In previous math sharing there was speculation about stealing human researcher's results or progress, via prompt inputs from those researchers, and sharing that as their own result. They're adjusting their process, and it seems ok.
Let’s be very clear, the alleged “stolen results” were largely the product of another LLM, not de novo human work. Also, it was false - they did not steal the results.
> “Following an investigation, we have confirmed that Buckmaster’s Codex prompts over the two months preceding this announcement and paper on September 8, 2026, could not have influenced the system in any way, including through training.”
Buckmaster himself said essentially all the progress they made was from July 15th onwards (with a new model on the problem) with no real progress prior to then.
I think it’s really cope to claim this was a human result being stolen.
I really don't get how people are still continuing with this "stolen results" narrative after today. Like NS was kinda insignificant compared to treasure trove they released now, thinking that the LLM needs to "steal" from some human is simply coping.
What’s the nuance? Two researchers alleged theft. OpenAI investigated and confirmed that their research was not in the model’s training data. The world decided to take the first part as objective truth and ignored the second.
> OpenAI investigated and confirmed that their research was not in the model’s training data.
You mean when they say it was impossible to confirm anything but one day after it was 100% confirmed that there was no theft? And here I'm not even talking about all the ethical problems related to trying to scoop another group when you hear they're close to success, or how current solutions follow extremely closely human-generated ideas, or about the lack of relevant citations in OpenAI's paper.
Believing that OpenAI's claims have any substance cannot be explained by naivety alone.
They didn't try to scoop another group; they thought the other group had already solved it, so maybe their latest model could take a shot too... and the model solved the full problem when the other group had not! They found out after the fact that the other group had only solved an important sub-problem.
The controversy was whether they had plagiarised that other work on the sub-problem, which they categorically denied after an investigation. And yes, a few days to investigate something like this is reasonable for a company as big as OpenAI. Having seen how data infra is set up when petabytes of data are flowing about, there are thousands of entwined data pipelines to figure out. Not quite as easy as running a query on a sqlite DB!
> Believing that OpenAI's claims have any substance cannot be explained by naivety alone.
Yes, they could be explained by a GitHub repo full of proofs :-)
Or are you suggesting there were hundreds of researchers who just happened to be close to solving hundreds of these long standing open problems using Codex, and OpenAI swooped in plagiarized them all? ;-)
Right? Math is the most open of our academic knowledge institutions, by virtue of what it is. It's easy to get any math publication, and I am not aware of any other fields where an anonymous person can publish their work informally in an anime discussion and enter the annals of math knowledge.
I think it's generally a good thing that OpenAI is noticing when their projects are harming human communities, and deciding to respect their norms, especially when their math discoveries do not have immediate application and build on the thousands of years of that community's work.
I don't! But there is no such qualifier in the announcement. Perhaps OpenAI ought to filter for the problems that have immediate applications, and leave those that are unclear for humans.
Said communities are doing that all on their own by caring about what AI is doing rather than just focusing on their own thing as they did before AI. It's a serious kind of envy IMO.
It is not about AI the technology, plenty of mathematicians are happy to use AI, it is about the AI companies. The tech only exists because of centuries of mathematical tradition in open science. Moreover, the livelihoods of mathematicians depend on research results and ideas which can be developed only by doing the hard work of exploring open problems.
The recent statement from mathematicians is about how the labs have spent tens of millions of dollars (resources even entire math groups at universities can only dream of) on what was essentially marketing bragging rights for their models. This directly harms the math community by depriving them of opportunities for both funding and fertile ground for new ideas, while at the same time being built on top of their entire body of work.
Now, have OpenAI decided to change their practices and stop publishing math just because they are disrupting an entire field? Not really, since this release still dumps a huge number of results to open problems without waiting for human understanding to catch up. But at least they have committed to funding programs and talking to members of the field to work out how to best evolve it in this new world. And we will still get the benefits of results that happen to have applications.
After how poorly OpenAI and Anthropic handled the previous cases, I approve of the more measured and cautious approach this time.
We cannot have them rushing to publish amidst tons of confusion, rumors of threats/scooping and outright plagiarism of existing work (by failing to cite said work).
If they're going to participate as scientists in these more rigorous fields, they're going to have to match that level of rigor, not lower it to the disastrous low that ML research publication is at.
I'm not referring to just that. For example, Anthropic published a half done report about some biology research that turned out to have already been discovered and patented.
The gate keeping, I'm afraid, will be now in the hands of various bubecks, responding directly to even more disgusting people.
With all the hierarchy present in mathematics, I would prefer it by far.
This thing named inappropriately "OpenAI" goal is just grabbing and monopolizing. Capitalists before could not really touch the deep of the human spirit with their filth, now they can.
