I think it can both true that 1) OpenAI is being inconsiderate/harmful/<pick-whatever-adjective> with their math releases, and 2) there is now a treasure trove of mathematical results ready for the taking.
Yes, the situation sucks overall and mathematics as a whole is in a turbulent time now.
But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem. #2 above is still true regardless of where it came from or how hard it can be to absorb.
While reading "The Mathocalypse" post [0] by Scott Aaronson, Scott described his wife Dana's reaction to one of the newly solved results in her primary domain of expertise, on which she'd been working for decades.
After her initial shock, and annoyance with the format/style, she decided to start using Astra - for the first time - to help her understand the new result. And he reported in the comments that she had made a lot of progress understanding it in one day, and may be even excited to give a talk about it!
That seems like a much healthier attitude towards these new results.
Yes, everything else sucks about this messy period. But there are still diamonds (in the rough) in this drop that perhaps should be looked into. If the author is too busy, perhaps one of their students can take a look? Someone will, eventually.
Why are you two-siding this. There is only one misaligned agent here and that is the company OpenAI. What OpenAI is doing sucks, and people are calling OpenAI out for sucking. However mathematicians (the main victims of OpenAI’s lousy behavior) behave is not the issue here.
If some mathematicians complain about OpenAI sucking, that is fine actually, and if others are more “mature” about it, that that is fine too. Neither of these reactions should be at put as an equivalence to the blame OpenAI deserves for this stunt.
Are they fully “doing math” in an aligned way though? They are finding mathematical proofs, which is important, but contextualizing results in the prior literature and clearly communicating the approach and implications is just as much part of mathematical research.
You might argue that these aspects of math are less important in the new AI accelerated math world, because agents will inevitably be smarter than humans, but I think clear framing and communication is even more important than before because with this technology we can choose to augment our intelligence instead of defer it
Paraphrasing Hardy, 'exposition is for second-rate minds'.
I don't believe this myself. But I do believe that if you've formed your very ideas about what is good and desirable on the basis of a culture that has held certain values dear for hundreds of years, and have fought against every doubt and difficulty in life for decades to mold yourself into that image, that it does not 'suck' that you are unable to adapt to a new reality overnight.
Very few people that would love to be craftsmen would love to be factory foremen. It is far too insensitive to the human experience to expect people to just deal.
> Paraphrasing Hardy, 'exposition is for second-rate minds'.
Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.
Some people told themselves they were the pinnacle, the first-rate mind, as opposed to all the second-rater. Well guess what, now your first-rate mind is a commodity and exposition is more valuable. They'd better learn to live with it.
It turns out your an expendable commodity, and my computer system is predicting that society will profit from your annihilation, really sorry about that and I hope there's no hard feelings.
> Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.
Thankfully, very few mathematicians share Hardy's opinion, just as very few share his opinion that "mathematics is a young man's game" (and indeed we now have prizes like the Abel Prize with no age limit).
In fact, many of the greatest mathematicians throughout history have taken exposition very seriously, e.g. Euclid, Euler, Lagrange, Cauchy, Dirichlet, Kolmogorov etc. all wrote textbooks. Many mathematicians today carry on that tradition of taking exposition seriously and write books and freely share their lecture notes.
So we should not take Hardy's opinion as representing the opinion of all mathematicians or even most mathematicians. In fact, Hardy's statement is somewhat self-contradictory since he himself wrote several expository books (e.g. "A Course of Pure Mathematics").
His statement was self-deprecating (in a not so endearing way), as he was referencing his young self as one of those first-rate minds but his current old self doing exposition as second-rate.
I know that it was self-deprecating, but that doesn't redeem it much to me. I also still find it pretty contradictory/ironic because he wrote A Course of Pure Mathematics when he was in his early thirties.
> But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem.
It might be a shock for you but they are very few in numbers. Most of researchers I know are always busy with something. They cannot just drop other responsibilities for something like this. They will take their own time getting through the proofs (if they want to).
> That seems like a much healthier attitude towards these new results.
Another thing to consider is not all mathematicians are from US or with good funding. The PI or graduate students cannot afford to pay 200/month.
I think the role of specific _human_ mathematicians at OpenAI should not be understated.
TFA was about a niche topic that OpenAI doesn't have in-house expertise in.
Otoh Aaronson is the co-author on Lijie Chen's (reasoning lead at OAI) top cited paper. OAI have deployed their resources more effectively against UGC that some of their staff are already familiar with
That's true. OpenAI has some of the best talents. In my experience, domain experts get the most benefits from the models. They can work much faster, catch false positives, and stir the model in right direction.
I wish they take a bit of more time to communicate the findings effectively.
There are good reasons not to delay publishing at all:
> They should release all their results immediately. (Imagine working on one of the problems they already solved.)
This is the most popular answer to a question regarding AI advisory group and immediate access on a popular website for professional mathematicians: https://mathoverflow.net/a/515442/473286
The whole debate regarding the behaviour of OpenAI is a red herring. Mathematics need to redefine their profession and how they work (like us software developers too). There are very good reasons to believe mathematics has an important role to play. If they could just stop talking about OpenAI and get back to work - they are very much needed, in particular now!
> If they could just stop talking about OpenAI and get back to work - they are very much needed, in particular now
This kind of phrasing sounds particularly empty. We are not in WWII researching the nuclear bomb. What are they so urgently needed for to drop everything and work on understanding openai's proof on partition principle and axiom of choice?
Where did I say they should "drop everything"? I hope to read more about how they envision their future, instead of all this regretting and whaling how one company (that I very much dislike too) published a large amount of proofs. They will get more of them, very soon - if they like it or not -, and I wish that would be the primary subject of the discussion. And yes, I'd also hope they engage with the published proofs. The more raw these proofs are, the better. If AI companies start selecting mathematicians to write nice expositions of their proofs, this is doomed to become a very elitist science.
Says who? The professional mathematician writing the article disagreed. Why should people start dancing the tune that openai wants to play for their own reasons and interests? And I do not see how taking the time and effort to write a proper exposition makes it "a very elitist science" when this exact effort and time is needed to actually get other experts understand and build on a result. Unless you equate spending time and effort learning math as "elitism", which is the ai-shilling moto some time now with everything time and effort related. I cannot see how spending time and effort to understand a field and then spend time and effort to make a proper exposition so that other people can also understand it as "elitist" vs throw everything out there "in raw form".
This was my opinion. But anyone arguing to publish "results immediately" is likely to imply something like it. I guess in chemistry we have the situation you envision - for different reasons: Laboratories holding back their data, until their scientists have published their papers or developed their products. There is a real danger AI companies will do something similar too.
Who do you expect they will select for the exposition?
On which basis do you want a (likely US based) AI company to decide who is to untangle a proof that their latest internal model has just spit out?
Do you expect this to fall to an aspiring, but still unknown mathematician at - say - the mathematics department of Nairobi university?! This is what I meant with my rather unclear "elite" reference: The first publication will always show the name of a mathematician already known to the field, more likely than not to come from the same country as the company ("Our message ... is, you’re a great American company, but you’ve got to hire great American workers"). Are you not worried at all? Don't you think it would be good, if anyone in mathematics had a chance to write that first paper on a new proof?
> Mathematics need to redefine their profession and how they work (like us software developers too). There are very good reasons to believe mathematics has an important role to play. If they could just stop talking about OpenAI and get back to work - they are very much needed, in particular now!
The root issue is OpenAI et al.'s thoughtlessness in their engagement with a field.
OpenAI has resources.
That they fail to allocate enough of those to cleaning up pre-print papers (that seem to be a corporate PR priority for them to release) so they can be consumed and engaged with by the field they're targeting is... acting like a jackass?
It's the same "Meta / Alphabet can't vs won't hire more human reviewers" problem.
OpenAI could, at an immaterial salary level to them, pay a ton of PhD students and mathematicians just to clean up their proofs and papers.
Not doing so is a leadership and financial choice.
I'd prefer AI companies don't decide who's "cleaning up pre-print papers". This should remain the job of mathematicians at universities, which I am happy to pay with my taxes. Ideally there was something like a Bermuda Principles declaration for mathematics (https://en.wikipedia.org/wiki/Bermuda_Principles). This gave mathematicians even at poor universities and beyond the chance to participate in mathematical progress.
What do you think is gained, if AI companies manage "cleaning up"? Tax money?
> But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem.
For me the problem is that rigth now the structure of incentives that has been built (e.g. you publish more = you get a grant; good exposition < solving a conjecture) is now broken. So, for instance, you would be very irresponsible if you throw your student into one of those AI papers, it's too much the risk. This part is mathematician's responsability, they need to change this incentives structure.
