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.
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.
> 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!
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.
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.
> 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").
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.
> 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.
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.
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.
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.
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 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
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.
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.
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.
"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.
> 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.
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?
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.
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.
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?
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.
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.
> 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.
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.
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?
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.
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.
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?
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".
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.
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.
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.
> 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.
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.
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.
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?
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".
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?
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.
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.
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.
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.)
"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.
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.
At first I thought this was going to be more Luddite babble, but it makes a good point. OpenAI isn't contributing if they are make unreadable papers. They should use a little more of their compute to nail interpretability. The difficulty will only get worse as AI plow deeper into the frontier and produce increasingly alien looking output. I suspect it's a workflow issue. If not, it's a bad oversight if the current generation of models are capable of making mathematical breakthroughs but can't explain how they build on existing frameworks.
Work this abstract almost certainly has no value outside the community that is (was) interested in the result. OpenAI should engage with the community to realize the value (beyond PR).
Is it just me or is this line of thinking fundamentally dishonest? It may be true that the papers are hard to read but the papers have extremely high signal towards the proof.
All of these comments seem to suggest that if papers are not 100% abiding by readable books their standards, they are basically the same as literal noise. This is highly dishonest.
I’m just a dude and even I’m able to understand the paper after using ChatGPT to help me through it.
There's certainly a conceit in saying if the math is not accessible to my community then it doesn't even count as math, and the last few days this has been a common ideological talking point.
Mathematicians struggle with the same problem as software engineers; you can let AI generate the artifact, but to understand fully what is going on is challenging. Perhaps even more for mathematicians.
Do you rely on the tests/Lean to accept correctness or not…
If there is a formal proof, and it is the proof of your precise statement (which I imagine is easy to check, otherwise I think that mathematicians would not accept the Navier Stokes result so quickly), then there is no way to ignore the result, however badly it is written.
This was always the essence of mathematics, and it must stay this way.
As much as I personally despise altmans, "darios", and their bootlickers, this is one aspect which is undoubtedly "good for the mathematical community" as a whole.
The fact that the validity of your statement does not depend any more on an expert opinion of some person with grants, but as it always should have had been, just on the validity of the chain of deductions.
> not at the Lean code, since I know very little of the actual usage of Lean, and that code was enormous
Dismissing results on the basis that Lean code is too long disqualifies this opinion. It is not hard at all to read the Lean result statement, even with very superficial Lean knowledge.
Here’s an idea I would love to see play out. Have one of the labs train a new model, using cutting edge architecture, on a whole lot of data and math papers from before 1905. Then see if it can come up with, or even understand, Einsteins theory of relativity.
Special relativity is one of those unusual theories that requires very little in the way of math or concepts to understand. You take the data from the 1887 Michelson-Morley experiment (which measures the same speed of light, despite different reference frames). You take the idea that the laws of physics work in any reference frame. You take some high-school math, et voilà, special relativity.
Except that the proofs are very likely valid. This is a country of Ramanujans in a data center. You're free to ignore them because they don't follow your style guide, the rest of us will enjoy seeing humans and AIs build on the results.
> the rest of us will enjoy seeing humans and AIs build on the results.
That would be nice, but the rest of the world wasn't interested in the results before and they won't be interested after.
I wonder what this means long term. Maybe mathematicians will keep plodding on as usual except sporadically when an AI company need a marketing boost so they spend millions of dollars to dunk on them. Because the mathematicians sure don't have that kind of money.
There is no nice way to tell someone that you’ve scooped them, and this is industrial scale scooping.
A few papers have been retracted, but it looks like many are withstanding intense scrutiny. Lean is making the results more likely to be correct, but I think making them harder to understand.
The world has changed and you’ll know a math department is making a serious attempt to adapt when it teaches a required Lean course in freshman year.
Why do you believe that learning Lean is a better use of time when the AI is clearly better at writing and interpreting Lean than it is writing quality papers? At this point, Lean is for autoformalization, no one is really supposed to read it.
That's fair, but I would argue that reading the specification is very easy by comparison. A quick one hour tutorial is usually enough judging from my students' experiences.
>OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why?
...
>So, no, I will not be sending Sam Altman a bottle of whisky anytime soon, nor I am planning on spending my time reading through that paper and trying to make sense of it.
Think about a hypothetical circumstance where we get radio communication with some aliens on another planet. They send over tons of math to help us advance our tech, we know the math they're sending us is correct, but their explanations are really hard to work through because they aren't humans and the math is so different from anything we've done. Should we whine about the results they sent to us and refuse to engage with it?
