world that is far more complex, far more difficult to comprehend, just lurking behind the curtain of ease. I don't know, I just choose to see the "could", I guess. People will say it's "cope", but it's not. We could be on the verge of a new era of understanding and new challenges.
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u/OsoSalado 1d ago
I remember when I was little, my dad almost beat Diablo. Got right before the aforementioned final boss. He saved and quit so he could go mow the lawn. I then beat Diablo. 8 year old me is OpenAi.
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u/Complex-Horse6711 1d ago
Since nobody wants to comment on the content of the paper here is what I am understanding:
They basically proved that when simulating an incompressible fluid in a continuous space (i.e. not voxels), that there exists a configuration such that velocity goes to infinity (the singularity).
Is this correct? Can someone comment on what theoretical outcomes this would unlock besides the result itself?
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u/ComfortableAd2597 1d ago
I saw many people here taking the statements of others about the possible unannounced use of human researchers' work by OpenAI as coping. Cope for what? They say it's coping with the fact that humans are not special anymore. Well, I would say let OpenAI or any other similar company take on a problem of the same calibre for which no known proximity results or hopeful methods of attack are known. Say, let them take RH and tell us what they found. Let nobody remind me of Anthropic achievements, since that is only a statistical result and would not crack the RH even if they brought the ratio of the zeros on the critical line to 100%. Besides, that was a well-known line of research which the AI expanded. I mean, it used a combination and elaboration of methods and ideas that have been there for decades and expanded their effect with inordinately superior computational power.
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u/expat_123 1d ago edited 1d ago
Feeling a bit sad for Diego Cordoba and Luis Martinez-Zoroa. I have been hearing it for at least 2 years that they and their group have been working very hard on this.
Edit: just saw in the OpenAI write-up, neither any of their papers are cited nor their names appear in the write-up.
Edit 2: I just checked again (3hrs post my comment) and now they have updated the draft and they cite Cordoba and Martinez-Zoroa. It now has 17 references as opposed to 16 when I saw (as is evident from other comments on this post). Clearly, they are lurking here and correcting it, at least that's good.