In any case, OpenAI is being a dickhead here. They throw millions of dollars at these problems, but they can't afford basic literature reviews (the drafts barely cite previous work)? Or checking that Lean's formalizations really correspond to what they claim to prove (even for Navier-Stokes they made this mistake)? It's obvious that for them this is just a PR stunt.
Let us not forget that there's much more to this than just OpenAI being lazy and incompetent and willingly ignoring the high standards that researchers usually holds themselves to.
There's also the case of ethical violations, straight up scientific misconduct, as when OpenAI steals results of others (their customers) and present them as their own.
> The result is also contained in a paper [8] released by OpenAI on October 6, 2026, in which the proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.
Of course it's hard to say what to make of that without knowing what exactly went into the machine, but it certainly looks bad. And there's obviously a non-zero probability that it is indeed another instance of plagiarism, given that that's how they operate.
In this case, the author is a grad student, so what we're looking at is a company willing to steal from a student, ignoring whatever impact that could have on their career prospects, for a tiny piece of marketing material.
At this point I would be surprised if internal sandboxes are not trivially by-passed and that openai's agents do not (at the very least) have complete read access to all user accounts, chat histories and uploaded documents. Orthonogally, openai could still be wholesale lying about not training on this user data, of course.
So... If you use ChatGPT for anything of value, including abstract stuff like obscure maths problems, you should assume that at some point in the future OpenAI will include that in their training set and sell it onto other people.
But this is even worse, because there is no way that OpenAI "trained" on this data between September 8, 2026, the date Chenglong Ma uploaded the paper to ChatGPT; and October 6, 2026, the date that OpenAI released a paper with "identical proof strategy and specific choices of notation" (Ma). That's one month, that's not the timescale for model training.
So this implies _not_ that OpenAI is training on user input, in the conventional sense of adjusting weights; but rather that they are *straight-up channeling ideas from user input*, and with a very short lag. You would think there would be about a million controls to prevent this.
This is next-level alarming. I would be very interested in knowing whether Chenlong activated the privacy (do not train, etc) options in ChatGPT, and any other details of their setup (which plan, etc). Also, note that "do not train" might be, in a lawyerly sense, considered by OpenAI to be strictly about weights, and not covering "we hoover up your results and regurgitate them".
> Part of me would like a little longer in the world where the problem is still open and I am still looking for its solution. But reaching a summit, even by someone else’s route, comes with a view. From here I can see new mountains, and I look forward to climbing them with my students, collaborators and the machines.
I think eventually there will be sort of a centralized more or less automated repository for ingesting and sorting ai-generated lean proofs and making them searchable and re-usable. On some level it kind of doesn't matter if mathematicians can ingest the results, if coding agents can just search for them online and use them in their own proofs.
I actually think it would be very smart for the big AI labs to get together to fund an independent organization to manage such a thing, and hire mathematicians to run it.
What is happening now is that some aspects of mathematics are turning into essentially an exercise in software engineering. It is well known that proofs and computer programs have an isomorphism, and I think the eventual merger is more or less inevitable.
That's not to say that there isn't an infinite amount of work remaining for mathematicians to do. There are only so many problems that are going to be amenable to this approach.
I can't relate to this at all. AI models will surely get better at writing "enjoyable proofs," but for now the situation is what it is. You're passionate about this problem, right? But you don't want to do the work to understand the result? Fine. There's a new generation of younger, hungry mathematicians that are highly interested in figuring out why the result is true and I am sure they'd be happy to wade through it and spoon-feed you the answer instead. Maybe they should be running things.
So OpenAI should be able to flood the world with AI pollution and ask scientists and mathematicians to wade through it all and tell us if there is any sense in it, then sit back and wait for them to report in?
Yes, they should. They have invented a magic button that can tell you the long-awaited answers to the burning mathematical questions that you've spent your life researching. The caveat is that the technology is still new, so the explanations "are not fun to read" like set theory papers usually are (lol). If you don't think that's a worthwhile tradeoff, that's your call, but it sure as hell isn't everyone's.
I don't think the claim is "they definitely have an oracle that solves the problem, and I reject it because it's hard to read". The claim is "OpenAI claims to have used an oracle to solve the problem. The proof is very difficult to read, and to even know if it does or not, we have to go through it with a fine-toothed comb, but they're going around claiming they definitely solved the problem (or at least getting press that claims that which they aren't pushing back against) and this might convince the people who sign grants even if it isn't true"
People who are invested in the idea that we've invented a general intelligence, now, which includes all these companies that are literally financially invested in this claim they are making, will tend to believe that its results can already be trusted in domains like this. Some mathematicians seem to believe some of the proofs written by their models, and some, like this one, don't. I do think it's valid for an expert to push back against the claim that the best use of their time right now is to verify the poorly written work of everyone who's claimed to solve the problem
Over the year, nothing they've released with a lean proof attached has turned out false (That's sort of the entire point. It's not impossible but it's really difficult). There's a reason most mathematicians, including the ones vehemently against OpenAI's dumping are not arguing the results are secretly false or have a high potential to be. And indeed, if that were the case, it would quickly become apparent and all this worry about grant signers would vanish into the wind. It's very easy to ignore nonsense. The problem is that it isn't nonsense.
I really don't know enough about it to know whether you're right or not, nor do I know whether or not you know enough to make the claim you're making, so I won't make an argument one way or another because it's non-sequitur to what I said anyway. The fact that you or I or Sam Altman or Terrence Tao believe the claim is irrelevant to whether this obligates the person who wrote the blog post to believe the claim, and it sounds like he's willing to consider the possibility that it is right, and would read the paper if it reached a threshold of comprehensibility expected of people making that kind of claim.
I's not a non sequitor because it cuts right to the point. He's under no obligation to read it sure, but that doesn't mean Open AI isn't justified in claiming to have proved it. The justification isn't Sam Altman's belief or Tao's or anyone else's authority. Results accompanied with lean-verified proofs whose formal statements match the problem at hand have arguably stronger justification than the vast majority of human math publications.
> Over the year, nothing they've released with a lean proof attached has turned out false
That's not true. [0]
> On July 25, Ramana Kumar published a repository containing a sorry-free "disproof" of the Collatz conjecture, produced with AI assistance. It is not a valid proof because it exploits a bug in the kernel's handling of nested inductive types.
Even in this dump we're talking about, it hasn't been true. [1]
> In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers.
1. That wasn't from Open AI or any major lab. I don't know what random people are getting to. It's curious also that it had no natural language proof attached. Usually these labs have a NL proof then translate to lean. Lot less possibility of lean maxxing.
2. None of the results Open AI retracted had an attached lean proof
The problem isn't just that the papers aren't fun to read. The problem is that a lot of the research that goes into solving these issues leads to other discovers, new fields to explore and people have to develop new approaches to solve them. The other part of it is, the quality and the enjoyment of working on these problems leads people to find new and other interest problems to work on.
If you just strip mine the answers and Sam Altmans magic button solves 100/100 problems, what's next? Who is left to come up with a new interesting question for the magic button to solve?
Lastly, life and the present moment is all there is, if there is no enjoyment in anything we do, then what's the point of all the "living for ever" Altman et al want to achieve.
We will live forever to read boring papers generated by LLMs? Literally sounds like an eternal hell.
Nuclear fusion is already proven by the universe to be a viable energy source by the fact that the sun exists but people still work on understanding and taking it and developing new approaches to accomplish it. People didn't stop experimenting with and developing programming languages because technically they're all turning complete and the first one was "enough." Y'all will be fine - every JavaScript framework that exists is someone looking at a theoretically correct and complete solution and deciding actually it sucks and they could do better. "I want to understand xyz but the proof is trash and I think it's ugly" will be plenty motivation for a lot of people to work on it.
You don't have to wade through the slop. The point is a giant star in the sky figured it out and that doesn't demotivate you from figuring it out yourself
He's tracking the community progress on sub-n log n multiplication. OpenAI started with 1 - 1.63e-55. The result has been now improved on 115 times, and the current record is "rohanarun"'s 1 - 9.87e-5. I'm sure by tomorrow it'll have improved again.
Does this look like people aren't having fun? Does it look like they aren't discovering stuff? It looks like it's spurred a cascade of interesting community activity. It doesn't really seem much different from what happened with the twin primes conjecture. Isn't that supposed to be the point of all this?