This is a tricky one, but I do sort of agree with you. However OpenAI doesn’t give most researchers access to the models which produced the work. So the gatekeeping goes both ways, I think.
GitHub is a significantly worse place to store important results than Arxiv. Of course, slop does not belong on Arxiv, buy slop should also not get published.
This is significant progress and released without all the drama. Some very important progress in Reinmann, Hodge and unique games theorem. Point the repo to your agent and ask for the significance! In a way this is probably 50-100 years of math progress by humans
Math is the tool humans use to compress knowledge. So until we can comprehend it there really isn't much progress. Math theorems are tautologies, the truth of which are not dependent on proofs and proofs are erasable, at least classically. But the AI progress is exciting and AI proofs are a gold mine for humans (at least non domain experts) to explore.
Academics have been treating it that way because they had no other choice, and its been a waste of everyone’s time and often times taxpayer resources
Look at that, taxpayer funding was cut and a private sector solution came in just the nick of time, far accelerating the holding patterns we’ve been in for decades
Humanity doesn’t need all iterations towards the blueprints, the blueprint is good enough, we all stand on the shoulders of giants
If you actually looked into how agents proved FLT you would be even more amazed by the fellow human beings who were able to keep all this in their head! I for one can only begin to grasp the scope with AI and scripts.
He spent years formalizing his sphere packing theorem because the proof (human produced) was already beyond the ability of peer review. Now his formalization efforts likely can be easily reproduced by a model. However one should read his experience about what a formal proof is: often the problem is the statement not the proof. The example he gave is the Jordan curve theorem. It's actually quite challenging to formalize the concept of a planar curve (there are space filling curves). So it is not necessary that someone can look at a formal statement and say aha it is about a planar curve, unlike FLT where there is not much problem in recognizing what the statement is about.
Fun challenge: find the formal definition of simple_closed_curve in the essay and tell me if you believe you learned anything about a planar curve.
BTW the essay is eminently readable for anyone interested in math. Hales wrote it in favor of formalized math and to educate his peers and students about it.
Not to pick on you specifically, but as someone who spends a lot of time unproductively reading AI math discourse it's truly shocking how incapable all the supposed math enthusiasts are of spelling Riemann.
If they’re mathematicians they have written this name down about a 100 different times throughout a standard Real Analysis course. Riemann was foundational in that field.
Let's figure it out! First, draw little boxes over all the letters. Then add up their areas. Then make the boxes smaller and repeat, until you have forgotten how to count.
Unique Games Conjecture [0] is a seminal conjecture in Complexity Theory, and is an underlying assumption for many, many inapproximability results. A valid proof is a big deal!
I also don't think there was general consensus on which way this would resolve prior to this (or is that a little out dated?) unlike some of the other major problem resolutions. I heard rumors that there would be a big result in TCS and speculation it would be UGC that or P neq PSPACE but I'm still a bit shocked.
I'm really glad that OpenAI is formalizing these things, because I'm not convinced that their current internal frontier models are particularly good at writing down their thoughts in English. From the (probably awesome) Unique Games Conjecture/Theorem paper, the first two sentences of section 1.1 start to define the problem:
> A Unique Games instance has a finite vertex set, a finite alphabet K, and a nonempty list of oriented constraints e = (u_e,v_e,π_e), where π_e is a permutation of K. A labeling a satisfies e when a(v_e) = π_e(a(u_e)).
I'm sorry, what? I admit it's been quite a few years since I've thought about the Unique Games Conjecture, and I never dug that deeply, but this part is very, very elementary graph theory and notation. So let's unpack it.
1. e is maybe a name of a list.
2. The elements of that list are tuples, where each tuple is (a vertex, a vertex, a permutation). So e indexes into the list and u_e is the source vertex for the e-th constraint in the list called e. Thanks.
3. a is a labeling. I'm fairly confident that, by "a labeling", they mean that e is a function from vertices to colors, where the colors are the elements of k.
4. That vertex coloring a satisfies the list e, when, for, um, an index e into e, a(v_e) = π_e(a(u_e)). But this isn't for all e, it's for some e, and the goal is to count them.
So maybe e isn't a list? Maybe e is a constraint that is represented as a tuple, so e = (u_e,v_e,π_e) and u, v, and π aren't sequences at all but are, in fact, the trivial unpacking functions that unpack the pieces of the tuple.
Reading this stuff is pointlessly painful, and it's extremely easy to make mistakes when being sloppy like this.
If this were my paper, or if I were trying to train a model to write math, I'd want something like:
A Unique Games instance has a finite vertex set V, a finite edge set E = (V × V), a finite alphabet K of possible vertex colors, and a nonempty list of oriented constraints. Let Π be the set of permutations of V. Each constraint e is a tuple in E × E × Π, where we write u_e ∈ E for the first element, v_e ∈ E for the second element and π_e ∈ Π for the third.
