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? 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.
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, relating results to and integrating them with that edifice.
Kinda sounds like computer science vs developing - in the sense that people with a master's in CS and are dedicated to the craft will write wonderfully artistic software, while it doesn't actually take a love for the process to write code and get hired at some tech company (even less so now with agentic development).
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?
The question is why the situation is what it is. Did OpenAI publish a large volume of unreadable proofs because that was their best attempt to contribute to the field of mathematics? Or does OpenAI feel that it’s more profitable for them if people come to see mathematics as something that’s less focused on understanding and more focused on using AI to generate proofs?
Yes, I guess it matters a lot whether this was quite close to the best they could do or the best they could do given specific resource constraints or whether they just didn’t bother to try doing better (eg to invest more tokens into readable papers)?
> I guess it matters a lot whether this was quite close to the best they could do
As the author of the post points out, there is no way this is “the best they could do”. It’s a write up that didn’t involve someone with the math + communication skills required to clearly explain the result.
Even with humans, the first publication is rarely the best expression of the lesson. Getting published does more than establish priority; it also frees up the community to build on the result. Nobody expects a human to wait until the proof is comprehensible to anyone except themselves and the referees.
I don’t think that’s true? I never did research math myself, but the people I’ve known who do would definitely invest time in making a proof clearer and better even if they had the idea basically correct. There’ve been multiple recent stories of researchers saying “we’re going to publish this lame proof that isn’t up to our standards because the AI companies let us know they’re going to scoop us if we don’t”.
Mathematicians care a lot about the exposition of their ideas, invest a lot of time in giving talks, writing, and don't publish too frequently, compared to other sciences.
They normally don't feel like they are in some kind of race to publish the results ASAP and claim priority. Cases like that are very rare (but they get media coverage because they are so unusual).
OpenAI did a publicity stunt, their motivation is not to make a good contribution to the field, which has very different standards and culture, compared to the AI labs.
You don't know what you're talking about. Just because it was created by an LLM, and verified in Lean, does not make it true. The whole point of writing a proof is for it to be understandable.
Suppose I directed some llm agents to factor the primes from network logs of your machine. I then publish the private and public key in full. You would not change your keys of course because its not true right?
Knowing a few PhD candidates and non-tenure track postdocs, the “younger, hungry mathematicians” are more worried about finding a damn job in the poorest job market - both academic and in industry - in a decade.
There are plenty of mathematicians who think the results are interesting. Not only do they have the "patience" you speak of, some even seem to be enjoying exploring the new results. You don't speak for everyone.
No idea why you're downvoted, my intial thought was that I would like to see some of this supposedly widespread sentiment as well.
I even think it's plausible a lot of mathematicians are excited by it, but the sweeping confidence of the comment you replied to without anything to back it up leaves some to be desired
Checking someone else's work carries a lot of opportunity cost, and is only fruitful if one can learn new methods which apply to the own work. This is pretty risky, especially without tenure!
There's a "Silicon Valley-ism" for you. We offer a thing in whatever form we want and people "who are passionate" will gobble it up, should gobble it up, 'cause they're "passionate".
I think this might feel about the same as getting a PR from Claude that purports to solve some issue that it deems exists, but it doesn’t conform to the contribution guide, isn’t clear in its objectives and looks quite likely to be utter bullshit. I close them without comment and lock the issue.
"AI models will surely get better at writing "enjoyable proofs,"" why? Why is that surely true? they've increased in all other capacities at shocking rates while still writing awful, slippery, turgid prose. Very silly to assume that this will just go away.
Every single day now, for close to 4 years, ever since ChatGPT 3.5 was released - there's been people dismissing AI progress. Every step of the way.
It is entirely possible that one day progress just stops or slows down, but with current evidence, I don't find that too likely - at least not in the near future. The sheer amount of resources being put into this (AI) race is mind-boggling.
So while past performance does not guarantee future results, I'm just going to kick back, and assume that many of the current issues will be fixed with future models.
The progress is clearly not uniform though, it’s shaped by how amenable things are to collecting data and verifying computation. I think writing clear and cogent prose is harder to quantify than formally verifiable logic, and this is why progress in coherent communication has been slower than raw problem solving ability
Maybe this is just a matter of what model developers choose to invest training resources in, but I don’t think it’s inevitable unless clarity is made a higher priority
only addresses it in a magical thinking "lines on a graph mean that tomorrow Claude will be so entertaining it'll make everyone on earth die in a stupor Infinite Jest style" sense. capabilities have increased while writing has either stagnated or gotten worse and more impenetrable. if you think quality of writing is going to fall to the bitter lesson that's fine you just actually have to make an argument, or in your case, I imagine, have Claude make it for you.