Love your metaphor here. I guess there will always be people who try to keep going and follow their current projects and say that only human math is real math and we should only use alien technology for proofreading mails and such but not their highly established and esteemed professions.
Or just keep your hubris low, update your priors, work towards progress.
In this hypothetical case funding agencies would probably happily pay for “alien maths translation grants” and you could write papers about advances in that field and get jobs etc. So arguably for better or worse it would create a specialised academic cottage industry that somehow interfaces with the rest of maths.
openai will take expert responses like this and improve the next set of papers
it won't be long before there's no more low hanging fruit like this to complain about, and the writing / explanations of the results are superhuman as well
separately, i really liked the author's denial-of-service analogy. super useful practical framing
> This is why I generally avoid using AI for mathematics (I am happy to ask LLMs to consolidate information for me, or to generate a useful infographic, or to proof read an email, etc.)
In other words, the author is OK with using LLMs to replace data analysts (that could consolidate information), to replace graphic designers (that could generate infographics), and to replace editors (that could proofread an email). But don't you dare use LLMs in their mathematics.
I don't know about this person, but for me and I'm guessing the average professional in basically any field, before LLMs, they simply ignored information that needed summarizing, made their own crappy slides, and didn't proofread their emails.
Very well written summary of the current situation
Imagine being someone who is working on one of these problems. You have no good guarantee that the problem was solved, but you will have the horrible homework of reading the AI slop. Also, if you do have something interesting to say about the problem, people will have less enthusiasm about it now
I am no mathematician, but I can definitely relate to the "horrible homework of reading AI slop". We've started allowing a non-developer to submit AI generated code into our codebase (in droves).
When I am tasked with reviewing that code. First, I don't know if it's valid. The person who wrote it doesn't know if it's valid. In order to validate it I must step back and understand the full problem space. Then, when I ask for revisions or clarifications, it's seen as either
A - Slowing progress, being resistant to change... or...
B - Thanks for catching that (Claude fix PR 532 with the review comments)
It's 100% removed the enthusiasm.
Perhaps, there is a point where we just "give up" the understanding and accept AI output as the ground truth, because the sheer amount of generation is too much for our puny human minds to comprehend, and a lot of the times it IS right, even if a little wonky.
The gradient into formalisms is steep and the bottom is deep. These are the worst results anyone will ever see again. The bottom of the internet is also deep, but won't be around much longer.
If OpenAI actually spent time writing good proofs that are readable, mathematicians would show *even more outrage*. So let’s not pretend this has anything to do with readability. It has all to do with people protecting their status in society.
It certainly feels that we are witnessing the early days of LLMs and math, similar to the early days of LLMs and code. I feel this entire post sounds so similar to angry computer engineers posts from 1 or 2 years ago. If we continue on this path, eventually many of these posts will ripen like milk in a desert.
> if this was an academic paper submitted to a journal, it should be issued a desk rejection for the quality
If Mr Tao had submitted a shitty, poorly-written proof of a famous outstanding problem, no journal would reject it. That extends to anyone with sufficient credibility. They might ask him to keep at it and fix it up, but nobody would begrudge him putting his shitty (but ultimately correct) draft of arXiv while he did so.
We're all getting disrupted, we all have feelings about it, but from the perspective of a software engineer who's been dealing with all of this for several years now, this post is just cope.
I would admit seeing more mathematicians irritated is a good popcorn show.
For what's worth it, this batch of results are not very tight intentionally by OpenAI and promising mathematicians already started to consume them and improve the results, while someone is still complaining on it.
> OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why? I am trying to finish several papers, I am supervising a number of Ph.D. students, and I have a lot of active research of my own to do. When am I supposed to sift through a badly written paper? Why should I bother, when they don't bother to communicate better?
The mathematicians who don't approve of the deliverables should boycott the proofs, that is the only way OpenAI will get what they deserve on this one.
I've seen my entire profession vanish overnight due to AI... well, not vanish. But, yeah, software development is WAYYYY different. And I couldn't be happier. I think it's amazing. I see the productivity boost. Even if it means I can't add nearly as much value as I used to.
Sorry, but I don't get why mathematicians are so upset. Like, just accept the knowledge and insights and acceleration in your field! If it isn't "fit for human consumption" because an AI produced, okay... it soon will be explained ELI5 by even better models.
Did you... Enjoy software development beforehand? Like there is a huge chunk of people that really enjoyed writing software and are bummed that that part of their job is being subsumed by models.