A vertex coloring a : V → K satisfies e when a(v_e) = π_e(a(u_e)).
In this particular case, though, I think my typoed version may be equivalent. An edge with no constraints has the same effect as no edge at all.
I definitely messed up the constraint definition, though: u_e and v_e refer to vertices, not edges. That’s what I get for writing it with minimal proofreading.
Let's hypothetically say I'm a PHD student who is half way through my studies and I have a halfway written version of one of these "preprints" - what do I do?
Seems like a lot of PHD students are doing to have to pivot the entire structure of their PHD studies? Or just produce something which is already written by OpenAI?
Precisely what all NLP researchers and the ML community at large did in the last few years: embrace the frontier and realize that attention is all you need.
This happens all the time, even without AI. Other researchers or PhD students can publish the same results before you. I say that based on my experience during my PhD.
Yes and no. It's pretty normal for students to get scooped, sometimes even multiple times (ask me how I know...).
It's much less common for students to have their entire thesis direction removed from under them, as might be the case for someone working in fine-grained complexity assuming 3SUM has no subquadratic algorithms, or working assuming ~UGC. Both of which (publicly) seemed like perfectly valid research directions until a couple hours ago.
There might be stuff to salvage from their conditional results anyway, but this is not your average scooping.
This has always been a challenge for PhD students and researchers, it's just far more likely to occur now it seems.
Getting scooped doesn't feel good, but it's a signal you've been thinking about things other people care about.
Interesting. If you don't mind, could you please share a little bit about that ? You already finished your dissertation ?
It was about the works of Doudna and Charpentier ?
I think eventually companies won't get as much stuff that's usable for marketing, so they'll stop investing so much into ai for math, so eventually cheap and poor graduate students will be able to do relevant work again without worrying about getting scooped by a company with a million GPUs :-/
That would be unfortunate but the world does not owe you anything and is not going to stop for you. Which is also a valuable thing to learn in your 20s (ideally earlier).
> Let's hypothetically say I'm a PHD student who is half way through my studies and I have a halfway written version of one of these "preprints" - what do I do?
I did get my PhD...before AI. And my honest advice (to myself back then, even) would be: quit the PhD, become an electrician, and work hard to buy a tiny house in the middle of nowhere to watch the world burn in this madness.
As others said, it's not that this isn't a phenomenon that is unique to now. It happens. I had to pivot a bit of my dissertation near the end because at a random conference I spoke with a researcher from another continent and realized one of my ideas was already out there in some form. I just missed it since it was in a conference proceedings outside the usual set I looked at. So, I had to scramble to adjust and still come up with something novel. I survived, and defended, but it wasn't that much fun at the time.
What isn't so normal is the probability and ease by which this kind of thing can happen today versus decades ago when I was in school. As OpenAI said, it only takes a few hours of compute to do what likely was much more than a few hours of human effort. The only reason this kind of scooping/overlapping was rare was mostly a function of how fast other humans could do the same work. With machines, that totally changes the relative pacing between the human trying to learn how to be a researcher and the machine that can grind out results.
I'm less worried about the phenomenon of overlap and scooping and such. I'm more worried about the long-term impact on fields (not just math), especially considering the early stage students and researchers entering the pipeline now. I'm not sure what happens to disciplines when that pipeline stalls.
At my (German) university, the solution would have been to change from a "cumulative" thesis (which requires peer-reviewed papers) to a monograph-style one. Because the general rule was that your undertaking must be novel ar the time you submit your thesis topic, not necessarily at the tome the thesis itself is submitted (years later).
I have had this conversation with my PhD students yesterday. I am 100% sure that all of their problems can be solved by publicly-available models now (I solved a case of one myself as a test, it took 15 minutes). So the challenge for them is to see how much they can accomplish in their allotted period, and still pass a defence on at the end of it all. The PhD defence is going to become all about a test of understanding, not a test of quantity of publication.
A much bigger issue is: What is the point of any research mathematician publishing anything now? I really hope that one positive effect of all this will be to finally topple the awful peer review model we currently have, with the biggest publishers gatekeeping with extortionate fees.
Frankly, I believe PhDs don't have to be novel in the absolute sense, only new research to the student. I can't remember how many times I've effectively invented something from a clean room approach only to realize someone already published something years ago or that my "new" algorithm has a name. So this really shouldn't be holding anyone back.
The follow up question then naturally would be how do phd advisors with people whose fields are in someway premised on making breakthroughs in theoretical fields that AI can solve work deal with it?
I appreciate you acknowledging the politics behind this. OpenAI does not intend to be a software company for long, they intend to be scientific infrastructure. They'll want to be faucet from which pours embryos, orbital calculation, geothermal/substructural rating, and etc.
