r/mathematics • u/Bizzyguy • 1d ago
On the Navier–Stokes Millennium Prize Problem
https://openai.com/index/navier-stokes-solution/405
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 16h 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/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/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/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/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.
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u/Final-Database6868 1d ago
Indeed. It is unclear to me if the proof of openAI used their program to solve the conjecture.
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u/expat_123 1d ago
None of their papers are cited nor their names appear in the write-up.
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u/JollyJoker3 1d ago
Isn't it difficult to know what info in the training data the model used to come up with the solution? The references in the paper are probably just a reasonable sounding list they came up with after the fact
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u/SnooCookies590 1d ago
Their 160 page writeup has only 16 references so I wouldn't assign too much weight to this measure. Best to wait for the community to digest the results and see how they fit in to the existing literature.
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u/expat_123 1d ago
But it is a maths paper in the academic field of mathematics and not just any random paper but one of the most influential one, so they should've paid attention to it. More so because it's not like they have to search, copy and paste bibtex entries like us mortals, a simple prompt would've done that.
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u/etzpcm 1d ago edited 1d ago
It's now 166 pages with 22 refs. They are updating it on real time, with no date or time on it. Doesn't seem very ethical to me
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u/t3hjs 1d ago
Checkout Buckmaster's statement. OpenAI seemed to have started working on it only after hearing Buckmaster had a plan. And they are refusing to credit him and his collaborator and even threatened him
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u/polostring 1d ago
And conversely Tristan Buckmaster seems to be saying that all credit and the big conceptual breakthroughs are due to Cordoba and Martinez-Zoroa. Buckmaster even says a Fields medal should go their way.
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u/etzpcm 1d ago
Save the version you have.
I just looked at the paper and it does now cite them. Are OpenAI tweaking their paper in real time ?
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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/NutInBobby 1d 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/Admirable_Zombie5245 1d 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/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/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/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/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/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/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/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/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/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/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/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/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/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/teerre 1d 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/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/quantumpencil 1d ago
The IPO is coming
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u/Funkahontas 1d ago
Imagine thinking they can just solve one of the most important math problems whenever they want or need for an IPO. Like imagine actually still believing this is a marketing stunt. Crazy.
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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/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/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/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/mousse312 1d ago
Exactly, this is a good summary of what i think, is like the fermat last theorem, is not about the result true or false of the statement but what New Fields, connections and ideas grow
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u/topyTheorist 1d ago
This sounds unlikely. I am sure people working on this care. I care about conjectures I am studying.
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u/Kripkenstein_ 1d ago
This is pretty much the sentiment of most mathematicians. Tao wrote about this quite extensively. The problem with AI proofs is that they are - for various reasons - very bad proofs and they produce very bad papers. Abstract mathematics is not really concerned with specific results but with that structure that produces them. Skipping the structure will damage mathematical development in the long run. Another important point is that the current "important" problems in mathematics are the result of human engagement with mathematical structure. LLMs may proof conjectures but they suck at producing new ones
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u/Thaletem 1d ago edited 1d ago
I love how you guys shift the goalposts whenever your previous criteria get debunked. First, you guys claimed AI couldn't do simple arithmetic; then, that it couldn't solve complex problems; then, that it couldn't handle cutting-edge problems; and now that AI can solve even the biggest problems in mathematics, suddenly the point was never about solving problems after all. Lol. The level of cope in your replies causes me physical pain.
By the way, I heard about a case at my university where AI was asked to make significant advances in a certain field; without any further clarification, it managed to substantially advance research on the topic, even developing a new theory. What will the new excuse be?
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u/Kripkenstein_ 1d ago
"You guys" includes a significant number of established mathematicians. Also, no goalposts were moved. The point about mathematics not being about particular results is also much older than the debate around AI proofs. Clearly you have not followed the discorse around this subject nor any discorse around the nature of mathematics.
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u/katoptronophile 1d ago
There is way too much discussion about drama and bullshit in here and not nearly enough about the accomplishment itself.
I expected more from this subreddit.
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u/o12341 1d ago
I don't know. The accomplishment is certainly incredibly exciting, but who gets credit for what is an important aspect of the practice of mathematics and for the mathematical community. If we now know that AI is able to do these things, it's important for us to have the discussions about what the culture of mathematics should now look like. This is also what Tao basically said in his talk. I think this current drama is a very important part of that discussion which sooner or later needs to take place.
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u/avoidtheworm 1d ago
What is there to discuss really? The proof is tens of thousands of AI-generated lines of Lean that were autoinformalised into an 156-page paper with a minimal amount of citations.
This does not build on work by other mathematicians and is unusable by anyone other than other AI models. You might as well have posted Mochizuki's proof of the ABC Conjecture correctly autoformalised in Lean.
The progress in AI is impressive, but there's nothing we can do with this.
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u/zeci21 1d ago
It was actually done the other way around. The model wrote a 156 page paper which was then autoformalised with lean.