People are already finding stuff in the release to get excited about, and as the models get better at distilling proofs to make them more coherent, this will only amplify. Of all the things to worry about, human curiosity and the ability to run with new ideas probably aren't at stake.
In fact, I can't remember a time when I was more excited about the future of science. This could herald an end to the replication crisis, and kill off bullshit science completely. The danger of course is that we end up with two companies effectively dominating cutting edge research in every field, but it remains to be seen if that's even possible given the pace of improvement in open weight models.
I don't understand. Why is this the onus of scientists and PhDs to review whatever results OpenAI had dumped out? If OpenAI had produced incomprehensible papers, surely any journals would just reject it, or demand the author to do a complete rewrite? Unless we are talking about a race to solve problems, which PhDs are afraid that they had been scooped up on?
What else should they do? See these models get smarter and smarter, somewhat-solve things but only to the tune of 90% what mathematicians (or experts in any other field) would deem acceptable, and then gate keep the findings for the next few years going through peer review and paywalled journals? I for one welcome the flood, bring on more in every possible industry and see where all that progress lands up. Sure it will upset a lot. A lot of things also upset the luddites.
Are you going to be doing the work to verify the results ? Will you just expecting other people to wade through the flood and reap the benefits later on?
Nobody is forced to verify the results. I am honestly not expecting anything other than AI to get smarter and smarter and people who are motivated and interested enough to pick up after it; and potentially reap all the long term benefits ahead of those who aren’t (seeing this happening with software development in my own field). But in the end; if you don’t like it, you’re not forced to do anything.
> this is an opportunity for people to pick up where the model left off and run with it
Like people enjoy racing in front of a stopped train? As soon as they turn on the engine again, they will run you over. The questions that remain will be only the low value ones, not worth the effort to vacuum up.
So no, the smarter, hungrier people are not the ones that are going to swoop in. It will be the most desperate.
> Some output is going to be wrong or incomplete
This is a very human take on the situation. No, the Lean proof is not going to be wrong, and it will be incomplete only in the sense that OpenAI didn’t try to push the results further.
They should certainly be allowed to share their findings. No one is forcing scientists and mathematicians to review the findings in general. It’s just the case that the findings are of such such a quality that it would not make sense to ignore them wholesale
> No one is forcing scientists and mathematicians to review the findings in general.
This is like "no one is forcing software engineers to use AI tooling" or "no one is forcing you to show your ID in the airport" or "no one is forcing you to own a car in your small midwestern city" - there can be no law requiring something and the practical consequences of not doing so can be so painful that you're effectively forced anyway.
That is exactly what I’m trying to say. The findings are of such such a quality that it would not make sense to ignore them wholesale.
That’s why it doesn’t make sense to present AI companies as dumping or burdening the scientific community into doing labor for them; the scientific community is self motivated to do so.
It's not self motivated. The motivation is not "this is doing amazing things for us", it's "if we don't review this, the bullshit headline complex and the bullshit-spewing (sorry, marketing) departments of tech giants are going to misinterpret/misrepresent everything and our grant money will be taken away".
You know, I kinda relate to the feeling of not wanting look at those outputs if I think of it from a layman's perspective.
I just imagined that instead of math papers, they released 700+ feature length films, and the only way to tell if one of them is any good is to watch it in its entirety.
That feels pretty unappealing to me.
I know it's the same for human made films, so what's the difference right? But those are good enough most of the time that it's a decent bet, and the people that made them had real skin in the game.
Contrast that with something made by a nondeterministic slop machine with no skin in the game where small details can be off in a way that's jarring. Right out the gate I have an aversion to committing that much time to something that very well may waste it.
That's actually a really interesting thought. Given Sora, and the amount of funding they have, they could have created started their own film festival and dropped 700+ feature length films, had they wanted to go in that direction. But they didn't. Hmm.
The best part is that when the academics fix OAI’s issues, the model gets better and OAI shareholders get richer and more powerful!
As someone who uses LLM tech occasionally, this is why I prefer using open local models. If I’m making myself obsolete, at least I’m not making some asshole richer and their closed model better.
OpenAI in fact didn't know what to do with results and didn't want to flood the world, so they asked mathematicians. Mathematicians recommended OpenAI to release them. My guess is it would have been better for OpenAI if they didn't release them. OpenAI is basically doing this as a goodwill.
People seem to have very misguided ideas about why OpenAI is doing this at all. It is not to brag or to torture mathematicians. It is an eval. OpenAI is known to be willing to pay large amount of money to get a good eval, think FrontierMath. FrontierMath is now saturated, so they need a replacement eval for math. Open math problems are actually a fairly good eval, although a proper eval is better (eg FrontierMath has known difficulty and have tiers from 1 to 4).
Mathematicians would prefer if OpenAI didn't use open math problems as an eval, but OpenAI is not obliged. I actually think OpenAI wouldn't point AI to open math problems if unsaturated FrontierMath Super Duper is available, as it just angers mathematicians, but such eval is not in fact available. Given OpenAI used open math problems as an eval, they could just throw out the result (this is in fact better as an eval since it will keep problems useful longer), but mathematicians preferred to see the result. So OpenAI released them.
As I said, a proper eval is better, but it measures something real that gives a good training signal, and there is lack of good alternatives for math eval. Since the result is 372/4000, it is also unsaturated.
I think this is right - it can be seen as trying to get free feedback from the community. In that way it’s reasonably described as exploitative, since it’s not a good faith effort. The problem of ai slop being submitted to conferences to get publication counts is similar.
"Mathematicians recommended OpenAI to release them."
This is a misleading characterisation of the mathematicians' position.
The very first paragraph of the AGMAI recommendations explicitly states:
"we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models." You appear to have acknowledged this by saying “Mathematicians would prefer if OpenAI didn't use open math problems as an eval…”.
The mathematicians did not ask OpenAI to produce these results. They explicitly asked AI labs to stop producing them in this manner. Their subsequent recommendations concern what labs should do if they have already produced significant results, not an endorsement of the practice.
Furthermore, the recommendation was not simply to release the results, but to responsibly release already existing results. Section 2.B, Step I, explicitly recommends "...labs that have AI mathematical output that is not understood by the people who prompted the AI systems", to search the literature for relevant prior work, provide appropriate attribution, and improve the exposition of AI-generated proofs before releasing them, rather than leaving this work to mathematicians afterwards.
OpenAI published the results on GitHub while still exploring repositories that meet the committee's guidelines. So they followed some of the recommendations, but not all of them and hence, did not release the results as requested by the mathematicians.
I do not think it is a settled matter whether this was done out of goodwill. This is because releasing these results as they were can benefit OpenAI more than releasing them according to the AGMAI recommendations. AGMAI recommended in section 2.B, Step 1.5 that "Each time a solution to a problem is released, it should be clearly documented how exactly AI came to be used on that particular problem. If many results are released at once, then in addition to the results themselves a further document should be written and made public that references all of the released results and explains how many other problems of comparable difficulty the models tried and failed to solve, as well as how the problems were chosen." If the results are released, it is easy to expect that the media will discuss the capabilities of the AI used in the work, as indeed happened. If this AGMAI recommendation was followed, the media would plausibly have also discussed the number of failed attempts and then the overall attitude would not be as favourable to OpenAI as it is now when it comes to the capabilities of the AI that was used. OpenAI did release on GitHub that approximately 4,000 problems were attempted and resulted in 719 manuscripts (after 3 containing suspected errors were removed by OpenAI) across 372 families of problems, but this does not give a calculable number of problems it failed to solve. I do not claim to know OpenAI's intentions or reasoning when these results were released and am not arguing that it was done with improper intentions, only that whether it was done out of goodwill is not a settled matter.
AGMAI's October 6 statement explicitly clarified that its advisory role should not be interpreted as an endorsement of OpenAI's process, and that it was up to the mathematical community to assess how successfully its recommendations had been followed.
Recommending how to responsibly handle the outcomes of something you oppose is not the same as asking for it to happen.
It is also worth adding that the Association for Human Mathematics published a statement (which Tao reposted on his blog) in which they explicitly say the following:
> Mathematicians did not ask for this work to be done. The Advisory Group on Mathematics and Artificial Intelligence, from whom OpenAI has claimed to derive its legitimacy, opened their initial advisory statement by saying that frontier AI corporations should not test advanced mathematical problems on internal models. In ignoring the central premise of the Advisory Group’s position, OpenAI has indicated total disregard for the norms of scientific research — norms that guarantee that mathematics remains trustworthy, ethically researched, and in the public interest.
>> I do not claim to know OpenAI's intentions or reasoning when these results were released and am not arguing that it was done with improper intentions, only that whether it was done out of goodwill is not a settled matter.