The same could go for mathematics or any field; there are lots of people who enjoy the process and aren't satisfied by being handed and opaque final result
I don’t get why you aren’t upset. In general I am actually quite disappointed by how meekly the software engineers handed our industry over to AI. But I am particularly revolted by those who exercise their free will to rise from the foetid swamp and say “come on in, the water’s great!”.
Most software developers (or people in any field, working for anyone) rarely own anything they do at work.
And the entrepreneurs running their own companies (which there's an explosion of atm largely because of AI) do indeed "own" the higher-level products and things they're producing, even if AI writes the code.
> OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions?
This is a strawman. OpenAI didn't say they are expecting all mathematicians to read the solutions, incomprehensible or not.
So mathematicians are upset with OpenAI for solving "their" math problems. Software engineers are even more affected by AI, yet mathematicians seem to be reacting more strongly. I don't get why.
It looks like the spent $20 on writing the actual papers.
If they actually wanted to do good for the world, they wouldn't have released these as the slop grenades they are.
In their current state, they are actively damaging the mathematics community.
It shows a lack of respect and care for the impact that their technology has.
It shows that they cannot be trusted for things like private data, AI safety, and company partnerships.
In math/science, repeatability and review are critical to the process.
The right way to handle this would have been to work with the mathematics community to co-develop and create meaningful proofs rather than slop grenades.
If they proceed in the current state, we'll just get a bunch of spaghetti math that won't do anything for helping people build an understanding.
Maybe some day, we won't need people to understand things, but that's certainly not the case at the moment, and likely won't be for several more years.
Perhaps this is projection, and the staff at OpenAI doesn't understand their work anymore? Not a great sign regardless.
OpenAI is doing science the right way. Making the information available as widely as possible so that anyone can check and verify it.
That is the scientific process working exactly as it should.
If that "damages the mathematics community" then all it means is the mathematics community is not doing science and should be ignored.
I cannot stress this enough. If you are complaining about "how they released it" or calling this stuff "slop cannons", you're an unscientific hack that's dragging down humanity.
Engage with the actual claims. Prove them or disprove them. Nothing else matters here.
> The right way to handle this would have been to work with the mathematics community to co-develop and create meaningful proofs rather than slop grenades.
The mathematics community can finish the job OpenAI started. Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
They didn't just "start" it though - they released slop papers.
That's finishing it - not starting it as far as scientific publishing is concerned.
> Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
Not exactly - but that is part of it.
I think what would have went over better is:
1. Immediately announce a solution has been found.
2. Do not publish the solution.
3. Put out an open request for anyone with experience in the area who wants to get involved to help collaborate on a construction and human-comprehensible paper. Accept anyone who can demonstrate potentially useful work/experience in the field/problem. Share the solution with them after they sign some kind of NDA that they won't independently publish or share the solution/work.
4. Work with people until a paper is ready (I mean actually ready - not the kind of slop that they released).
5. Publish. Include names of everyone who made meaningful contributions to the paper (not just the proof).
EDIT: Notice the incentive with my proposed second path is that it gives OpenAI an incentive to improve the interpretability of its proofs. This is a good thing! The maths community would be thrilled to actually gain understanding from such releases, and OpenAI would be happy because they could more quickly and independently publish their results. At the moment the "value" of their mathematics research "product" is low because of the lack of this interpretability, and this current approach is simultaneously destroying the opportunity value of the community as well as the incentive for OpenAI to ever improve on what's missing.
Is a proof that cannot be understood worthless? How would this be framed philosophically?
In fact, the academic system is a kind of worldview created by humans. And as it is shared and the community grows, the problem will gradually become more complex. Because when a discipline develops sufficiently, just as in a mine where rich veins are easy to extract early on but become very hard to extract once much has been dug out... in that sense, as things gradually become more complex, once a certain threshold is reached, won't scholarship surpass the limits of human understanding? Of course, scholarship is entirely for humans, but at some point the system itself may face its limits, and then wouldn't it again reduce the existing normalized minimum within that discipline and establish a new normalization of a new logical system?
In my view, perhaps for very complex work like today, AI will do it, and then there will be work that normalizes and further simplifies the results of that AI. Then, coming back to the human fold, if humans create the initial skeleton, the LLM will learn that again and it will become complex work again, and won't this create a continuing cycle?
I think verification and understanding can be separated. If the proof targets a correctly formalized proposition and passes a reliable proof checker, isn't it valuable? We have obtained knowledge justified as true, but there is simply no new theory that understands that knowledge.
As was the case with the Four Color Theorem...