I think it's a damned if they do, damned if they don't scenario. I think they would be afraid to seem like they're claiming that the selected scientists deserve the praise of an invention or something, when it's "just the machine who did the work"
Yeah, that's probably right. But, it's a "new world" - invent a new standard - "Written by Claude Foo X.Y; initial review by John Doe".
With a deluge of results, having some human expert vouch that it even might be worthwhile would help. (e.g. see the link on HN yesterday, "Two Room-Temperature Antiferromagnetic Semiconductor Candidates" - I see it not worth looking at unless a subject expert vouches for it).
Looking at the quality of the writing in these documents (or at least, the ones that relate to problems I've worked on), I do not think humans reviewed them.
And that means that the recommendations of the reference group has not been followed. The only improvement here is that it is version tracked? No authors, no careful write-ups with exposition.
The Advisory Group states in its recommendations [1]:
"We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models."
To me, this is a take against progress so that mathematicians can keep their jobs. What would we do if, instead of math, we were talking about diseases? Are we going to keep diseases around so that doctors can keep their jobs too?
It all hinges on the definition of “progress”. The debate of the past month is all about questioning whether formally proving outstanding unproven theorems without human understanding constitutes progress. This is quite different from solving diseases.
I don't think this is a reasonable take at all. Most work on maths has no real benefit other than to further human understanding of maths - it's more like an art. Nothing is gained from OpenAI solving all these problems but taking jobs from mathematicians. Other than advertising for OpenAI at least.
It could not be more different from having AI work on disease research etc.
Many mathematicians I know are shaken or depressed by these news of machiines that might put them out of business. Especially those who don't have tenure yet.
> At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community. Our recommendations are formulated with this practical context in mind. However, ideally, they would not do so. We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.
To me, the issue is that the models are proprietary which are only accessible to a few people in 2 digits. It's not about progress but access.
The trope you're drawing a parallel with has a (to me) compelling counter though: there being a cure for every disease wouldn't stop people from getting sick.
I'd really like some clarity on what that means. OpenAI has 'cheated' with this in the past, claiming that AlphaZero only took 4 hours to reach super-human chess levels while conveniently leaving out the fact that it was 4 hours x 5000+ TPUs. Sure it's impressive that it only took 4 hours wall-clock but it's very misleading as to cost.
Can we get a number in Blackwell GPU-hours, or kWh?
It means the level of effort that a ChatGPT Pro plan summons when thinking. For 3 hours.
If folks are going to analyze this claim with a critical eye, I'd be zeroing in on "average" rather than acting like this measurement is somehow unclear.
...even if it's 7 days, is it a big deal? This thing is solving stuff that multiple people have been trying to solve for years. Plus, even if it's 7 days today, it will very likely be 1 day next year and 6 hours in 2 years.
It's more and more evident that you can buy speed (up to a certain point).
With so many results in so many different areas no way they even remotely spot checked well enough.
Prediction: one of these is wrong and this (publicity stunt) will backfire.
Edit: don't tell me about lean. For lean to function as a proof certificate you need to represent the theorem correctly. Again: good luck doing that across such a broad swath of problems.
> Some of the unformalized results could have issues. We will endeavor to fix any such issues quickly. We are also exploring community-hosted repositories for these materials.
I'm a software engineering/biology/ML guy who loves when clever math ideas get turned into real solutions (https://en.wikipedia.org/wiki/Compressed_sensing). I am curious if any of the results have immediate applications in any kind of engineering or science.
It's fine if not, but it'd be great if even just one of these helped us solve a long-running problem.
Same. I have agents analyzing the papers here to see which of these are actually new approaches, novel application of unusual approaches, etc. If there are new intuitions and ideas, those are the mostly powerful reusable components by my estimation.
I was talking with a number of physicists this evening, and of the papers who's problem statement we understood, I don't think any of them will have near-term applications. For most of them, they were results that I think the physics community believed to be true, and the paper provides the first rigorous proof. For several it was news to me that they weren't already theorems! These results are important advances in mathematical physics, but they don't tend to have much impact on experiment.
From what I can tell, all of the physics results here are quite mathematical. But I am very curious how the internal model they used would perform on more applied problems.
It feels odd to me that they wouldn't prefer applied problems. Seems like an easy way to profitability. Probably based on what attributes they're looking for in a problem when picking them.
You can't really profit from proving theorems of applied problems (that are widely regarded to be true). Those who need to apply those theorems on real problems would have already done so (and if they don't work in some cases, well, congratulations... you found the counter example!)
At first this was my take as well. That plus, well, maybe they are just on a serious PR kick with maths. But I am starting wonder if they have determined, or strongly suspect, that the road to exponential model improvement must first be paved with extraordinary improvements in math. Like in some sense this seems like a test case for where their true intensions might go: vast improvements in the efficiency / size / speed of models and their training. Hard to imagine trusting the models in all those spaces without first trusting them / training them to address new or unsolved math.