That's right honourable of you but for me it is very clear that the only incentive in AI companies' effort to produce mathematical results is to advertise their technology. There is no reason at all to assume they have any other motive; certainly not any kind of interest in mathematics as such.
The problem here is that while you can call what OpenAI does "mathematics", I would hesitate to call it science. Science as a process of acquiring and developing knowledge within a domain involves a lot more than just dumping unfinished work on the scientific community. Among other things, it involves developing frameworks and understanding of the domain, formulating questions, creating results in a fashion suitable for verification/testing/replication, and relating these results to and integrating them with that edifice.
Kinda sounds like computer science vs developing - in the sense that people with a master's in CS and are dedicated to the craft will write wonderfully artistic software, while it doesn't actually take a love for the process to write code and get hired at some tech company (even less so now with agentic development).
Not what I am getting at. In fact, the problem I am getting at is the abolition of existing scientific and engineering principles and processes without a replacement and applies to programming with agents as well. This is not about artistry, but about building durable things.
Have you looked around recently? Because there are plenty of mathematicians that are excited to read and learn about all of the new results. They've improved on the sub-n log n result and have even made a web site to track progress on it: https://beyond-n-log-n.netlify.app/
It looks like people are enjoying themselves, having fun with the new results, and generally doing all of the things you say "science" is supposed to be about. So what's the problem?
I didn't say it is useless. Consider Ramanujan, whose work gave rise to a lot of interesting math, even (and sometimes, especially) the parts that lacked proofs or had other gaps (probably because it was obvious to him unlike us mere mortals). But a singular genius, whether a person or a machine, does not science make.
The question is why the situation is what it is. Did OpenAI publish a large volume of unreadable proofs because that was their best attempt to contribute to the field of mathematics? Or does OpenAI feel that it’s more profitable for them if people come to see mathematics as something that’s less focused on understanding and more focused on using AI to generate proofs?
Yes, I guess it matters a lot whether this was quite close to the best they could do or the best they could do given specific resource constraints or whether they just didn’t bother to try doing better (eg to invest more tokens into readable papers)?
> I guess it matters a lot whether this was quite close to the best they could do
As the author of the post points out, there is no way this is “the best they could do”. It’s a write up that didn’t involve someone with the math + communication skills required to clearly explain the result.
Even with humans, the first publication is rarely the best expression of the lesson. Getting published does more than establish priority; it also frees up the community to build on the result. Nobody expects a human to wait until the proof is comprehensible to anyone except themselves and the referees.
I don’t think that’s true? I never did research math myself, but the people I’ve known who do would definitely invest time in making a proof clearer and better even if they had the idea basically correct. There’ve been multiple recent stories of researchers saying “we’re going to publish this lame proof that isn’t up to our standards because the AI companies let us know they’re going to scoop us if we don’t”.
Mathematicians care a lot about the exposition of their ideas, invest a lot of time in giving talks, writing, and don't publish too frequently, compared to other sciences.
They normally don't feel like they are in some kind of race to publish the results ASAP and claim priority. Cases like that are very rare (but they get media coverage because they are so unusual).
OpenAI did a publicity stunt, their motivation is not to make a good contribution to the field, which has very different standards and culture, compared to the AI labs.
You don't know what you're talking about. Just because it was created by an LLM, and verified in Lean, does not make it true. The whole point of writing a proof is for it to be understandable.
Suppose I directed some llm agents to factor the primes from network logs of your machine. I then publish the private and public key in full. You would not change your keys of course because its not true right?
Knowing a few PhD candidates and non-tenure track postdocs, the “younger, hungry mathematicians” are more worried about finding a damn job in the poorest job market - both academic and in industry - in a decade.
There are plenty of mathematicians who think the results are interesting. Not only do they have the "patience" you speak of, some even seem to be enjoying exploring the new results.
No idea why you're downvoted, my intial thought was that I would like to see some of this supposedly widespread sentiment as well.
I even think it's plausible a lot of mathematicians are excited by it, but the sweeping confidence of the comment you replied to without anything to back it up leaves some to be desired
Checking someone else's work carries a lot of opportunity cost, and is only fruitful if one can learn new methods which apply to the own work. This is pretty risky, especially without tenure!
There's a "Silicon Valley-ism" for you. We offer a thing in whatever form we want and people "who are passionate" will gobble it up, should gobble it up, 'cause they're "passionate".
I think this might feel about the same as getting a PR from Claude that purports to solve some issue that it deems exists, but it doesn’t conform to the contribution guide, isn’t clear in its objectives and looks quite likely to be utter bullshit. I close them without comment and lock the issue.
"AI models will surely get better at writing "enjoyable proofs,"" why? Why is that surely true? they've increased in all other capacities at shocking rates while still writing awful, slippery, turgid prose. Very silly to assume that this will just go away.
Every single day now, for close to 4 years, ever since ChatGPT 3.5 was released - there's been people dismissing AI progress. Every step of the way.
It is entirely possible that one day progress just stops or slows down, but with current evidence, I don't find that too likely - at least not in the near future. The sheer amount of resources being put into this (AI) race is mind-boggling.
So while past performance does not guarantee future results, I'm just going to kick back, and assume that many of the current issues will be fixed with future models.
The progress is clearly not uniform though, it’s shaped by how amenable things are to collecting data and verifying computation. I think writing clear and cogent prose is harder to quantify than formally verifiable logic, and this is why progress in coherent communication has been slower than raw problem solving ability
Maybe this is just a matter of what model developers choose to invest training resources in, but I don’t think it’s inevitable unless clarity is made a higher priority
> There's a new generation of younger, hungry mathematicians that are highly interested in figuring out why the result is true
The problem is that right now mathematicians don't have the economical incentive to read these AI generated results. Even if you love mathematics and all that, it's always more important to get a job, and for that it doesn't seem like a good idea to invest time around problems that AI touches because you can't compete with it and you don't know if tomorrow they'll improve by x10 the sota.
I am a mathematician, and I do have the incentive to read the results. Two results in the drop were two major life goals of mine, and all I got was three lousy citations. :) But a third question I've spent a lot of time on is a not-so-hard consequence of one of the lemmas in there. So, yeah, I do have the incentive.
Of course, it's not clear at this point whether reporting such a result even matters, but still. In its own right, it's a very cool result.
I think quite a few mathematicians would be interested in using AI to figure out the answer.
But providing the answer in gibberish along with a certificate is not that, it's at best a cruel way to do it, but I'm leaning towards the idea that it's a fundamental misunderstanding of what it means to do math and what it means to communicate a result.
If you think sending an answer in gibberish is acceptable just because it's true then SSdtIG5vdCBzdXJlIHdoYXQgdG8gdGVsbCB5b3UsIGJ1dCB3ZSBkaXNhZ3JlZSBvbiB0aGF0.
Very sensible comments. It is along the lines of the fury I get when I am confronted with an 11 page dump of an issue analysis created by an AI agent that makes no sense but I have to go through because customer shared it.
If you did’t bother to write it, I shouldn’t be bothered to read it.
Perhaps AI agents can have their own publications and magazines where they are the chairs and associate editors and reviewers.
Nobody came to him and forced him to read it, just like nobody is forcing you to read code I had chatgpt write.
If AI can solve such grand, outstanding math problems, and mathematicians argue these pure math problems are important, what’s the problem with them needing to read the output if they want to understand it?
I’m not sure OpenAI shouldn’t have released math papers because some guy made a wager about one of the problems that loosely socially obligated him to read material about a solution to that problem.
The absolutely funny thing is, he is obligated precisely because the proof is very likely to be correct.
The alternative you are proposing implicitly is even crazier. OpenAI should not release a proof that is most likely correct so that it doesn’t burden others. What? It’s not about that guy dude. It’s about the society TM. One can’t delay progress because a guy may be burdened.
“Guys plz don’t release this thing that is absolutely correct but I’m kinda busy with other things ok?”
> The alternative you are proposing implicitly is even crazier. OpenAI should not release a proof that is most likely correct so that it doesn’t burden others.
The alternative is that they do the work to properly present the results. They spend billions of dollars in AI training and inference but can't afford to even cite the literature properly? They're doing the bare minimum because they're inly interested in doing a PR stunt.
they will do it. in a year, the same mathematicians will cry about (O)AI making their lives hard by not only solving more problems, but also presenting them with "enjoyable proofs". They'll still cry because the current excuse is a veil.
Bare minimum is still _solving_ the open problem standing there for years. Nobody owns math. Nobody owns giving enjoyable proofs to someone else.