I am always curious what shape the newly compressed new discipline will take. At that time, I hope even people like me, who are intellectually behind, will be able to learn that discipline.
> Indeed, at least two people asked if I plan on sending Sam Altman a bottle of whisky, as promised in my Problems page. The answer to that is no. And let me explain to you why
> I took a brief look at the preprint released by OpenAI. It sucked. It is unclear, muddled, and has a strange structure.
I see an argument about the paper being poorly written, which I believe, but I don’t see how that relates to honest final paragraph about mathematicians being chefs or whatever.
It’s clear from the author’s tone about lean, emails, infographics, etc. that he thinks automating those away is fine. Why should math be any different?
This whole "oh no this problem is solved now who would ever want to work on it" thing is quite funny. Mathematicians, let me introduce you to something called bike shedding. Folks proved 1s and 0s are turing complete decades ago and yet we have 27 new JavaScript web frameworks every week (or every day or minute now with ai). Y'all will be fine. Thinking a solution is ugly and that you could do better is also a perfectly good motivator and most of the sciences and engineering are "ok, so we know xyz to be true about the world because like, I'm looking at it, but wtf is going on." The theorems were true false or otherwise before some random openai model solved them. And if you don't understand the proof nothing of significance has changed except you've got a bit of a hint now.
Cathedral and Bazaar. Maths professors are used to working diligently behind closed doors before releasing artifacts of high quality whose authorship they guard jealously. The researchers at OpenAI, who come from a software background, are used to working in the open, releasing anything to anyone and expecting nothing but also guaranteeing nothing.
The amount of time the OP attacks OpenAI for errors of form and not substance is unfortunate. Do they also attack amateurs who try to contribute like this?
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.
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.
[0] https://scottaaronson.blog/?p=10169
> 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
https://scholar.google.com/citations?user=T_OhvOsAAAAJ
https://finance.biggo.com/news/B0eMxZsBy4YEFZDUVPWh
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.
> I wish they take a bit of more time
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!
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.
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.
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.
> 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").
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.
> 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.
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.
doing math is not "misaligned"
write down "LLM's will cure cancer" on sticky note, put it on your desk and recite that every day, a hundred times and in the bathroom if you have to
If you can't fight them, join them.
If you can't leave them, love them
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.
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.
They don’t have any more patience for this.
Seems like an excellent opportunity to learn how these new proofs work and be at the frontier.
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 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.
Your point would be stronger with links to such discussion.
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
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.
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.
why are AI sites so hard to read... is it the terrible contrast? or something? any designers here?
There’s so much information, but it has no idea where to put the focus. Why is the number of PRs the same size as the actual best result?
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.
Except for the fact that academia today is bs:
https://www.youtube.com/watch?v=LKiBlGDfRU8 https://www.youtube.com/watch?v=shFUDPqVmTg
"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.
> 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.
Like all the junior devs getting opportunities left and right.
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?
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.
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.
How about the scenario where they are already better if you give them more time/tokens/…? Would it be a more relatable concern in that case?
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?
Nice idea.
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.
(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.
How is solving unsolved problems a good eval? Once a problem is solved and released, you can’t evaluate a future model’s ability to solve it.
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.
https://www.ahmath.org/
Any idea what sort of percentage the sentence
> supported by a clear plurality of respondents
was referring to?
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.
> 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.
[0] https://leodemoura.github.io/blog/2026-8-24-postmortem-for-t...
[1] https://github.com/openai/math/blob/main/history.md
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.
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?
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.
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.
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.
How is the journey to understand fusion related to not wanting to spent your limited time on earth wading through AI slop?
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
Here's a guy who's made a "beyond n log n" tracker: https://x.com/aurel_pr/status/2108214135179944096
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?
Some people are having fun doesn't negate the rest of the issues with this sort of thing.
then the rest of them can pound sand.
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".
add "no one is forcing you to own a smartphone"
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.
No, they don't have to ask. Those interested enough will jump at the opportunity, even if it's just to be "one of the first to get it".
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.
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.
Exactly.. this is an opportunity for people to pick up where the model left off and run with it. Like you don't have to, nobody is forcing you to.
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.
> 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.
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.
Wondering if you read the article?
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.
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?
My argument is that LLM generation and a correlated Lean verification are not sufficient conditions. Both are falliable.
"true" != "understandable"
It's a necessary condition
You're passionate about this problem, right?
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".
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?
Can't you read the article and understand how he kind is obligated to engage with it ?
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.
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.
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.
That is an incredibly loose use of the word "forced"
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.