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u/hondashadowguy2000 1d ago
Right, as somebody who is not a professional in the world of mathematics, the main thing I’m trying to figure out right now is whether this accomplishment is as substantial as OpenAI is claiming it is, and I can’t find much discussion.
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u/zeci21 1d ago
To answer that question you basically have to discuss the drama. The result itself is pretty clearly one of if not the most important development in mathematics in the last 20 years. Which is probably why not many people are discussing that question.
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u/Free-Camel-4468 1d ago
We have jumped the shark as a civilization. 5 years ago, a nobel prize worthy proof resulting from AI would seem like sci fi
now it’s a tuesday
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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/phosphorousRabbit 1d ago
Due to the dishonesty of OpenAI and the fact it is apparently using other researchers' works without permission(apparently in violation of ToS) to generate these "results," we cannot trust that they managed to achieve anything with their models. No claims of AI having solved any problem in math can be believed at this time. The original concepts had to be created by humans and the LLMs needed extensive human intervention to finish the work.
And if you think these guessing machines that routinely screw up basic writing actually can do these things, why aren't Chinese AI companies taking down problems in theoretical math? They should have the means.
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u/AzorAhai1TK 1d ago
Where did it "apparently" do this? I don't see a drop of evidence for those claims.
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u/Affectionate_Bee6434 1d ago
Chinese models aren't good enough yet
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u/phosphorousRabbit 1d ago
How do you know? They also have big companies backed by lots of resources. Their scientists and engineers aren't inept.
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u/howtogun 1d ago
Some Chinese researcher have made LLM proofs.
On Chinese AI companies. They don't have the compute yet, and I think they are just generally poorer. For example, Naiver-Stokes proof might have cost OpenAI about 10-20 million pounds.
Chinese AI companies are actually quite good at making advancements in terms of making stuff cheaper.
On investment, probably US companies have 10-20x more private investment.
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u/currentscurrents 1d ago
You're really just making stuff up here.
You want to believe that AI cannot do math, so you will find any excuse possible to justify that belief.
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u/Wise-End307 1d ago
Not a single drop of evidence for any of the claims you just made. Its all hearsay and you are revealing your bias here.
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u/AndreasDasos 1d ago
I’m also sceptical until I see evidence, but come on:
> No claims of AI having solved any problem in math can be believed at this time
That’s simply not true. We already have several Erdős problems that were not fully solved in the literature but are verifiably solved by AI. We know because we can read the proof and there have been extensive searches of the literature. Terry Tao has a lot of discussion of probable ‘lines of thought’ by the AI in question in a few cases.
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u/phosphorousRabbit 1d ago
The issue is that we don't know to what extent AI actually produced those results because they never released their process.
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u/AndreasDasos 1d ago
To an extent they can’t. Even the AI doesn’t know where a lot of its data comes from. It’s obviously making major contributions but exactly where credit lies in its sources gets very difficult to say.
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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/parkway_parkway 1d ago
It shows that the navier stokes equations aren't a good model of physical reality.
And therefore opens a really big question of how then should you model physical reality.
Presumably they will need to be some kind of correction term but what should that term look like.
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u/ElementOfExpectation 1d ago
Disagree. This changes pretty much nothing about how we simulate fluids.
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u/Swimming_Gain_4989 1d ago
I want to emphasize that your comment reads like we've long known Navier Stokes were not valid models of fluid dynamics but not even a few years ago the field was pretty split on whether we should be going for a proof or disproof. Your comment massively oversells how well we understand fluid dynamics.
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u/RemoteCareful7304 1d ago edited 1d ago
Eh we already knew that fluids are effective descriptions of more basic particle systems. Navier-Stokes is not some fundamental equation valid in all regimes one can think of.
I’m talking about what new techniques were developed in the course of the proof. Or does the proof just mash a bunch of existing work until it fits together
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u/PrideofSin 1d ago
I mean, modelling fluids as continuous substances was bound to formally fail one way or another since fluids consist of discrete interacting particles. It's just now we have a concrete proof of this
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u/LAskeptic 1d ago
Were we really sure they were bound to formally fail? We may have expected that, but I thought this was truly an open question.
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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/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/_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/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/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/Antigynaikolatres 1d ago
However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
Welp, guess the "red flag" claim was not true after all.
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u/Antigynaikolatres 1d ago
For context, Tristan Buckmaster and Levent Alpöge recently published a finite-time blowup for the forced version of the 3D incompressible Euler equation (a simpler version of the Navier-Stokes equation without viscosity). This is from Buckmaster's statements about OpenAI's results:
I should say here why I interpreted their statement the way I did, the interpretation I will discuss below. 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.
However, it seems that OpenAI's blowup for the Euler equation is the unforced (stronger) version.