I think it’s silly to ignore the sheer rate of progress that’s occurred in the last 5 years. Compare gpt 2 output to latest foundation models and then re-read your comment. You’ll realise just how out of touch you sound.
people replying to this seem to be incapable of strawmanning that I am denying the rate of progress. I am not. 6 months ago they were good for an occasional technical lemma and now they can solve major open problems. The writing has only gotten worse (the papers in the big drop are completely unreadable, even to experts in the appropriate fields). If you're going to respond to a comment try to respond to what it's actually saying.
> 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 statements of the lemmas are quite clear. We can write it up if we spot that they have important consequences. The proofs are impenetrable to me, for three reasons: they are very complex, they are badly structured, and they use math unfamiliar to me. So I haven't looked too deeply yet. Maybe when they get their autoformalization stamps of approval.
Of course, everyone is curious about these results, we're mathematicians after all. But by incentives I refer to those things that really sustain the system: obtaining permanent positions, grants for future projects, ideas for PhD theses, etc.
The future is uncertain, so the safe thing to do is write it up if we discover some useful connection between our research and the openai results. Maybe it matters for getting positions grants etc, maybe not. Ideas for new results: the openai drop is full of those.
Maybe I misunderstood the question. I'll give it a second go, maybe I'll fail again. Feel free to reformulate.
The term SOTA suggest that you approach this from a perspective other than a pure mathematician's, maybe ML or computational complexity? The openai results help me answer other open questions. It's a yes/no thing: is question answered or not? It's not a question of "okay, but will AI win back the SOTA from me again?"
I think quite a few mathematicians would be interested in using AI to figure out the answer.
But providing the answer in gibberish along with a certificate is not that, it's at best a cruel way to do it, but I'm leaning towards the idea that it's a fundamental misunderstanding of what it means to do math and what it means to communicate a result.
If you think sending an answer in gibberish is acceptable just because it's true then SSdtIG5vdCBzdXJlIHdoYXQgdG8gdGVsbCB5b3UsIGJ1dCB3ZSBkaXNhZ3JlZSBvbiB0aGF0.
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
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.
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.
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.
OpenAI is publishing the math because they want mathematicians to read along and verify the work they are doing. The author complained that even the citations don't make a lot of sense. This is completely consistent with my experience of using AI for coding. When I task my agent a hard problem and it comes back with a 5000 line PR that I don't follow I reject it and work it into a better shape. I certainly don't slam it into production because it has a 'high signal' of the program I asked for. The mathematician's situation is a lot worse because they have no view over the process that created the artifact like we do with coding agents.
> When I task my agent a hard problem and it comes back with a 5000 line PR that I don't follow I reject it and work it into a better shape. I certainly don't slam it into production because it has a 'high signal' of the program I asked for.
??? That's literally what everyone does. You are creating a hypothetical that is nonsensical. Here's your hypothetical:
1. Agent gives you 5000 lines of slop
2. You reject it and just do it yourself
This is reality
1. Agent gives you 5000 lines of slop
2. you realise that it has done a lot of research and is mostly in the correct direction and you ask it nicely to refine it
3. verify that you understood it and push it to prod
Are mathematicians babies that they need a completely different approach?
The mathematician in this case didn't ask an AI for the proof, they were handed a badly written artifact and other people are messaging him asking for analysis. He has no visibility into the process that produced the paper because it came from an internal OpenAI model. The bad behavior here isn't coming from the complaining mathematician. OpenAI hasn't sufficiently developed their workflow to create cutting edge research AND publish it intelligibly, which is odd because the latter should be easier. OpenAI has perverse incentive to do this because spamming badly written papers can still give them priority credit for solving open problems at the expense of mathematicians (who are currently indispensable because they decide whether claims are credible). What Mr. Karagila is trying to enforce are the old standards that review should come after refined explanation of the solution. If that was the case before AI, I can't see a reality in which that isn't the standard now that papers can be pumped out at faster-than-human time scales.
It doesn't seem like the paper is really hard to read, but rather that the terminology is "a bit off", with "unexpected theorems" and references that are correct but that could point to more useful targets (read: papers that will increase the citation count of the researcher being cites...). None of which are valid reasons to be dismissive of a good result.
> I’m able to understand the paper after using ChatGPT to help me through it.
How could you possibly know that? If you don't have the knowledge to understand the paper without using a chatbot, you don't have the knowledge to verify that what the chatbot said is the same thing as what's in the paper.
> 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.
> 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).
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 is great - I think we're getting close to the core disagreement here because I disagree with almost all of that, and I think its because we have different conceptions of what science is.