Those are perfect examples because those are also hyperbolic and unserious uses of the word “forced”.
Merriam Webster seems to agree with me: https://www.merriam-webster.com/dictionary/force#dictionary-...
> 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.
it takes two keystrokes to type NO
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.)
These takes forget that OpenAI is doing all this as a PR stunt. They're utilizing the field without worrying about any consequence to it.
"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.
Isn't it obvious that the feasible way to respond is to start developing AIs that rewrite proofs for human understanding
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.
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.
At first I thought this was going to be more Luddite babble, but it makes a good point. OpenAI isn't contributing if they are make unreadable papers. They should use a little more of their compute to nail interpretability. The difficulty will only get worse as AI plow deeper into the frontier and produce increasingly alien looking output. I suspect it's a workflow issue. If not, it's a bad oversight if the current generation of models are capable of making mathematical breakthroughs but can't explain how they build on existing frameworks.
If you don't think they have contributed anything then you can safely ignore them.
Exactly what the author is doing.
Work this abstract almost certainly has no value outside the community that is (was) interested in the result. OpenAI should engage with the community to realize the value (beyond PR).
Is it just me or is this line of thinking fundamentally dishonest? It may be true that the papers are hard to read but the papers have extremely high signal towards the proof.
All of these comments seem to suggest that if papers are not 100% abiding by readable books their standards, they are basically the same as literal noise. This is highly dishonest.
I’m just a dude and even I’m able to understand the paper after using ChatGPT to help me through it.
There's certainly a conceit in saying if the math is not accessible to my community then it doesn't even count as math, and the last few days this has been a common ideological talking point.
That’s right and readability argument is a distraction
https://news.ycombinator.com/item?id=50016860
Mathematicians struggle with the same problem as software engineers; you can let AI generate the artifact, but to understand fully what is going on is challenging. Perhaps even more for mathematicians.
Do you rely on the tests/Lean to accept correctness or not…
If there is a formal proof, and it is the proof of your precise statement (which I imagine is easy to check, otherwise I think that mathematicians would not accept the Navier Stokes result so quickly), then there is no way to ignore the result, however badly it is written.
This was always the essence of mathematics, and it must stay this way.
As much as I personally despise altmans, "darios", and their bootlickers, this is one aspect which is undoubtedly "good for the mathematical community" as a whole. The fact that the validity of your statement does not depend any more on an expert opinion of some person with grants, but as it always should have had been, just on the validity of the chain of deductions.
> not at the Lean code, since I know very little of the actual usage of Lean, and that code was enormous
Dismissing results on the basis that Lean code is too long disqualifies this opinion. It is not hard at all to read the Lean result statement, even with very superficial Lean knowledge.
He's probably talking about understanding the structure of the Lean proof, which is 233,891 lines of Lean (including blank lines).
Here’s an idea I would love to see play out. Have one of the labs train a new model, using cutting edge architecture, on a whole lot of data and math papers from before 1905. Then see if it can come up with, or even understand, Einsteins theory of relativity.
Special relativity is one of those unusual theories that requires very little in the way of math or concepts to understand. You take the data from the 1887 Michelson-Morley experiment (which measures the same speed of light, despite different reference frames). You take the idea that the laws of physics work in any reference frame. You take some high-school math, et voilà, special relativity.
In short, we’ve reinvented cranks sending unsolicited, poorly written putative proofs
Except that the proofs are very likely valid. This is a country of Ramanujans in a data center. You're free to ignore them because they don't follow your style guide, the rest of us will enjoy seeing humans and AIs build on the results.
> the rest of us will enjoy seeing humans and AIs build on the results.
That would be nice, but the rest of the world wasn't interested in the results before and they won't be interested after.
I wonder what this means long term. Maybe mathematicians will keep plodding on as usual except sporadically when an AI company need a marketing boost so they spend millions of dollars to dunk on them. Because the mathematicians sure don't have that kind of money.
There is no nice way to tell someone that you’ve scooped them, and this is industrial scale scooping.
A few papers have been retracted, but it looks like many are withstanding intense scrutiny. Lean is making the results more likely to be correct, but I think making them harder to understand.
The world has changed and you’ll know a math department is making a serious attempt to adapt when it teaches a required Lean course in freshman year.
Why do you believe that learning Lean is a better use of time when the AI is clearly better at writing and interpreting Lean than it is writing quality papers? At this point, Lean is for autoformalization, no one is really supposed to read it.
Well, you don't necessarily need to read the proof, but the proof is useless if you don't read the specification.