If you don't like to engage with OAI proof dumbs in current state, don't. Maybe others will. Or maybe _these_ mathematicians are afraid that _other_ mathematicians will do it. Just elitism and gate keeping.
> but also presenting them with "enjoyable proofs".
> Or maybe _these_ mathematicians are afraid that _other_ mathematicians will do it. Just elitism and gate keeping.
Ok, I don't see the point of discussing with you. It's clear that you decided what to believe in and no evidence will convince you that reality is more complex. The proof is that you ignored all the nuances expressed here by simply sticking to your simplistic interpretation, without any explanation of why such nuances are invalid.
Whats the nuance here? Your post implied that the problem was unreadable proof and we are saying that this is not central to the discussion. Unreadable proofs are actually very very irrelevant to this whole drama
I think you’re out of touch with the discourse in the mathematical community, it’s quite relevant because clear communication is an important aspect of intelligence
Proofs can be unreadable for more than one reason. Are these ones unreadable because the math is super advanced or because current agents suck at clear writing? Maybe a bit of both?
Fine and we are saying that this is not central to the discussion because even if models wrote it nicely, there'd be even more outrage.
Do you disagree with this? For example, if openai had provided really readable proofs with utmost care but still dropped 400 at once, would there have been less outrage?
> if openai had provided really readable proofs with utmost care but still dropped 400 at once, would there have been less outrage?
Less criticism, yes
There’s always going to be outraged people, but outrage isn’t the word I would choose to describe the positions of the mathematicians I’ve read on this topic, including TFA. There’s a lot of optimism mixed with frustration that something important is missing
Why should it change when there's good chance it's just slop? That's exactly the standard that human mathematicians are held to -- and it's their job to refine and polish the work to make it understandable by the community. And standards have evolved that way because otherwise there's too much slop to wade through (eg. you'd be surprised how many papers the typical theoretical physicist gets claiming to have proven Einstein wrong -- from absolute crackpots who don't understand the basics of the subject). This will just multiply now with AI, and doesn't change just because the prompter happens to be on OpenAI payroll.
We'll see what the final slop rate is, but the three papers they retracted yesterday were for a trivial sign error. If they didn't catch that, that means OpenAI isn't bothered to put in the minimum effort of sifting through their own garbage and making sense of it.
It's not like they needed to hurry out this release before carefully vetting. They're just "hacking" the math system and disrupting the work of thousands of researchers to create a gigantic RL dataset for themselves.
Really, what's the bloody hurry?
They could have released 1-5 papers, worked with researchers to understand what methods work and what don't, how to prompt the models better, how to build better guardrails for reasoning, etc. And give those researchers access to latest models and empower then to solve thousands of problems!
Instead OpenAI wants to piss all over the city to claim territory and now human mathematicians have to go around cleaning up that slop, only so that OpenAI can made some bullshit statement like: math is solved [mistakes are next].
--
Imagine someone gave you a million line PR claiming to have vibecoded the operating system of the future (or whatever your application domain). Would you drop all your other work to focus on this? And they generate enough PR that your manager and company leadership and public all start pressing you to accept it quickly? Guess what, it's your lucky day! You have not one, but 700 breakthrough PRs!
A lot of the comments are claiming that "no one is forcing them to engage with AI proofs" and that's not the case, as explained in the article. The author is forced to engage with the public by the very nature of being a prominent researcher on this problem. The public is drowning him in messages regarding this result. So yes, he is being forced.
Academics have always been required to engage with hacks and cranks to some extent; the deluge of AI proof writing has only exacerbated the problem.
I am not a native speaker but in my experience it is an accurate use of the word “forced”.
English speakers generally use this word in a very broad sense “and now Netflix is forcing ads on paying users”, “because there was no sink, I was forced to drink the whole thing”. It is only when you are literally describing a crime where this word has this strict meaning you are alluding to.
"not at the Lean code, since I know very little of the actual usage of Lean, and that code was enormous"
This part I don't understand. Not that anyone should read the entire Lean code of any proof, but if the statement of the theorem to be proven in lean seems to be correct, then I would think there would be at least some interest if in fact there was a formal proof (which might or might not correspond to the written proof) of something I was working on. That to me would be interesting. Or you are saying you doubt the validity of the formal proof, which would also be interesting. But saying it is of no consequence doesn't make any sense to me.
I think TFA’s point is that it’s interesting - it’s just not feasible to do what follows after “it’s interesting”, which is to try to make heads or tails of the stack of writing that we’ve been given. Engaging with a well-written proof of a similar scope is enough of a task already.
Some of the lean proofs are apparently incomprehensible.
It would be like trying to look at a completed video game's assembly code, being told that it was call of duty, and then being asked questions about the high level code architecture.
AI models are perhaps unsurprisingly good at low level translation (see the progress being made for decomp games)
These models have surpassed human capabilities at math/machine code, but they can't "simplify" yet - in part because they don't have the same need to due to their comparative lack of cognitive constraints. AI Slop code is getting better, but it takes time. At the moment, its embarrassing frankly. It will come eventually, but right now OpenAI is not handling this with the care, respect, or concern that it deserves.
Have you ever wrote some code/algo that seemed "simple/obvious" to you yet to someone else, it seemed incomprehensible?
If you have a 20-40 IQ points gap with another developer, this happens a lot.
The baseline of "simplify" is wildly different based on your IQ points. That's precisely why exceptional students are usually bad in teaching. They try to break things down, simplify, but things still go over the head of normies.
However, we can intervene/train the models. So it should be possible to focus on the simplification, and as you said, it will come eventually.
I've been mostly reading here but created an account to disagree with this statement: The smartest people I know were always amazing at explaining. This was true for me as undergrad and graduate student where the smartest peers and the most renowned professor were always also the best at explaining, and it is true now at research level in a related field.
When I am not sure if I really understood something to the core, I try to find a colleague who knows very little about it; if they understand my explanation well, that's a good sign.
Those who really understand a topic are usually also able (and great at) explaining it in very clear and "simple" terms. This may be part of my personal bias; I see theory builders as those who advance the field the most, and these are usually also amazing at explaining it. On the other hand, those who mostly "grind" through problems (approach them as complicated puzzles) with effort/time were often bad at explaining.
I observed the same for programming: the "architects" usually explain very well, the "debuggers" often don't.
LLMs very much remind of the grind/puzzle approach. It does makes sense that RLVR, which in my understanding enables a lot of these results, would lead to a more mechanical approach.
Of course, I can't make any predictions on whether it will stay that way. But I strongly suspect that we need different ways of training for LLMs to write better text and explain better (I suspect the vagueness of LLM language is the result of RLHF as vague expression is less often incorrect).
I agree, and I disagree. There are plenty of published mathematical papers that are just as poorly written as OpenAI's. Nobody says nothing because the authors are big names. In some cases, the proofs are not even correct, but everybody has a feeling the result are true nonetheless, so they pretend not to see it.
So I agree that OpenAI should have done a better job of writing down the results, probably by paying working mathematicians like Anthropic did.
But I disagree that this low-quality writing is somehow a good reason to be angry at OpenAI specifically, otherwise you would have to be angry at a lot of people.
> There are plenty of published mathematical papers that are just as poorly written as OpenAI's. Nobody says nothing because the authors are big names.
Can you provide some evidence of this claim? "Nobody says nothing" probably works on reddit but I generally expect higher quality discourse on hackernews.
I am a working mathematician. A problem that I cared about greatly (and probably spent > 3000 hours working on) was on their list. I looked at the paper, and I have to say it is more clearly written than about 30% of the papers I typically referee. I don't want to name poorly written papers, but I agree that "there are plenty of published papers that are just as poorly written as OpenAI's".
And which papers do you typically referee? Without that information this claim is meaningless. For example, if you referee free-for-all papers that today are likely written by LLMs as well then sure I can understand that. But if you referee papers from grad students then that's more concerning.
I have only twice (knowingly) refereed AI slop. I'm mostly talking about refereeing in the period 2010 - 2020. (However, looking here https://proofsandprompts.com/2026/10/08/100-reactions-to-100... it seems that many other consider many of the papers poorly written. I just wanted to give one datapoint.)
The response by some in the field of mathematics to this repo is ... I guess not unexpected; but it's quite disappointing.
I sympathize with those who've worked on some problem for years and now don't have something to work on; it's been a part of their identity. I also especially sympathize with those whose career tracks and plans were thrown in disarray.