To me, science is not a database of facts and data, and the scientific process is not just the process of adding to this database.
It is more than that.
Science is building the database of facts and data, but it is also sharing/disseminating that database.
We both agree that "openness" is critical for this, but to me, the scientific process includes things like the actual words that a scientist uses to communicate their ideas/data, the paper they wrote, the collaborations they had, the work that they built upon. Science is not like a database only - its more like a distributed system, and the scientific community is like a living, breathing thing. It is the health of that system which has been damaged in my opinion.
So I have no problem that OpenAI updated the database.
They didn't just make the information available though.
They updated the knowledge database, then released low quality slop papers.
They made it clear that they don't give a damn about sharing/disseminating information.
They are trying to fundamentally say "we can do science without prioritizing sharing.
We don't think its important. We'll release the proof because it makes our stock go up, but we're gonna keep going and building and not spend any time on communication or comprehension because we think that it doesn't matter, and your contributions don't matter, and AI is gonna do all of this independently anyway. We spent $20m on the proof because it made our stock go up $20b, but we'll spend 20 min on the paper. Priorities clear.
I don't disagree that having comprehensible papers is useful. There is undoubtedly value in having well written, easy to understand documents that make it easier for third parties to validate the work presented.
The thing is, that is a "nice to have", not a condition to make science.
If people believe that such things are useful, then the appropriate response is to reproduce, simplify and otherwise make the proofs provided into more easily digestible pieces.
The scientific process is fundamentally indifferent to whatever shibollets and cultural hangups that its presumed participants may have. An alien with fundamentally different norms from us, who experiments to determine the boiling temperature of water is doing science just as much as a human, even if he never submits a paper to a journal.
The issue you're having is that you're under the mistaken belief that the scientific process is the "community" and "norms" that happen to have developed over the past few centuries by this "scientific" priesthood.
It is not. It has never been. It will never be.
This "scientific" priesthood has simply used their power and reputation to enforce their own self-aggrandizing norms, much like the religious priesthood they replaced. They should not be taken seriously, and to go along with these norms when they are unnecessary is frankly ridiculous and shameful for anyone who actually prizes results.
I would urge you to reconsider your stance, and in particular to put deep thought into why you believe these norms are so important.
Those are quite a lot of reactions so i have not read all of them. That said, the sample of 30 or so reactions i did read seems to simply confirm my stance.
Fundamentally the main points being made seem to boil down to this excerpt from Tristan Humbert:
>Open AI claimed a proof of the conjecture in full generality this morning and my first impression was sadness to see my favorite problem get “killed” by AI ; it is definitely easier to ignore a problem when it does not affect you directly. Next, I felt stressed because I am currently applying for postdocs and more of my research plan was now obsolete and I spent the whole morning rewriting everything and sending emails to my advisors in panic. Finally, I felt anger after opening the paper and observing that it was mostly unreadable slop.
They're essentially angry at "They did before i could", and "Now i don't have a job" and "I dislike how it is written".
It just reinforces the "scientific priesthood" theme.
These are people who had their livelihoods and status derived from this thing which is now fundamentally obsolete, and they are scared and upset that they will no longer have those things.
That's fine, its a normal human reaction. God knows i'm not sure i will have a job in 5 years because of AI!
But we should not be taking it with any more seriousness than we would take a ludite gripping about the mechanization of cloth manufacturing.
The truth is, the value produced by their job just fell off a cliff. They need to find something else that provides value to replace it. That's it. Being upset about it isn't going to be productive.
Perhaps the value they can make is to rewrite the AI proofs to a more understandable format. Perhaps it is to go flip burgers at McDonalds. That's up to them, but i would suspect that calling releasing valuable information as "bad for science" is not very value accretive.
"not at the Lean code, since I know very little of the actual usage of Lean, and that code was enormous"
This part I don't understand. Not that anyone should read the entire Lean code of any proof, but if the statement of the theorem to be proven in lean seems to be correct, then I would think there would be at least some interest if in fact there was a formal proof (which might or might not correspond to the written proof) of something I was working on. That to me would be interesting. Or you are saying you doubt the validity of the formal proof, which would also be interesting. But saying it is of no consequence doesn't make any sense to me.
I think TFA’s point is that it’s interesting - it’s just not feasible to do what follows after “it’s interesting”, which is to try to make heads or tails of the stack of writing that we’ve been given. Engaging with a well-written proof of a similar scope is enough of a task already.
Some of the lean proofs are apparently incomprehensible.
It would be like trying to look at a completed video game's assembly code, being told that it was call of duty, and then being asked questions about the high level code architecture.