This is a really interesting observation, especially given their current valuation and circumstances. Probably the verifiability of mathematics is enabling this progress, and making progress on science and engineering is not so straightforward. You can be sure that this is a top priority for them, especially now that there is concrete evidence that LLMs can achieve super-human performance at math. A model that achieves similarly super-human performance at things like material or drug design would be incredibly valuable. In fact, maybe this is why Anthropic hasn't been making such enormous strides in mathematics - they have been prioritizing biology instead.
This includes a proof of Barnette's Conjecture, which is one of the graph theory conjectures that I tried attacking with SOTA models a few months ago. I like it because it is to understand with a basic knowledge of graph theory. I spent quite a bit of time on it and failed. Their proof looks approachable at first glance.
The fact that this is plausible should be deeply disturbing and disqualifying for openAI. The fact that they may prevail and win is a travesty of our failed system.
Disqualifying for what? If you develop a proof you aren’t competing for something, you’re expanding the frontier of knowledge. It’s a binary state of the world, either it’s proven or not. Prevail and win what exactly?
Disqualifying for participation in civil society and the social contract. Why do they get to participate in and receive economic benefits, be shielded from liability, and effectuate their will to amass more power and influence such as monopolization of computer, training data, capital other resources. I have multiple founder friends that have been told firms are allocating less capital because they are reserving it for the OpenAI and anthropic IPOs.
Its a capitalistic issue, not a company/technology issue.
If we would have discovered this breakthrough of LLM/ML on scale in a non capitalistic world, we would all work together advancing it faster than it goes right now for the benefit of humanity.
And I don't live forever (at least for now) i def want to see were this road is heading.
Its a conflict of interest for sure, a cnflict of the future of a lot of humans
I hear you and would have what would probably feel like pedantic push back (we are not in capitalism as much as the unchecked end result of unregulated capitalism that becomes monopolistic corporatism), but it’s hard for me to see how this would be different in mercantilism, feudalism, or even communism as the human tendency to seek and hoard resources is universal for some fraction of people so as long as that confers an advantage then AI would be used by the designers in antisocial self enrichment.
I’d love to hear more thought experiments if you have some so my failure of imagination or lack of awareness can be overcome.
My personal system would be based on resource points: Define the amount of resources our planet has in a sustainable fashion, everyone gets the same and can use them how they like.
Technocracy had this already in form of Energy accounting.
Unfortunate something like communism sounds similar and just because we have seen that it didn't work due to technology issues (planning ahead without necessary information is hard?) and no gain of function which would push people, the basic idea is similiar to energy accounting.
Another thing this system needs might be a way for the system to protect itself.
I do think so that a society as diverse as ours will continue struggling with this as long as we do not give abundance resources to everyone or educate/indoctrinate people the 'right' way.
One thought I have regarding AI: IF it happens to slow, people will get used to the status quo and inequality and we will see a future of a handful rich people and a lot more poor people. IF it happens too fast, people might be more desprate to standup and demand something better.
Crazy how all these problems were simultaneously on the precipice of being solved before ScoopenAI (I came up with that) stole their work. The rate that mathematicians have suddenly made progress is only bested by the rate that OAI has ramped up their theft haha it's nuts.
Not sure if I didn't lay it on thick enough, or if (based on the other subthread) people think that's actually what happened and are mad. It would seem we're all in a Poe's law standoff. Oh well.
Presumably it's mainly the better model, I don't see much evidence of a particularly advanced harness based on the reasoning traces that they provided.
The internal model they used to solve the Navier-Stoke's problem was significantly better than the public Astra model, and they also used 10,000 agents.
Astra wasn't even released 3mo ago. It would not be surprising in the slightest that a public model from 3mo would not be capable of solving this problem, but an internal one from current day would be.
my speculation is that they have math-specialized model retrain, so it doesn't need to have all world info in weights, but can focus on math RL training.
I'm going to guess the ability to hold a million individual details in an attention space at once, compared to the typical human capacity for about six or seven
I've been messing with that problem since 2002. I'm curious if you were trying the dual spanning tree direction (which is what the purported proof is using) or working with cycle construction on the original graph. I was working heavily with edge-Kempe swaps but couldn't quite get there.
I am now very interested in the explicit calculation of Hamiltonian cycles in the non-bipartite case, and/or the calculation of their absence. If P=NP I think that's going to be a great route of attack.
It fascinates me that there's something like this in something as solid and rigid like matrix multiplication. What causes something so rigid to break apart and "leak" at very large scale? Why does the "optimization" appear to be very, very small? Why does galactic algorithm exists? I can't imagine long division suddenly breaking apart after a billion digit, the structure seems very stable? I have heard before that matrix multiplication is apparently optimize-able at very, very large scale.