That being said, I absolutely cannot understand how one can't be excited and happy and enthused about these advances in one's field. Assuming just that the ones with formal lean proofs are actually true, these are reportedly huge advances. Even if folks don't understand it YET.
I'm just amazed at how quickly we moved from "AI is just a parrot and can't do anything useful" to "AI can solve toy problems but not anything of value" to "when AI pushes the state of the art, it can't quite get the proper citations in its preprints".
Maybe the reason the AI could find this proof is exactly what the author is complaining about: that it left the beaten path of theorems expected in a paper like this and went off in an unexpected direction.
239 comments
Yes, the situation sucks overall and mathematics as a whole is in a turbulent time now.
But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem. #2 above is still true regardless of where it came from or how hard it can be to absorb.
While reading "The Mathocalypse" post [0] by Scott Aaronson, Scott described his wife Dana's reaction to one of the newly solved results in her primary domain of expertise, on which she'd been working for decades.
After her initial shock, and annoyance with the format/style, she decided to start using Astra - for the first time - to help her understand the new result. And he reported in the comments that she had made a lot of progress understanding it in one day, and may be even excited to give a talk about it!
That seems like a much healthier attitude towards these new results.
Yes, everything else sucks about this messy period. But there are still diamonds (in the rough) in this drop that perhaps should be looked into. If the author is too busy, perhaps one of their students can take a look? Someone will, eventually.
[0] https://scottaaronson.blog/?p=10169
If some mathematicians complain about OpenAI sucking, that is fine actually, and if others are more “mature” about it, that that is fine too. Neither of these reactions should be at put as an equivalence to the blame OpenAI deserves for this stunt.
You might argue that these aspects of math are less important in the new AI accelerated math world, because agents will inevitably be smarter than humans, but I think clear framing and communication is even more important than before because with this technology we can choose to augment our intelligence instead of defer it
I don't believe this myself. But I do believe that if you've formed your very ideas about what is good and desirable on the basis of a culture that has held certain values dear for hundreds of years, and have fought against every doubt and difficulty in life for decades to mold yourself into that image, that it does not 'suck' that you are unable to adapt to a new reality overnight.
Very few people that would love to be craftsmen would love to be factory foremen. It is far too insensitive to the human experience to expect people to just deal.
Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.
Some people told themselves they were the pinnacle, the first-rate mind, as opposed to all the second-rater. Well guess what, now your first-rate mind is a commodity and exposition is more valuable. They'd better learn to live with it.
Thankfully, very few mathematicians share Hardy's opinion, just as very few share his opinion that "mathematics is a young man's game" (and indeed we now have prizes like the Abel Prize with no age limit).
In fact, many of the greatest mathematicians throughout history have taken exposition very seriously, e.g. Euclid, Euler, Lagrange, Cauchy, Dirichlet, Kolmogorov etc. all wrote textbooks. Many mathematicians today carry on that tradition of taking exposition seriously and write books and freely share their lecture notes.
So we should not take Hardy's opinion as representing the opinion of all mathematicians or even most mathematicians. In fact, Hardy's statement is somewhat self-contradictory since he himself wrote several expository books (e.g. "A Course of Pure Mathematics").
Wait, who are those people? Who is that Hardy and what did he really say? What did he really mean? Who else said or meant the same things?
Who are you criticising, exactly?
It might be a shock for you but they are very few in numbers. Most of researchers I know are always busy with something. They cannot just drop other responsibilities for something like this. They will take their own time getting through the proofs (if they want to).
> That seems like a much healthier attitude towards these new results.
Another thing to consider is not all mathematicians are from US or with good funding. The PI or graduate students cannot afford to pay 200/month.
TFA was about a niche topic that OpenAI doesn't have in-house expertise in.
Otoh Aaronson is the co-author on Lijie Chen's (reasoning lead at OAI) top cited paper. OAI have deployed their resources more effectively against UGC that some of their staff are already familiar with
https://scholar.google.com/citations?user=T_OhvOsAAAAJ
https://finance.biggo.com/news/B0eMxZsBy4YEFZDUVPWh
I wish they take a bit of more time to communicate the findings effectively.
There are good reasons not to delay publishing at all:
> They should release all their results immediately. (Imagine working on one of the problems they already solved.)
This is the most popular answer to a question regarding AI advisory group and immediate access on a popular website for professional mathematicians: https://mathoverflow.net/a/515442/473286
The whole debate regarding the behaviour of OpenAI is a red herring. Mathematics need to redefine their profession and how they work (like us software developers too). There are very good reasons to believe mathematics has an important role to play. If they could just stop talking about OpenAI and get back to work - they are very much needed, in particular now!
This kind of phrasing sounds particularly empty. We are not in WWII researching the nuclear bomb. What are they so urgently needed for to drop everything and work on understanding openai's proof on partition principle and axiom of choice?
Says who? The professional mathematician writing the article disagreed. Why should people start dancing the tune that openai wants to play for their own reasons and interests? And I do not see how taking the time and effort to write a proper exposition makes it "a very elitist science" when this exact effort and time is needed to actually get other experts understand and build on a result. Unless you equate spending time and effort learning math as "elitism", which is the ai-shilling moto some time now with everything time and effort related. I cannot see how spending time and effort to understand a field and then spend time and effort to make a proper exposition so that other people can also understand it as "elitist" vs throw everything out there "in raw form".
This was my opinion. But anyone arguing to publish "results immediately" is likely to imply something like it. I guess in chemistry we have the situation you envision - for different reasons: Laboratories holding back their data, until their scientists have published their papers or developed their products. There is a real danger AI companies will do something similar too.
Who do you expect they will select for the exposition?
On which basis do you want a (likely US based) AI company to decide who is to untangle a proof that their latest internal model has just spit out?
Do you expect this to fall to an aspiring, but still unknown mathematician at - say - the mathematics department of Nairobi university?! This is what I meant with my rather unclear "elite" reference: The first publication will always show the name of a mathematician already known to the field, more likely than not to come from the same country as the company ("Our message ... is, you’re a great American company, but you’ve got to hire great American workers"). Are you not worried at all? Don't you think it would be good, if anyone in mathematics had a chance to write that first paper on a new proof?
The root issue is OpenAI et al.'s thoughtlessness in their engagement with a field.
OpenAI has resources.
That they fail to allocate enough of those to cleaning up pre-print papers (that seem to be a corporate PR priority for them to release) so they can be consumed and engaged with by the field they're targeting is... acting like a jackass?
It's the same "Meta / Alphabet can't vs won't hire more human reviewers" problem.
OpenAI could, at an immaterial salary level to them, pay a ton of PhD students and mathematicians just to clean up their proofs and papers.
Not doing so is a leadership and financial choice.
What do you think is gained, if AI companies manage "cleaning up"? Tax money?
For me the problem is that rigth now the structure of incentives that has been built (e.g. you publish more = you get a grant; good exposition < solving a conjecture) is now broken. So, for instance, you would be very irresponsible if you throw your student into one of those AI papers, it's too much the risk. This part is mathematician's responsability, they need to change this incentives structure.
In any case, OpenAI is being a dickhead here. They throw millions of dollars at these problems, but they can't afford basic literature reviews (the drafts barely cite previous work)? Or checking that Lean's formalizations really correspond to what they claim to prove (even for Navier-Stokes they made this mistake)? It's obvious that for them this is just a PR stunt.
There's also the case of ethical violations, straight up scientific misconduct, as when OpenAI steals results of others (their customers) and present them as their own.
One particularly bad one came yesterday: https://arxiv.org/abs/2610.10072
> The result is also contained in a paper [8] released by OpenAI on October 6, 2026, in which the proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.
Of course it's hard to say what to make of that without knowing what exactly went into the machine, but it certainly looks bad. And there's obviously a non-zero probability that it is indeed another instance of plagiarism, given that that's how they operate.
In this case, the author is a grad student, so what we're looking at is a company willing to steal from a student, ignoring whatever impact that could have on their career prospects, for a tiny piece of marketing material.
But this is even worse, because there is no way that OpenAI "trained" on this data between September 8, 2026, the date Chenglong Ma uploaded the paper to ChatGPT; and October 6, 2026, the date that OpenAI released a paper with "identical proof strategy and specific choices of notation" (Ma). That's one month, that's not the timescale for model training.
So this implies _not_ that OpenAI is training on user input, in the conventional sense of adjusting weights; but rather that they are *straight-up channeling ideas from user input*, and with a very short lag. You would think there would be about a million controls to prevent this.