AI models are perhaps unsurprisingly good at low level translation (see the progress being made for decomp games)
These models have surpassed human capabilities at math/machine code, but they can't "simplify" yet - in part because they don't have the same need to due to their comparative lack of cognitive constraints. AI Slop code is getting better, but it takes time. At the moment, its embarrassing frankly. It will come eventually, but right now OpenAI is not handling this with the care, respect, or concern that it deserves.
Have you ever wrote some code/algo that seemed "simple/obvious" to you yet to someone else, it seemed incomprehensible?
If you have a 20-40 IQ points gap with another developer, this happens a lot.
The baseline of "simplify" is wildly different based on your IQ points. That's precisely why exceptional students are usually bad in teaching. They try to break things down, simplify, but things still go over the head of normies.
However, we can intervene/train the models. So it should be possible to focus on the simplification, and as you said, it will come eventually.
I've been mostly reading here but created an account to disagree with this statement: The smartest people I know were always amazing at explaining. This was true for me as undergrad and graduate student where the smartest peers and the most renowned professor were always also the best at explaining, and it is true now at research level in a related field.
When I am not sure if I really understood something to the core, I try to find a colleague who knows very little about it; if they understand my explanation well, that's a good sign.
Those who really understand a topic are usually also able (and great at) explaining it in very clear and "simple" terms. This may be part of my personal bias; I see theory builders as those who advance the field the most, and these are usually also amazing at explaining it. On the other hand, those who mostly "grind" through problems (approach them as complicated puzzles) with effort/time were often bad at explaining.
I observed the same for programming: the "architects" usually explain very well, the "debuggers" often don't.
LLMs very much remind of the grind/puzzle approach. It does makes sense that RLVR, which in my understanding enables a lot of these results, would lead to a more mechanical approach.
Of course, I can't make any predictions on whether it will stay that way. But I strongly suspect that we need different ways of training for LLMs to write better text and explain better (I suspect the vagueness of LLM language is the result of RLHF as vague expression is less often incorrect).
I don't disagree with you. However, you are ignoring one key point that I made: the difference of base intelligence.
Let's assume you have an IQ of 135. You are not that far from even the crazy smarts at 150 and as long as they have some social skills, it will work out. I, myself, never had issue with understanding the smart people.
Now let's assume you have an IQ of 110. Unless 140/150 IQ people are spending inordinate amount of time formulating how to simplify things for you, things will fly above your head.
This does not mean just because someone is 150, and someone is 110, the 110 is always the problem.
This also does not mean an 120 explaining something to 140, and failing is 120's fault or the other ones'.
Every combination is possible as we are talking about personalities/ability to articulate oneself.
However, I was talking about a specific scenario, which I have faced myself and saw it happen a lot of times (to other people), where someone's simplification level is still higher than someone's max understanding level simply because the deviation between their caliber is too great. In most cases, this can be worked around by the explainer spending inordinate amount of time.
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!”.
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?
Why should it change when there's good chance it's just slop? That's exactly the standard that human mathematicians are held to -- and it's their job to refine and polish the work to make it understandable by the community. And standards have evolved that way because otherwise there's too much slop to wade through (eg. you'd be surprised how many papers the typical theoretical physicist gets claiming to have proven Einstein wrong -- from absolute crackpots who don't understand the basics of the subject). This will just multiply now with AI, and doesn't change just because the prompter happens to be on OpenAI payroll.
We'll see what the final slop rate is, but the three papers they retracted yesterday were for a trivial sign error. If they didn't catch that, that means OpenAI wants credit for solving problems, without the effort of sifting through their own garbage and making sense of it.
It's not like they needed to hurry out this release before carefully vetting. They're just "hacking" the math system and disrupting the work of thousands of researchers to create a gigantic RL dataset for themselves.
Really, what's the bloody hurry?
They could have released 1-5 papers, worked with researchers to understand what methods work and what don't, how to prompt the models better, how to build better guardrails for reasoning, etc. And give those researchers access to latest models and empower then to solve thousands of problems!
Instead OpenAI wants to piss all over the city to claim territory and now human mathematicians have to go around cleaning up that slop, only so that OpenAI can made some bullshit statement like: math is solved [mistakes are next].
--
Imagine someone gave you a million line PR claiming to have vibecoded the operating system of the future (or whatever your application domain). Would you drop all your other work to focus on this?
And they generate enough PR that your manager and company leadership and public all start pressing you to accept it quickly?
Imagine someone gave you a million line PR claiming to have vibecoded the operating system of the future (or whatever your application domain). Would you drop all your other work to focus on this?