Does anyone have an intuition to what causes it? What happens at these large scale (or very small)?
One way to think about it is that the classical algorithms are the ones that are fast for small numbers. Galactic algorithms often work for small inputs, it's just that to be faster you need big inputs. A common case of this is a requirement that log(n)<<klog(log(n)). If k=100 then this algorithm will take huge sizes to win
even though the constant is tiny, this breaks the long held assumption that nlogn is the minimal possible bound, so further research seemed unfruitful. this discovery will now trigger more research in this area, and probably more optimal algorithms will be discovered.
Like matrix multiplication, the common assumption was that it cannot be improved past n^3. Then Strassen broke the barrier (with a more significant constant) which caused intensive research - and now we are around n^2.3..2.4.
A lot of these seem to be proving conjectures rather than finding counterexamples, a lot of people used that to claim that these models are not really smart/creative etc.
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[ 1.6 ms ] story [ 323 ms ] threadhttps://openai.com/index/navier-stokes-solution/
I think it’s really cope to claim this was a human result being stolen.
If anything, the fact that they didn’t immediately deny it leads me to believe that they at least took the concern seriously.
The facts are much more nuanced than how you're presenting them here.
You mean when they say it was impossible to confirm anything but one day after it was 100% confirmed that there was no theft? And here I'm not even talking about all the ethical problems related to trying to scoop another group when you hear they're close to success, or how current solutions follow extremely closely human-generated ideas, or about the lack of relevant citations in OpenAI's paper.
Believing that OpenAI's claims have any substance cannot be explained by naivety alone.
This was a low-key hilarious replay of George Dantzig and his homework problems: https://en.wikipedia.org/wiki/George_Dantzig
The controversy was whether they had plagiarised that other work on the sub-problem, which they categorically denied after an investigation. And yes, a few days to investigate something like this is reasonable for a company as big as OpenAI. Having seen how data infra is set up when petabytes of data are flowing about, there are thousands of entwined data pipelines to figure out. Not quite as easy as running a query on a sqlite DB!
> Believing that OpenAI's claims have any substance cannot be explained by naivety alone.
Yes, they could be explained by a GitHub repo full of proofs :-)
Or are you suggesting there were hundreds of researchers who just happened to be close to solving hundreds of these long standing open problems using Codex, and OpenAI swooped in plagiarized them all? ;-)
There's no gatekeeping here!
https://proofsandprompts.com/2026/10/07/on-openais-release-o...
How do you know? Seems statistically unlikely with 720 problems, most of them well known
Said communities are doing that all on their own by caring about what AI is doing rather than just focusing on their own thing as they did before AI. It's a serious kind of envy IMO.
It is not about AI the technology, plenty of mathematicians are happy to use AI, it is about the AI companies. The tech only exists because of centuries of mathematical tradition in open science. Moreover, the livelihoods of mathematicians depend on research results and ideas which can be developed only by doing the hard work of exploring open problems.
The recent statement from mathematicians is about how the labs have spent tens of millions of dollars (resources even entire math groups at universities can only dream of) on what was essentially marketing bragging rights for their models. This directly harms the math community by depriving them of opportunities for both funding and fertile ground for new ideas, while at the same time being built on top of their entire body of work.
Now, have OpenAI decided to change their practices and stop publishing math just because they are disrupting an entire field? Not really, since this release still dumps a huge number of results to open problems without waiting for human understanding to catch up. But at least they have committed to funding programs and talking to members of the field to work out how to best evolve it in this new world. And we will still get the benefits of results that happen to have applications.
We cannot have them rushing to publish amidst tons of confusion, rumors of threats/scooping and outright plagiarism of existing work (by failing to cite said work).
If they're going to participate as scientists in these more rigorous fields, they're going to have to match that level of rigor, not lower it to the disastrous low that ML research publication is at.
With all the hierarchy present in mathematics, I would prefer it by far.
This thing named inappropriately "OpenAI" goal is just grabbing and monopolizing. Capitalists before could not really touch the deep of the human spirit with their filth, now they can.
Look at one of their examples of an initial prompt: https://github.com/openai/math/blob/main/reasoning_traces/re...
Interesting that its only an excerpt. I wonder what else they include but didn't share.
https://wikimediafoundation.org/news/2026/10/05/openai-rogue...
Who is "we" here exactly?