That's fair, but I would argue that reading the specification is very easy by comparison. A quick one hour tutorial is usually enough judging from my students' experiences.
The Lean proof to Fermat's Last Theorem is 13 mil lines.
The one for the quasi-Riemann Hypothesis is half a million.
>OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why?
...
>So, no, I will not be sending Sam Altman a bottle of whisky anytime soon, nor I am planning on spending my time reading through that paper and trying to make sense of it.
Think about a hypothetical circumstance where we get radio communication with some aliens on another planet. They send over tons of math to help us advance our tech, we know the math they're sending us is correct, but their explanations are really hard to work through because they aren't humans and the math is so different from anything we've done. Should we whine about the results they sent to us and refuse to engage with it?
> to help us advance our tech
The major discussion is about whether this will in fact advance our tech.
In the Three Body Problem, the alien race shows us “miracles” in an attempt to discourage us from the pursuit of science. Consider that possibility.
Love your metaphor here. I guess there will always be people who try to keep going and follow their current projects and say that only human math is real math and we should only use alien technology for proofreading mails and such but not their highly established and esteemed professions. Or just keep your hubris low, update your priors, work towards progress.
In this hypothetical case funding agencies would probably happily pay for “alien maths translation grants” and you could write papers about advances in that field and get jobs etc. So arguably for better or worse it would create a specialised academic cottage industry that somehow interfaces with the rest of maths.
openai will take expert responses like this and improve the next set of papers
it won't be long before there's no more low hanging fruit like this to complain about, and the writing / explanations of the results are superhuman as well
separately, i really liked the author's denial-of-service analogy. super useful practical framing
Look forward to seeing an LLM write something well, that will truly be a breakthrough in the field.
Love this!
> This is why I generally avoid using AI for mathematics (I am happy to ask LLMs to consolidate information for me, or to generate a useful infographic, or to proof read an email, etc.)
In other words, the author is OK with using LLMs to replace data analysts (that could consolidate information), to replace graphic designers (that could generate infographics), and to replace editors (that could proofread an email). But don't you dare use LLMs in their mathematics.
I don't know about this person, but for me and I'm guessing the average professional in basically any field, before LLMs, they simply ignored information that needed summarizing, made their own crappy slides, and didn't proofread their emails.
Very well written summary of the current situation
Imagine being someone who is working on one of these problems. You have no good guarantee that the problem was solved, but you will have the horrible homework of reading the AI slop. Also, if you do have something interesting to say about the problem, people will have less enthusiasm about it now
I read one of these papers (a relatively short one), solving a big problem in a field I used to work in, and it's exposition was above average.
I am no mathematician, but I can definitely relate to the "horrible homework of reading AI slop". We've started allowing a non-developer to submit AI generated code into our codebase (in droves).
When I am tasked with reviewing that code. First, I don't know if it's valid. The person who wrote it doesn't know if it's valid. In order to validate it I must step back and understand the full problem space. Then, when I ask for revisions or clarifications, it's seen as either
A - Slowing progress, being resistant to change... or... B - Thanks for catching that (Claude fix PR 532 with the review comments)
It's 100% removed the enthusiasm.
Perhaps, there is a point where we just "give up" the understanding and accept AI output as the ground truth, because the sheer amount of generation is too much for our puny human minds to comprehend, and a lot of the times it IS right, even if a little wonky.
The gradient into formalisms is steep and the bottom is deep. These are the worst results anyone will ever see again. The bottom of the internet is also deep, but won't be around much longer.
If he doesn’t like the paper’s structure he can just prompt gpt pro to review and amend.
I know the model that produced these proofs is still private, but it’s worth a shot tackling the proofs with the current consumer-available frontier.
If OpenAI actually spent time writing good proofs that are readable, mathematicians would show *even more outrage*. So let’s not pretend this has anything to do with readability. It has all to do with people protecting their status in society.
You just wait. This will come :)
Stereotyping mathematicians, well played sir.
It certainly feels that we are witnessing the early days of LLMs and math, similar to the early days of LLMs and code. I feel this entire post sounds so similar to angry computer engineers posts from 1 or 2 years ago. If we continue on this path, eventually many of these posts will ripen like milk in a desert.
> if this was an academic paper submitted to a journal, it should be issued a desk rejection for the quality
If Mr Tao had submitted a shitty, poorly-written proof of a famous outstanding problem, no journal would reject it. That extends to anyone with sufficient credibility. They might ask him to keep at it and fix it up, but nobody would begrudge him putting his shitty (but ultimately correct) draft of arXiv while he did so.