If it verifiably works and solves important outstanding issues, then quite possibly yes.
If a human mathematician had to retract three of their papers a day after posting publicly, they'd lose all credibility and their mathematical career would be all but finished.
If a human published 700 papers and only 3 (or 30) ended up having significant errors, I'd call that a pretty good batting average, considering that the typical rate of errors may be around a third (https://lamport.azurewebsites.net/pubs/statistics.pdf). But for some reason people hold AI output to an absurd standard where if it's not 100% perfect then it's useless.
You're basically asking them to turn off their immune system
I'm not asking "them" to do anything. They can do whatever they want, including rejecting obviously useful tools. But then they shouldn't be surprised when they're quickly surpassed by others who don't share their ideological blinders.
If you see three ants in the kitchen, the best estimate of the number of ants in the kitchen is much more than three.
The math peer review process can take months/years to decide on the correctness of a solution -- especially those written as sloppily as these AI proofs. Let's see what the numbers are once the dust settles -- how many of the 700 are correct, and how many of those are valuable.
> Let's see what the numbers are once the dust settles
I don't think you have a consistent argument or stance.
It seems your argument is that nobody should be reading the "AI slop" proofs, because if they were seriously studied, a lot of them will turn out to contain errors, and you know this because people have checked and found 1% of them to be wrong, which you knew even before anyone checked them, because nobody should be reading those proofs in the first place.
At least you'd be consistent if you keep arguing that it's going to be a waste of time to check them. You knew it right? Why even bother to see what the numbers turned out to be?
>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?
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.
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.
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.
> 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.
People seem to be very likely to say that LLMs are good at things that they don't want to do. That's also why you see so much of "well of course they can't do x, but they're great at y" but everyone has a different x and y.
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.
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.
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.
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.
the rest of the world wasn't interested in the results before and they won't be interested after
I can't speak for the rest of the world, but I think it's amazing that multiplication and 3SUM are sub-quadratic despite that being "obviously" impossible.
I wonder what this means long term.
Long term, stronger models than what OpenAI used will be available to everyone. Some mathematicians will take advantage of those tools and do great things; others will continue their whiny gatekeeping and become irrelevant.
> 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?
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?
I think it can both true that 1) OpenAI is being inconsiderate/harmful/<pick-whatever-adjective> with their math releases, and 2) there is now a treasure trove of mathematical results ready for the taking.
Yes, the situation sucks overall and mathematics as a whole is in a turbulent time now.
But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem. #2 above is still true regardless of where it came from or how hard it can be to absorb.
While reading "The Mathocalypse" post [0] by Scott Aaronson, Scott described his wife Dana's reaction to one of the newly solved results in her primary domain of expertise, on which she'd been working for decades.
After her initial shock, and annoyance with the format/style, she decided to start using Astra - for the first time - to help her understand the new result. And he reported in the comments that she had made a lot of progress understanding it in one day, and may be even excited to give a talk about it!
That seems like a much healthier attitude towards these new results.
Yes, everything else sucks about this messy period. But there are still diamonds (in the rough) in this drop that perhaps should be looked into. If the author is too busy, perhaps one of their students can take a look? Someone will, eventually.
Why are you two-siding this. There is only one misaligned agent here and that is the company OpenAI. What OpenAI is doing sucks, and people are calling OpenAI out for sucking. However mathematicians (the main victims of OpenAI’s lousy behavior) behave is not the issue here.
If some mathematicians complain about OpenAI sucking, that is fine actually, and if others are more “mature” about it, that that is fine too. Neither of these reactions should be at put as an equivalence to the blame OpenAI deserves for this stunt.
Dredging every inch of the lake to catch every single fish and dumping them all in one big pile the town square is just “solving fishing and releasing the fish to the public”, this anti-trawler hysteria is getting really funny.
Paraphrasing Hardy, 'exposition is for second-rate minds'.
I don't believe this myself. But I do believe that if you've formed your very ideas about what is good and desirable on the basis of a culture that has held certain values dear for hundreds of years, and have fought against every doubt and difficulty in life for decades to mold yourself into that image, that it does not 'suck' that you are unable to adapt to a new reality overnight.
Very few people that would love to be craftsmen would love to be factory foremen. It is far too insensitive to the human experience to expect people to just deal.
> Paraphrasing Hardy, 'exposition is for second-rate minds'.
Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.
Some people told themselves they were the pinnacle, the first-rate mind, as opposed to all the second-rater. Well guess what, now your first-rate mind is a commodity and exposition is more valuable. They'd better learn to live with it.
It turns out your an expendable commodity, and my computer system is predicting that society will profit from your annihilation, really sorry about that and I hope there's no hard feelings.
> Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.
Thankfully, very few mathematicians share Hardy's opinion, just as very few share his opinion that "mathematics is a young man's game" (and indeed we now have prizes like the Abel Prize with no age limit).
In fact, many of the greatest mathematicians throughout history have taken exposition very seriously, e.g. Euclid, Euler, Lagrange, Cauchy, Dirichlet, Kolmogorov etc. all wrote textbooks. Many mathematicians today carry on that tradition of taking exposition seriously and write books and freely share their lecture notes.
So we should not take Hardy's opinion as representing the opinion of all mathematicians or even most mathematicians. In fact, Hardy's statement is somewhat self-contradictory since he himself wrote several expository books (e.g. "A Course of Pure Mathematics").
His statement was self-deprecating (in a not so endearing way), as he was referencing his young self as one of those first-rate minds but his current old self doing exposition as second-rate.
I know that it was self-deprecating, but that doesn't redeem it much to me. I also still find it pretty contradictory/ironic because he wrote A Course of Pure Mathematics when he was in his early thirties.
A first rate mind communes with mathematics not matter terrestrial. An Uber-Erdos entering to lecture is indifferent to the auditorium as well as it's contents. He's at the board silently communicating new mathematics. Not for himself, not for you, but for mathematics.
> 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
I think the role of specific _human domain_ experts 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 this TCS problem that some of the staff are already familiar with
> But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem.
For me the problem is that rigth now the structure of incentives that has been built (e.g. you publish more = you get a grant; good exposition < solving a conjecture) is now broken. So, for instance, you would be very irresponsible if you throw your student into one of those AI papers, it's too much the risk. This part is mathematician's responsability, they need to change this incentives structure.
In any case, OpenAI is being a dickhead here. They throw millions of dollars at these problems, but they can't afford basic literature reviews (the drafts barely cite previous work)? Or checking that Lean's formalizations really correspond to what they claim to prove (even for Navier-Stokes they made this mistake)? It's obvious that for them this is just a PR stunt.
Let us not forget that there's much more to this than just OpenAI being lazy and incompetent and willingly ignoring the high standards that researchers usually holds themselves to.
There's also the case of ethical violations, straight up scientific misconduct, as when OpenAI steals results of others (their customers) and present them as their own.
> The result is also contained in a paper [8] released by OpenAI on October 6, 2026, in which the proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.
Of course it's hard to say what to make of that without knowing what exactly went into the machine, but it certainly looks bad. And there's obviously a non-zero probability that it is indeed another instance of plagiarism, given that that's how they operate.
In this case, the author is a grad student, so what we're looking at is a company willing to steal from a student, ignoring whatever impact that could have on their career prospects, for a tiny piece of marketing material.
At this point I would be surprised if internal sandboxes are not trivially by-passed and that openai's agents do not (at the very least) have complete read access to all user accounts, chat histories and uploaded documents. Orthonogally, openai could still be wholesale lying about not training on this user data, of course.
The relevant question here seems to be -- does anyone trust OpenAI to respect ethical and privacy boundaries when it slows their progress in an area they have identified as a corporate priority?
So... If you use ChatGPT for anything of value, including abstract stuff like obscure maths problems, you should assume that at some point in the future OpenAI will include that in their training set and sell it onto other people.
But this is even worse, because there is no way that OpenAI "trained" on this data between September 8, 2026, the date Chenglong Ma uploaded the paper to ChatGPT; and October 6, 2026, the date that OpenAI released a paper with "identical proof strategy and specific choices of notation" (Ma). That's one month, that's not the timescale for model training.
So this implies _not_ that OpenAI is training on user input, in the conventional sense of adjusting weights; but rather that they are *straight-up channeling ideas from user input*, and with a very short lag. You would think there would be about a million controls to prevent this.
This is next-level alarming. I would be very interested in knowing whether Chenlong activated the privacy (do not train, etc) options in ChatGPT, and any other details of their setup (which plan, etc). Also, note that "do not train" might be, in a lawyerly sense, considered by OpenAI to be strictly about weights, and not covering "we hoover up your results and regurgitate them".
They’re inhaling the plain text conversations of millions of people, why wouldn’t they have summarizers and anomaly detection sitting on top of conversation logs. What assurances does OAI provide that they are not reading your messages for any purpose? Don’t they “review conversations for safety” ? How would they do that if they couldn’t just query everything you ever said to the chatbot. If you can see it so can they.
> Part of me would like a little longer in the world where the problem is still open and I am still looking for its solution. But reaching a summit, even by someone else’s route, comes with a view. From here I can see new mountains, and I look forward to climbing them with my students, collaborators and the machines.