Look at that, taxpayer funding was cut and a private sector solution came in just the nick of time, far accelerating the holding patterns we’ve been in for decades
Humanity doesn’t need all iterations towards the blueprints, the blueprint is good enough, we all stand on the shoulders of giants
He spent years formalizing his sphere packing theorem because the proof (human produced) was already beyond the ability of peer review. Now his formalization efforts likely can be easily reproduced by a model. However one should read his experience about what a formal proof is: often the problem is the statement not the proof. The example he gave is the Jordan curve theorem. It's actually quite challenging to formalize the concept of a planar curve (there are space filling curves). So it is not necessary that someone can look at a formal statement and say aha it is about a planar curve, unlike FLT where there is not much problem in recognizing what the statement is about.
BTW the essay is eminently readable for anyone interested in math. Hales wrote it in favor of formalized math and to educate his peers and students about it.
Which either replaces us in the long term, augments us or makes us better (gentherapy).
If the proofs work thennwe can put them to work doing more things.
It is not particularly important that Einstein discovered relativity, just that it was discovered (Maxwell was very close).
Wow, this comment really shows how low this community fell.
I feel gaslighted.
[0] https://en.wikipedia.org/wiki/Unique_games_conjecture [1] https://github.com/openai/math/blob/main/preprints/The-Uniqu...
> A Unique Games instance has a finite vertex set, a finite alphabet K, and a nonempty list of oriented constraints e = (u_e,v_e,π_e), where π_e is a permutation of K. A labeling a satisfies e when a(v_e) = π_e(a(u_e)).
I'm sorry, what? I admit it's been quite a few years since I've thought about the Unique Games Conjecture, and I never dug that deeply, but this part is very, very elementary graph theory and notation. So let's unpack it.
1. e is maybe a name of a list.
2. The elements of that list are tuples, where each tuple is (a vertex, a vertex, a permutation). So e indexes into the list and u_e is the source vertex for the e-th constraint in the list called e. Thanks.
3. a is a labeling. I'm fairly confident that, by "a labeling", they mean that e is a function from vertices to colors, where the colors are the elements of k.
4. That vertex coloring a satisfies the list e, when, for, um, an index e into e, a(v_e) = π_e(a(u_e)). But this isn't for all e, it's for some e, and the goal is to count them.
So maybe e isn't a list? Maybe e is a constraint that is represented as a tuple, so e = (u_e,v_e,π_e) and u, v, and π aren't sequences at all but are, in fact, the trivial unpacking functions that unpack the pieces of the tuple.
Reading this stuff is pointlessly painful, and it's extremely easy to make mistakes when being sloppy like this.
If this were my paper, or if I were trying to train a model to write math, I'd want something like:
A Unique Games instance has a finite vertex set V, a finite edge set E = (V × V), a finite alphabet K of possible vertex colors, and a nonempty list of oriented constraints. Let Π be the set of permutations of V. Each constraint e is a tuple in E × E × Π, where we write u_e ∈ E for the first element, v_e ∈ E for the second element and π_e ∈ Π for the third.
A vertex coloring a : V → K satisfies e when a(v_e) = π_e(a(u_e)).
E ⊆ V × V
In this particular case, though, I think my typoed version may be equivalent. An edge with no constraints has the same effect as no edge at all.
I definitely messed up the constraint definition, though: u_e and v_e refer to vertices, not edges. That’s what I get for writing it with minimal proofreading.
Basically "Here you go, have fun with this, fuck all your demands, by the way we're gonna be releasing the model stay tuned!"
Seems like a lot of PHD students are doing to have to pivot the entire structure of their PHD studies? Or just produce something which is already written by OpenAI?
Precisely what all NLP researchers and the ML community at large did in the last few years: embrace the frontier and realize that attention is all you need.
It's much less common for students to have their entire thesis direction removed from under them, as might be the case for someone working in fine-grained complexity assuming 3SUM has no subquadratic algorithms, or working assuming ~UGC. Both of which (publicly) seemed like perfectly valid research directions until a couple hours ago.
There might be stuff to salvage from their conditional results anyway, but this is not your average scooping.
I guess the only answer is to adapt with the tools. If we can't do that, then yeah, we're in trouble.
I did get my PhD...before AI. And my honest advice (to myself back then, even) would be: quit the PhD, become an electrician, and work hard to buy a tiny house in the middle of nowhere to watch the world burn in this madness.
Very hard question.
Your work makes you one of the very few people who really understands the problem and solution and its significance.
What isn't so normal is the probability and ease by which this kind of thing can happen today versus decades ago when I was in school. As OpenAI said, it only takes a few hours of compute to do what likely was much more than a few hours of human effort. The only reason this kind of scooping/overlapping was rare was mostly a function of how fast other humans could do the same work. With machines, that totally changes the relative pacing between the human trying to learn how to be a researcher and the machine that can grind out results.
I'm less worried about the phenomenon of overlap and scooping and such. I'm more worried about the long-term impact on fields (not just math), especially considering the early stage students and researchers entering the pipeline now. I'm not sure what happens to disciplines when that pipeline stalls.