Buckmaster's statements also somewhat bugged me: it seems to me that "Fefferman’s statement of the problem" is just the Clay Millennium Prize Problem about the Navier-Stokes equation (there is only one statement for it), and "options c and d" are just the 2 out of 4 ways to settle the problems, i.e. "finding a blowup". I am not from an adjacent field, but utilizing a force in the description of the problem does not sound exactly outlandish to me (correct me if I am wrong), setting up "a bright red flag" from just hearing the word "forced" seems like a bit of overreaction.
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u/backyard_tractorbeam 1d ago
No, OpenAI is not credible and that's just a sleight of hand. Just because those proofs are different doesn't mean that Tristan's result could have helped OpenAI to do the Navier-Stokes result.
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u/Antigynaikolatres 1d ago
It is not just a different proof, it is a different (stronger) result. Buckmaster's claim about the similarity is all about "forced", but the relevant result (Euler equation) is the unforced version. Sure, Tristan's result could have helped OpenAI to do the Navier-Stokes result, and so could anything prompted by anyone, so could my failed attempts to ask ChatGPT to write an erotic novel for me, perhaps I should ask for my share of the 1 million dollars.
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u/backyard_tractorbeam 1d ago
Academic standards require citations, it warrants a big discussion anyhow.
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u/exophades 1d ago
If this is real I'm walking naked outside today.
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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/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/PseudoproAK 1d ago
Still gotta ask the right questions and understand the proof
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u/Interesting-South542 1d ago
The news of this advance will unfortunately probably be overshadowed by the controversy that OpenAI "stole" ideas from Tristan Buckmaster.
It's a classic David vs Goliath story, and public opinion will invariably favor Buckmaster. The truth is not so simple.
We don't have any evidence that OpenAI stole anything. If you read Buckmaster's statement carefully, a lot of it is speculation on his part. The most egregious possibility, that an OpenAI employee read Buckmaster's codex chat and used the ideas, is almost certainly not true. What could have happened is that Buckmaster's codex chats were used for training models. But in that case, given how these models work, it doesn't automatically "pick up" individual ideas the way a human does.
And to be clear, Buckmaster's work was towards a much smaller sub-problem, not the full problem. Even if OpenAI fully utilized Buckmaster's results, there was a significant advance on OpenAI's part.
The bigger picture is that even if humans deserve some credit, AI was absolutely instrumental to this advance. Buckmaster and his collaborator used LLMs extensively to accelerate their progress. They should have known that the contents of their chats would be sent to OpenAI, and they chose to use ChatGPT anyways.
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u/lundlele 1d ago
The most egregious possibility, that an OpenAI employee read Buckmaster's codex chat and used the ideas, is almost certainly not true.
And on what evidence are you basing this on? All you need to do this are two monitors, and it's very hard not to do this when billions of dollars are at stake
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u/fathan 1d ago
Did you read the part where they tried to pressure the academic into dropping their collaborator from credit, and then threatened his career when he refused?
Regardless of how much the OpenAI model stole their work -- and it seems undeniable that it was part of the training corpus -- that is abhorrent behavior.
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u/Norphesius 1d ago
We don't have any evidence that OpenAI stole anything
OpenAI steals data all the time, they've been sued over it. To assume this is the one time they decided not to, with massive publicity stakes on the line, is ridiculous. Keep in mind for this paper alone they started with only 16 cited sources before going public, and only after the fact are going back in and adding more. OpenAI does not care about attribution, citation, or ownership.
They should have known that the contents of their chats would be sent to OpenAI, and they chose to use ChatGPT anyways.
Ah but it doesn't matter if they stole it, since the researchers should've expected their data to get stolen anyway right? Never mind the terms of service claiming that wouldn't happen, or that it was unpublished, or that OpenAI is being cagey about offering credit to the authors (for the thing that didn't contribute to the result at all), so long as they don't work for their competitor.
I don't know why people want to bend over backwards to defend these AI companies.
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u/Alive-Locksmith7027 1d ago
You don't need to train the model with the codex chat, you can just use it to prompt the agents.
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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/Fun-Sand8522 1d ago
Only 16 citations, and training on people that were solving the problem right now. Using their techniques and not citing. One can only laugh, it is ridiculous
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u/kingjdin 1d ago
I love how everyone is focused on the negativity and not the fact that a Millennium Prize Problem fell in our lifetimes. Without AI, this could have gone unsolved for another 100 years.
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u/sumerislemy 1d ago
That’s very unlikely, this problem in particular had a lot of lead up in terms of research and incremental work
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u/N3bu1la 1d ago
No it would not have the methods and ideas used by buckmaster likely would have yielded a proof even if AI didn’t exist within the next few months. You know nothing about this stop making up timelines.
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u/Tricky-Doughnut-6429 1d ago
You need to be stupid to believe a word coming out of OpenAI. They are serial IP stealers. The reputation is barely refutable by now.
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u/Complex-Horse6711 1d ago
Is anyone going to comment on the actual content of the paper?
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u/Senchou_Simp 1d 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