I think eventually there will be sort of a centralized more or less automated repository for ingesting and sorting ai-generated lean proofs and making them searchable and re-usable. On some level it kind of doesn't matter if mathematicians can ingest the results, if coding agents can just search for them online and use them in their own proofs.
I actually think it would be very smart for the big AI labs to get together to fund an independent organization to manage such a thing, and hire mathematicians to run it.
What is happening now is that some aspects of mathematics are turning into essentially an exercise in software engineering. It is well known that proofs and computer programs have an isomorphism, and I think the eventual merger is more or less inevitable.
That's not to say that there isn't an infinite amount of work remaining for mathematicians to do. There are only so many problems that are going to be amenable to this approach.
I think people sometimes overestimate what proving something means. For example the 4 color problem was a computer assisted proof from a long time ago. I doubt that many people actually read the proof even though leafing through the book is kind of fun if you can find a copy. Another example is the Kepler conjecture on sphere packing. The peer reviewers said they couldn't vouche for its correctness. While reviewers are volunteers with busy schedules, a lack of interest surely was part of the issue. This motivated Hales to formaly check his own proof (Gonthier formalized the four color problem earlier). But you can be sure that no one had been waiting for the Kepler conjecture to be proved in order to pack their spheres. Otoh, at the opposite extreme, the proof of FLT greatly advanced the field because the modularity theorem behind Wiles' proof is at the heart of a great section of math theory.
> there are still diamonds (in the rough) in this drop that perhaps should be looked into.
Right, and for some reason that "trillion dollar" company with mathematicians on staff didn't "look into" their own results. Almost like they don't care about engaging with the actual community they're dumping on.
To make an analogy: math is like OSS. You are free to fork and create your own feature, maintainer has no obligation to look at your PR and improve it to a state that’s worth merging.
Eg This happened to Zig where the Bun team maintained a fork for a while. And I’m sure there’re countless examples.
An instance of a maintainer finding a PR so interesting and keep digesting it and eventually even give a talk about it, is irrelevant. It is entirely their free will to do so.
These aren't results yet. They're potential results, but to find out we'd have to get a human mathematician to sift through a metric shitload of LLM hallucinations to see if there's a nugget of truth somewhere in there.
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.
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.
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.
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[ 0.23 ms ] story [ 16.4 ms ] threadIt looks like people are enjoying themselves, having fun with the new results, and generally doing all of the things you say "science" is supposed to be about. So what's the problem?
https://www.youtube.com/watch?v=LKiBlGDfRU8
As the author of the post points out, there is no way this is “the best they could do”. It’s a write up that didn’t involve someone with the math + communication skills required to clearly explain the result.
They normally don't feel like they are in some kind of race to publish the results ASAP and claim priority. Cases like that are very rare (but they get media coverage because they are so unusual).
OpenAI did a publicity stunt, their motivation is not to make a good contribution to the field, which has very different standards and culture, compared to the AI labs.
They don’t have any more patience for this.
I even think it's plausible a lot of mathematicians are excited by it, but the sweeping confidence of the comment you replied to without anything to back it up leaves some to be desired
There's a "Silicon Valley-ism" for you. We offer a thing in whatever form we want and people "who are passionate" will gobble it up, should gobble it up, 'cause they're "passionate".
It is entirely possible that one day progress just stops or slows down, but with current evidence, I don't find that too likely - at least not in the near future. The sheer amount of resources being put into this (AI) race is mind-boggling.
So while past performance does not guarantee future results, I'm just going to kick back, and assume that many of the current issues will be fixed with future models.
Maybe this is just a matter of what model developers choose to invest training resources in, but I don’t think it’s inevitable unless clarity is made a higher priority
The problem is that right now mathematicians don't have the economical incentive to read these AI generated results. Even if you love mathematics and all that, it's always more important to get a job, and for that it doesn't seem like a good idea to invest time around problems that AI touches because you can't compete with it and you don't know if tomorrow they'll improve by x10 the sota.
Of course, it's not clear at this point whether reporting such a result even matters, but still. In its own right, it's a very cool result.
What do you do if those results suck like in the article?
The term SOTA suggest that you approach this from a perspective other than a pure mathematician's, maybe ML or computational complexity? The openai results help me answer other open questions. It's a yes/no thing: is question answered or not? It's not a question of "okay, but will AI win back the SOTA from me again?"
But providing the answer in gibberish along with a certificate is not that, it's at best a cruel way to do it, but I'm leaning towards the idea that it's a fundamental misunderstanding of what it means to do math and what it means to communicate a result.