We're all getting disrupted, we all have feelings about it, but from the perspective of a software engineer who's been dealing with all of this for several years now, this post is just cope.
I would admit seeing more mathematicians irritated is a good popcorn show.
For what's worth it, this batch of results are not very tight intentionally by OpenAI and promising mathematicians already started to consume them and improve the results, while someone is still complaining on it.
Reading though these comments I truly understand why the hardest part of my career in "IT" has been personalities.
The lack of emotional maturity and empathy is very on par with my experience thus far.
Or there are people who don't define "standing in the way of progress" as a valid item in the list of "emotional maturity/empathy".
> OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why? I am trying to finish several papers, I am supervising a number of Ph.D. students, and I have a lot of active research of my own to do. When am I supposed to sift through a badly written paper? Why should I bother, when they don't bother to communicate better?
Excellent point.
I don't blame the AI for this - I blame OpenAI.
Literal slop grenade (see https://fortune.com/2026/09/17/shopify-tobias-lutke-ai-slop-...)
The mathematicians who don't approve of the deliverables should boycott the proofs, that is the only way OpenAI will get what they deserve on this one.
I've seen my entire profession vanish overnight due to AI... well, not vanish. But, yeah, software development is WAYYYY different. And I couldn't be happier. I think it's amazing. I see the productivity boost. Even if it means I can't add nearly as much value as I used to.
Sorry, but I don't get why mathematicians are so upset. Like, just accept the knowledge and insights and acceleration in your field! If it isn't "fit for human consumption" because an AI produced, okay... it soon will be explained ELI5 by even better models.
Did you... Enjoy software development beforehand? Like there is a huge chunk of people that really enjoyed writing software and are bummed that that part of their job is being subsumed by models.
The same could go for mathematics or any field; there are lots of people who enjoy the process and aren't satisfied by being handed and opaque final result
Loved it... love it even more now. So darn fast.
> I don't get why mathematicians are so upset
Their field is at the stage where the humans are “debugging” the AI slop.
They are still imagining how to escape from having to read the generated code. Hopefully they find a way.
I don’t get why you aren’t upset. In general I am actually quite disappointed by how meekly the software engineers handed our industry over to AI. But I am particularly revolted by those who exercise their free will to rise from the foetid swamp and say “come on in, the water’s great!”.
You will own nothing and you will be happy.
I don't see how this quote is relevant here.
Most software developers (or people in any field, working for anyone) rarely own anything they do at work.
And the entrepreneurs running their own companies (which there's an explosion of atm largely because of AI) do indeed "own" the higher-level products and things they're producing, even if AI writes the code.
What is supposed to have changed?
> OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions?
This is a strawman. OpenAI didn't say they are expecting all mathematicians to read the solutions, incomprehensible or not.
So mathematicians are upset with OpenAI for solving "their" math problems. Software engineers are even more affected by AI, yet mathematicians seem to be reacting more strongly. I don't get why.
OpenAI spent $20m on this at least.
It looks like the spent $20 on writing the actual papers.
If they actually wanted to do good for the world, they wouldn't have released these as the slop grenades they are.
In their current state, they are actively damaging the mathematics community.
It shows a lack of respect and care for the impact that their technology has.
It shows that they cannot be trusted for things like private data, AI safety, and company partnerships.
In math/science, repeatability and review are critical to the process.
The right way to handle this would have been to work with the mathematics community to co-develop and create meaningful proofs rather than slop grenades.
If they proceed in the current state, we'll just get a bunch of spaghetti math that won't do anything for helping people build an understanding.
Maybe some day, we won't need people to understand things, but that's certainly not the case at the moment, and likely won't be for several more years.
Perhaps this is projection, and the staff at OpenAI doesn't understand their work anymore? Not a great sign regardless.
No, you're just straight up wrong.
OpenAI is doing science the right way. Making the information available as widely as possible so that anyone can check and verify it.
That is the scientific process working exactly as it should.
If that "damages the mathematics community" then all it means is the mathematics community is not doing science and should be ignored.
I cannot stress this enough. If you are complaining about "how they released it" or calling this stuff "slop cannons", you're an unscientific hack that's dragging down humanity.
Engage with the actual claims. Prove them or disprove them. Nothing else matters here.
This. So much this. (and I dont even like OAI)
> The right way to handle this would have been to work with the mathematics community to co-develop and create meaningful proofs rather than slop grenades.
The mathematics community can finish the job OpenAI started. Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
> the job OpenAI started.