This is next-level alarming. I would be very interested in knowing whether Chenlong activated the privacy (do not train, etc) options in ChatGPT, and any other details of their setup (which plan, etc). Also, note that "do not train" might be, in a lawyerly sense, considered by OpenAI to be strictly about weights, and not covering "we hoover up your results and regurgitate them".
No it doesn't. Hundreds of open problems in a STEM field getting solved at once does not suck at all.
You would have to be deeply jaded and cynical to conclude that.
https://dakshitakhurana.substack.com/p/classical-at-heart
I actually think it would be very smart for the big AI labs to get together to fund an independent organization to manage such a thing, and hire mathematicians to run it.
What is happening now is that some aspects of mathematics are turning into essentially an exercise in software engineering. It is well known that proofs and computer programs have an isomorphism, and I think the eventual merger is more or less inevitable.
That's not to say that there isn't an infinite amount of work remaining for mathematicians to do. There are only so many problems that are going to be amenable to this approach.
Nice idea.
People who are invested in the idea that we've invented a general intelligence, now, which includes all these companies that are literally financially invested in this claim they are making, will tend to believe that its results can already be trusted in domains like this. Some mathematicians seem to believe some of the proofs written by their models, and some, like this one, don't. I do think it's valid for an expert to push back against the claim that the best use of their time right now is to verify the poorly written work of everyone who's claimed to solve the problem
That's not true. [0]
> On July 25, Ramana Kumar published a repository containing a sorry-free "disproof" of the Collatz conjecture, produced with AI assistance. It is not a valid proof because it exploits a bug in the kernel's handling of nested inductive types.
Even in this dump we're talking about, it hasn't been true. [1]
> In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers.
[0] https://leodemoura.github.io/blog/2026-8-24-postmortem-for-t...
[1] https://github.com/openai/math/blob/main/history.md
2. None of the results Open AI retracted had an attached lean proof
If you just strip mine the answers and Sam Altmans magic button solves 100/100 problems, what's next? Who is left to come up with a new interesting question for the magic button to solve?
Lastly, life and the present moment is all there is, if there is no enjoyment in anything we do, then what's the point of all the "living for ever" Altman et al want to achieve.
We will live forever to read boring papers generated by LLMs? Literally sounds like an eternal hell.
He's tracking the community progress on sub-n log n multiplication. OpenAI started with 1 - 1.63e-55. The result has been now improved on 115 times, and the current record is "rohanarun"'s 1 - 9.87e-5. I'm sure by tomorrow it'll have improved again.
Does this look like people aren't having fun? Does it look like they aren't discovering stuff? It looks like it's spurred a cascade of interesting community activity. It doesn't really seem much different from what happened with the twin primes conjecture. Isn't that supposed to be the point of all this?
In fact, I can't remember a time when I was more excited about the future of science. This could herald an end to the replication crisis, and kill off bullshit science completely. The danger of course is that we end up with two companies effectively dominating cutting edge research in every field, but it remains to be seen if that's even possible given the pace of improvement in open weight models.
However, there are always smarter, hungrier people out there and this is a buffet.
Some output is going to be wrong or incomplete. I am willing to bet even those have nuggets that can be used elsewhere.
Like people enjoy racing in front of a stopped train? As soon as they turn on the engine again, they will run you over. The questions that remain will be only the low value ones, not worth the effort to vacuum up.
So no, the smarter, hungrier people are not the ones that are going to swoop in. It will be the most desperate.
> Some output is going to be wrong or incomplete
This is a very human take on the situation. No, the Lean proof is not going to be wrong, and it will be incomplete only in the sense that OpenAI didn’t try to push the results further.
This is like "no one is forcing software engineers to use AI tooling" or "no one is forcing you to show your ID in the airport" or "no one is forcing you to own a car in your small midwestern city" - there can be no law requiring something and the practical consequences of not doing so can be so painful that you're effectively forced anyway.
That’s why it doesn’t make sense to present AI companies as dumping or burdening the scientific community into doing labor for them; the scientific community is self motivated to do so.
I just imagined that instead of math papers, they released 700+ feature length films, and the only way to tell if one of them is any good is to watch it in its entirety.
That feels pretty unappealing to me.
I know it's the same for human made films, so what's the difference right? But those are good enough most of the time that it's a decent bet, and the people that made them had real skin in the game.
Contrast that with something made by a nondeterministic slop machine with no skin in the game where small details can be off in a way that's jarring. Right out the gate I have an aversion to committing that much time to something that very well may waste it.
As someone who uses LLM tech occasionally, this is why I prefer using open local models. If I’m making myself obsolete, at least I’m not making some asshole richer and their closed model better.
(See https://agmai.org/general-sep29/ for the recommendation in question.)
People seem to have very misguided ideas about why OpenAI is doing this at all. It is not to brag or to torture mathematicians. It is an eval. OpenAI is known to be willing to pay large amount of money to get a good eval, think FrontierMath. FrontierMath is now saturated, so they need a replacement eval for math. Open math problems are actually a fairly good eval, although a proper eval is better (eg FrontierMath has known difficulty and have tiers from 1 to 4).
Mathematicians would prefer if OpenAI didn't use open math problems as an eval, but OpenAI is not obliged. I actually think OpenAI wouldn't point AI to open math problems if unsaturated FrontierMath Super Duper is available, as it just angers mathematicians, but such eval is not in fact available. Given OpenAI used open math problems as an eval, they could just throw out the result (this is in fact better as an eval since it will keep problems useful longer), but mathematicians preferred to see the result. So OpenAI released them.
> supported by a clear plurality of respondents
was referring to?
This is a misleading characterisation of the mathematicians' position.
The very first paragraph of the AGMAI recommendations explicitly states:
"we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models." You appear to have acknowledged this by saying “Mathematicians would prefer if OpenAI didn't use open math problems as an eval…”.
The mathematicians did not ask OpenAI to produce these results. They explicitly asked AI labs to stop producing them in this manner. Their subsequent recommendations concern what labs should do if they have already produced significant results, not an endorsement of the practice.
Furthermore, the recommendation was not simply to release the results, but to responsibly release already existing results. Section 2.B, Step I, explicitly recommends "...labs that have AI mathematical output that is not understood by the people who prompted the AI systems", to search the literature for relevant prior work, provide appropriate attribution, and improve the exposition of AI-generated proofs before releasing them, rather than leaving this work to mathematicians afterwards.
OpenAI published the results on GitHub while still exploring repositories that meet the committee's guidelines. So they followed some of the recommendations, but not all of them and hence, did not release the results as requested by the mathematicians.
I do not think it is a settled matter whether this was done out of goodwill. This is because releasing these results as they were can benefit OpenAI more than releasing them according to the AGMAI recommendations. AGMAI recommended in section 2.B, Step 1.5 that "Each time a solution to a problem is released, it should be clearly documented how exactly AI came to be used on that particular problem. If many results are released at once, then in addition to the results themselves a further document should be written and made public that references all of the released results and explains how many other problems of comparable difficulty the models tried and failed to solve, as well as how the problems were chosen." If the results are released, it is easy to expect that the media will discuss the capabilities of the AI used in the work, as indeed happened. If this AGMAI recommendation was followed, the media would plausibly have also discussed the number of failed attempts and then the overall attitude would not be as favourable to OpenAI as it is now when it comes to the capabilities of the AI that was used. OpenAI did release on GitHub that approximately 4,000 problems were attempted and resulted in 719 manuscripts (after 3 containing suspected errors were removed by OpenAI) across 372 families of problems, but this does not give a calculable number of problems it failed to solve. I do not claim to know OpenAI's intentions or reasoning when these results were released and am not arguing that it was done with improper intentions, only that whether it was done out of goodwill is not a settled matter.
AGMAI's October 6 statement explicitly clarified that its advisory role should not be interpreted as an endorsement of OpenAI's process, and that it was up to the mathematical community to assess how successfully its recommendations had been followed.
Recommending how to responsibly handle the outcomes of something you oppose is not the same as asking for it to happen.
> Mathematicians did not ask for this work to be done. The Advisory Group on Mathematics and Artificial Intelligence, from whom OpenAI has claimed to derive its legitimacy, opened their initial advisory statement by saying that frontier AI corporations should not test advanced mathematical problems on internal models. In ignoring the central premise of the Advisory Group’s position, OpenAI has indicated total disregard for the norms of scientific research — norms that guarantee that mathematics remains trustworthy, ethically researched, and in the public interest.
https://www.ahmath.org/
That's right honourable of you but for me it is very clear that the only incentive in AI companies' effort to produce mathematical results is to advertise their technology. There is no reason at all to assume they have any other motive; certainly not any kind of interest in mathematics as such.