A much bigger issue is: What is the point of any research mathematician publishing anything now? I really hope that one positive effect of all this will be to finally topple the awful peer review model we currently have, with the biggest publishers gatekeeping with extortionate fees.
Some math PhDs would spend a year or so doing things with AI and lean, and graduate. And keep doing more math afterwards.
Some others, with more stubborn advisors, will keep trying to find a gap where there's no AI progress.
CS subfields go through this every ten or so years.
beyond naive.
1: Author 2: Verifier
/s
With a deluge of results, having some human expert vouch that it even might be worthwhile would help. (e.g. see the link on HN yesterday, "Two Room-Temperature Antiferromagnetic Semiconductor Candidates" - I see it not worth looking at unless a subject expert vouches for it).
"We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models."
To me, this is a take against progress so that mathematicians can keep their jobs. What would we do if, instead of math, we were talking about diseases? Are we going to keep diseases around so that doctors can keep their jobs too?
[1] https://agmai.org/general-sep29/
> "I believe that AI can contribute positively in all of these directions [NB: exposition, community building, new directions of study]"
https://mathstodon.xyz/@tao/117395269325940185
It's been a while since I was reminded of this xkcd: https://xkcd.com/435/
> At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community. Our recommendations are formulated with this practical context in mind. However, ideally, they would not do so. We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.
To me, the issue is that the models are proprietary which are only accessible to a few people in 2 digits. It's not about progress but access.
Not so for maths.
Can we get a number in Blackwell GPU-hours, or kWh?
That doesn't sound right
If folks are going to analyze this claim with a critical eye, I'd be zeroing in on "average" rather than acting like this measurement is somehow unclear.
It's more and more evident that you can buy speed (up to a certain point).
Prediction: one of these is wrong and this (publicity stunt) will backfire.
Edit: don't tell me about lean. For lean to function as a proof certificate you need to represent the theorem correctly. Again: good luck doing that across such a broad swath of problems.
> Some of the unformalized results could have issues. We will endeavor to fix any such issues quickly. We are also exploring community-hosted repositories for these materials.
It's fine if not, but it'd be great if even just one of these helped us solve a long-running problem.
From what I can tell, all of the physics results here are quite mathematical. But I am very curious how the internal model they used would perform on more applied problems.
https://github.com/openai/math/blob/main/preprints/Paired-st...
We are in danger.
US/world deviate more and more from social contracts. Money matters way more, and OpenAI wins here.
If we would have discovered this breakthrough of LLM/ML on scale in a non capitalistic world, we would all work together advancing it faster than it goes right now for the benefit of humanity.
And I don't live forever (at least for now) i def want to see were this road is heading.
Its a conflict of interest for sure, a cnflict of the future of a lot of humans
I am always looking for leftist writing imagining a positive vision for AI. Is there any which you'd recommend?
There's quite a lot of progressive positive writing.
On the economic side the Australian Council of Trade Unions statement is about a positive future: https://www.actu.org.au/speeches-and-opinion/joint-statement...
I’d love to hear more thought experiments if you have some so my failure of imagination or lack of awareness can be overcome.
Technocracy had this already in form of Energy accounting.
Unfortunate something like communism sounds similar and just because we have seen that it didn't work due to technology issues (planning ahead without necessary information is hard?) and no gain of function which would push people, the basic idea is similiar to energy accounting.
Another thing this system needs might be a way for the system to protect itself.
I do think so that a society as diverse as ours will continue struggling with this as long as we do not give abundance resources to everyone or educate/indoctrinate people the 'right' way.
One thought I have regarding AI: IF it happens to slow, people will get used to the status quo and inequality and we will see a future of a handful rich people and a lot more poor people. IF it happens too fast, people might be more desprate to standup and demand something better.
The model is probably comically big and inefficient but big enough
Finally, size really does matter!
Astra wasn't even released 3mo ago. It would not be surprising in the slightest that a public model from 3mo would not be capable of solving this problem, but an internal one from current day would be.
I am now very interested in the explicit calculation of Hamiltonian cycles in the non-bipartite case, and/or the calculation of their absence. If P=NP I think that's going to be a great route of attack.
109. Integer multiplication below n log n
Surprising that this is possible.
158. The Euclidean plane cannot be colored with five colors.
Only 6 and 7 remain!
LMAO, I don't think I ever saw such a small number in a CS result.
Does anyone have an intuition to what causes it? What happens at these large scale (or very small)?
It seems n would have to be unimaginably large for this to make any difference. What changes about multiplication / FFT at large enough size ?
I guess nobody expected that it did before this result.
Like matrix multiplication, the common assumption was that it cannot be improved past n^3. Then Strassen broke the barrier (with a more significant constant) which caused intensive research - and now we are around n^2.3..2.4.
That copium didn't last for what, three months?