They didn't just "start" it though - they released slop papers.
That's finishing it - not starting it as far as scientific publishing is concerned.
> Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
Not exactly - but that is part of it.
I think what would have went over better is:
1. Immediately announce a solution has been found.
2. Do not publish the solution.
3. Put out an open request for anyone with experience in the area who wants to get involved to help collaborate on a construction and human-comprehensible paper. Accept anyone who can demonstrate potentially useful work/experience in the field/problem. Share the solution with them after they sign some kind of NDA that they won't independently publish or share the solution/work.
4. Work with people until a paper is ready (I mean actually ready - not the kind of slop that they released).
5. Publish. Include names of everyone who made meaningful contributions to the paper (not just the proof).
EDIT: Notice the incentive with my proposed second path is that it gives OpenAI an incentive to improve the interpretability of its proofs. This is a good thing! The maths community would be thrilled to actually gain understanding from such releases, and OpenAI would be happy because they could more quickly and independently publish their results. At the moment the "value" of their mathematics research "product" is low because of the lack of this interpretability, and this current approach is simultaneously destroying the opportunity value of the community as well as the incentive for OpenAI to ever improve on what's missing.
or they just release as it is and keep on improving until they can one shot human comprehensible paper.
Is a proof that cannot be understood worthless? How would this be framed philosophically?
In fact, the academic system is a kind of worldview created by humans. And as it is shared and the community grows, the problem will gradually become more complex. Because when a discipline develops sufficiently, just as in a mine where rich veins are easy to extract early on but become very hard to extract once much has been dug out... in that sense, as things gradually become more complex, once a certain threshold is reached, won't scholarship surpass the limits of human understanding? Of course, scholarship is entirely for humans, but at some point the system itself may face its limits, and then wouldn't it again reduce the existing normalized minimum within that discipline and establish a new normalization of a new logical system?
In my view, perhaps for very complex work like today, AI will do it, and then there will be work that normalizes and further simplifies the results of that AI. Then, coming back to the human fold, if humans create the initial skeleton, the LLM will learn that again and it will become complex work again, and won't this create a continuing cycle?
I think verification and understanding can be separated. If the proof targets a correctly formalized proposition and passes a reliable proof checker, isn't it valuable? We have obtained knowledge justified as true, but there is simply no new theory that understands that knowledge. As was the case with the Four Color Theorem...
I am always curious what shape the newly compressed new discipline will take. At that time, I hope even people like me, who are intellectually behind, will be able to learn that discipline.
> Is a proof that cannot be understood worthless?
No.
But its worth a lot less than one that can be understood.
They really should be trying to partner with the mathematics community to add maximum value.
Their current approach is reckless and risks doing more harm than good.
If no one understands a proof, then it is not a proof
> Indeed, at least two people asked if I plan on sending Sam Altman a bottle of whisky, as promised in my Problems page. The answer to that is no. And let me explain to you why
> I took a brief look at the preprint released by OpenAI. It sucked. It is unclear, muddled, and has a strange structure.
https://img.getfn.io/images/e3245d47a159592b06570ffbd64d5af8...
I see an argument about the paper being poorly written, which I believe, but I don’t see how that relates to honest final paragraph about mathematicians being chefs or whatever.
It’s clear from the author’s tone about lean, emails, infographics, etc. that he thinks automating those away is fine. Why should math be any different?
Wow talk about sour grapes! No one is forcing you or any other mathematician at gun point to engage with this release at all. Ridiculous drivel.
I just read a childish rant
This whole "oh no this problem is solved now who would ever want to work on it" thing is quite funny. Mathematicians, let me introduce you to something called bike shedding. Folks proved 1s and 0s are turing complete decades ago and yet we have 27 new JavaScript web frameworks every week (or every day or minute now with ai). Y'all will be fine. Thinking a solution is ugly and that you could do better is also a perfectly good motivator and most of the sciences and engineering are "ok, so we know xyz to be true about the world because like, I'm looking at it, but wtf is going on." The theorems were true false or otherwise before some random openai model solved them. And if you don't understand the proof nothing of significance has changed except you've got a bit of a hint now.
Cathedral and Bazaar. Maths professors are used to working diligently behind closed doors before releasing artifacts of high quality whose authorship they guard jealously. The researchers at OpenAI, who come from a software background, are used to working in the open, releasing anything to anyone and expecting nothing but also guaranteeing nothing.
The amount of time the OP attacks OpenAI for errors of form and not substance is unfortunate. Do they also attack amateurs who try to contribute like this?