It looks like people are enjoying themselves, having fun with the new results, and generally doing all of the things you say "science" is supposed to be about. So what's the problem?
https://www.youtube.com/watch?v=LKiBlGDfRU8 https://www.youtube.com/watch?v=shFUDPqVmTg
As the author of the post points out, there is no way this is “the best they could do”. It’s a write up that didn’t involve someone with the math + communication skills required to clearly explain the result.
They normally don't feel like they are in some kind of race to publish the results ASAP and claim priority. Cases like that are very rare (but they get media coverage because they are so unusual).
OpenAI did a publicity stunt, their motivation is not to make a good contribution to the field, which has very different standards and culture, compared to the AI labs.
They don’t have any more patience for this.
I even think it's plausible a lot of mathematicians are excited by it, but the sweeping confidence of the comment you replied to without anything to back it up leaves some to be desired
There's a "Silicon Valley-ism" for you. We offer a thing in whatever form we want and people "who are passionate" will gobble it up, should gobble it up, 'cause they're "passionate".
It is entirely possible that one day progress just stops or slows down, but with current evidence, I don't find that too likely - at least not in the near future. The sheer amount of resources being put into this (AI) race is mind-boggling.
So while past performance does not guarantee future results, I'm just going to kick back, and assume that many of the current issues will be fixed with future models.
Maybe this is just a matter of what model developers choose to invest training resources in, but I don’t think it’s inevitable unless clarity is made a higher priority
The problem is that right now mathematicians don't have the economical incentive to read these AI generated results. Even if you love mathematics and all that, it's always more important to get a job, and for that it doesn't seem like a good idea to invest time around problems that AI touches because you can't compete with it and you don't know if tomorrow they'll improve by x10 the sota.
Of course, it's not clear at this point whether reporting such a result even matters, but still. In its own right, it's a very cool result.
What do you do if those results suck like in the article?
But providing the answer in gibberish along with a certificate is not that, it's at best a cruel way to do it, but I'm leaning towards the idea that it's a fundamental misunderstanding of what it means to do math and what it means to communicate a result.
If you think sending an answer in gibberish is acceptable just because it's true then SSdtIG5vdCBzdXJlIHdoYXQgdG8gdGVsbCB5b3UsIGJ1dCB3ZSBkaXNhZ3JlZSBvbiB0aGF0.
If you did’t bother to write it, I shouldn’t be bothered to read it.
Perhaps AI agents can have their own publications and magazines where they are the chairs and associate editors and reviewers.
If AI can solve such grand, outstanding math problems, and mathematicians argue these pure math problems are important, what’s the problem with them needing to read the output if they want to understand it?
The alternative you are proposing implicitly is even crazier. OpenAI should not release a proof that is most likely correct so that it doesn’t burden others. What? It’s not about that guy dude. It’s about the society TM. One can’t delay progress because a guy may be burdened.
“Guys plz don’t release this thing that is absolutely correct but I’m kinda busy with other things ok?”
The alternative is that they do the work to properly present the results. They spend billions of dollars in AI training and inference but can't afford to even cite the literature properly? They're doing the bare minimum because they're inly interested in doing a PR stunt.
Bare minimum is still _solving_ the open problem standing there for years. Nobody owns math. Nobody owns giving enjoyable proofs to someone else.
If you don't like to engage with OAI proof dumbs in current state, don't. Maybe others will. Or maybe _these_ mathematicians are afraid that _other_ mathematicians will do it. Just elitism and gate keeping.
Ok, I don't see the point of discussing with you. It's clear that you decided what to believe in and no evidence will convince you that reality is more complex. The proof is that you ignored all the nuances expressed here by simply sticking to your simplistic interpretation, without any explanation of why such nuances are invalid.
Proofs can be unreadable for more than one reason. Are these ones unreadable because the math is super advanced or because current agents suck at clear writing? Maybe a bit of both?
Do you disagree with this? For example, if openai had provided really readable proofs with utmost care but still dropped 400 at once, would there have been less outrage?
Less criticism, yes
There’s always going to be outraged people, but outrage isn’t the word I would choose to describe the positions of the mathematicians I’ve read on this topic, including TFA. There’s a lot of optimism mixed with frustration that something important is missing
You don't think this changes when the thing in question is a proof of a STEM problem no human has ever been able to solve?
We'll see what the final slop rate is, but the three papers they retracted yesterday were for a trivial sign error. If they didn't catch that, that means OpenAI isn't bothered to put in the minimum effort of sifting through their own garbage and making sense of it.
It's not like they needed to hurry out this release before carefully vetting. They're just "hacking" the math system and disrupting the work of thousands of researchers to create a gigantic RL dataset for themselves.
Really, what's the bloody hurry?
They could have released 1-5 papers, worked with researchers to understand what methods work and what don't, how to prompt the models better, how to build better guardrails for reasoning, etc. And give those researchers access to latest models and empower then to solve thousands of problems!
Instead OpenAI wants to piss all over the city to claim territory and now human mathematicians have to go around cleaning up that slop, only so that OpenAI can made some bullshit statement like: math is solved [mistakes are next].
--
Imagine someone gave you a million line PR claiming to have vibecoded the operating system of the future (or whatever your application domain). Would you drop all your other work to focus on this? And they generate enough PR that your manager and company leadership and public all start pressing you to accept it quickly? Guess what, it's your lucky day! You have not one, but 700 breakthrough PRs!
Academics have always been required to engage with hacks and cranks to some extent; the deluge of AI proof writing has only exacerbated the problem.
English speakers generally use this word in a very broad sense “and now Netflix is forcing ads on paying users”, “because there was no sink, I was forced to drink the whole thing”. It is only when you are literally describing a crime where this word has this strict meaning you are alluding to.
> forced; forcing
> transitive verb
> 1 :to compel by physical, moral, or intellectual means
> A player was forced out of bounds; They forced the CEO to resign; I forced myself to finish.
This part I don't understand. Not that anyone should read the entire Lean code of any proof, but if the statement of the theorem to be proven in lean seems to be correct, then I would think there would be at least some interest if in fact there was a formal proof (which might or might not correspond to the written proof) of something I was working on. That to me would be interesting. Or you are saying you doubt the validity of the formal proof, which would also be interesting. But saying it is of no consequence doesn't make any sense to me.
It would be like trying to look at a completed video game's assembly code, being told that it was call of duty, and then being asked questions about the high level code architecture.
AI models are perhaps unsurprisingly good at low level translation (see the progress being made for decomp games)
These models have surpassed human capabilities at math/machine code, but they can't "simplify" yet - in part because they don't have the same need to due to their comparative lack of cognitive constraints. AI Slop code is getting better, but it takes time. At the moment, its embarrassing frankly. It will come eventually, but right now OpenAI is not handling this with the care, respect, or concern that it deserves.
If you have a 20-40 IQ points gap with another developer, this happens a lot.
The baseline of "simplify" is wildly different based on your IQ points. That's precisely why exceptional students are usually bad in teaching. They try to break things down, simplify, but things still go over the head of normies.
However, we can intervene/train the models. So it should be possible to focus on the simplification, and as you said, it will come eventually.
Those who really understand a topic are usually also able (and great at) explaining it in very clear and "simple" terms. This may be part of my personal bias; I see theory builders as those who advance the field the most, and these are usually also amazing at explaining it. On the other hand, those who mostly "grind" through problems (approach them as complicated puzzles) with effort/time were often bad at explaining.
I observed the same for programming: the "architects" usually explain very well, the "debuggers" often don't. LLMs very much remind of the grind/puzzle approach. It does makes sense that RLVR, which in my understanding enables a lot of these results, would lead to a more mechanical approach.
Of course, I can't make any predictions on whether it will stay that way. But I strongly suspect that we need different ways of training for LLMs to write better text and explain better (I suspect the vagueness of LLM language is the result of RLHF as vague expression is less often incorrect).
Please don't tell me how I should feel. Stick with the facts.
Can you provide some evidence of this claim? "Nobody says nothing" probably works on reddit but I generally expect higher quality discourse on hackernews.
Were you satisfied with the paper?
Having read the paper, do you understand "what you missed" in those 3000 hours?
I sympathize with those who've worked on some problem for years and now don't have something to work on; it's been a part of their identity. I also especially sympathize with those whose career tracks and plans were thrown in disarray.
That being said, I absolutely cannot understand how one can't be excited and happy and enthused about these advances in one's field. Assuming just that the ones with formal lean proofs are actually true, these are reportedly huge advances. Even if folks don't understand it YET.