If you think sending an answer in gibberish is acceptable just because it's true then SSdtIG5vdCBzdXJlIHdoYXQgdG8gdGVsbCB5b3UsIGJ1dCB3ZSBkaXNhZ3JlZSBvbiB0aGF0.
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
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.
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.
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.
??? That's literally what everyone does. You are creating a hypothetical that is nonsensical. Here's your hypothetical:
1. Agent gives you 5000 lines of slop
2. You reject it and just do it yourself
This is reality
1. Agent gives you 5000 lines of slop
2. you realise that it has done a lot of research and is mostly in the correct direction and you ask it nicely to refine it
3. verify that you understood it and push it to prod
Are mathematicians babies that they need a completely different approach?
1. the proofs are hard to read
2. but are still sufficiently high enough signal to understand the proof
3. blaming OpenAI for releasing high signal information on important problems is wrong. OpenAI did the right thing here.
4. the mathematicians can take however long they want to digest it and verify it. They have no legal obligation to do it immediately
This is exactly how I'd like society to work. Publish and let information get democratised quickly.
How could you possibly know that? If you don't have the knowledge to understand the paper without using a chatbot, you don't have the knowledge to verify that what the chatbot said is the same thing as what's in the paper.
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.
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).
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.
To me, science is not a database of facts and data, and the scientific process is not just the process of adding to this database.
It is more than that.
Science is building the database of facts and data, but it is also sharing/disseminating that database.
We both agree that "openness" is critical for this, but to me, the scientific process includes things like the actual words that a scientist uses to communicate their ideas/data, the paper they wrote, the collaborations they had, the work that they built upon. Science is not like a database only - its more like a distributed system, and the scientific community is like a living, breathing thing. It is the health of that system which has been damaged in my opinion.
So I have no problem that OpenAI updated the database.
They didn't just make the information available though.
They updated the knowledge database, then released low quality slop papers.
They made it clear that they don't give a damn about sharing/disseminating information.
They are trying to fundamentally say "we can do science without prioritizing sharing.
We don't think its important. We'll release the proof because it makes our stock go up, but we're gonna keep going and building and not spend any time on communication or comprehension because we think that it doesn't matter, and your contributions don't matter, and AI is gonna do all of this independently anyway. We spent $20m on the proof because it made our stock go up $20b, but we'll spend 20 min on the paper. Priorities clear.
Does any of that make sense?
The thing is, that is a "nice to have", not a condition to make science.
If people believe that such things are useful, then the appropriate response is to reproduce, simplify and otherwise make the proofs provided into more easily digestible pieces.
The scientific process is fundamentally indifferent to whatever shibollets and cultural hangups that its presumed participants may have. An alien with fundamentally different norms from us, who experiments to determine the boiling temperature of water is doing science just as much as a human, even if he never submits a paper to a journal.
The issue you're having is that you're under the mistaken belief that the scientific process is the "community" and "norms" that happen to have developed over the past few centuries by this "scientific" priesthood.
It is not. It has never been. It will never be.
This "scientific" priesthood has simply used their power and reputation to enforce their own self-aggrandizing norms, much like the religious priesthood they replaced. They should not be taken seriously, and to go along with these norms when they are unnecessary is frankly ridiculous and shameful for anyone who actually prizes results.
I would urge you to reconsider your stance, and in particular to put deep thought into why you believe these norms are so important.
https://proofsandprompts.com/2026/10/08/100-reactions-to-100...
And then tell me that this has not damaged the mathematics community.
I would urge you to reconsider your stance, and in particular to put deep thought into why you believe OpenAI is not going about this wrong.
Fundamentally the main points being made seem to boil down to this excerpt from Tristan Humbert:
>Open AI claimed a proof of the conjecture in full generality this morning and my first impression was sadness to see my favorite problem get “killed” by AI ; it is definitely easier to ignore a problem when it does not affect you directly. Next, I felt stressed because I am currently applying for postdocs and more of my research plan was now obsolete and I spent the whole morning rewriting everything and sending emails to my advisors in panic. Finally, I felt anger after opening the paper and observing that it was mostly unreadable slop.
They're essentially angry at "They did before i could", and "Now i don't have a job" and "I dislike how it is written".
It just reinforces the "scientific priesthood" theme.
These are people who had their livelihoods and status derived from this thing which is now fundamentally obsolete, and they are scared and upset that they will no longer have those things.
That's fine, its a normal human reaction. God knows i'm not sure i will have a job in 5 years because of AI!
But we should not be taking it with any more seriousness than we would take a ludite gripping about the mechanization of cloth manufacturing.
The truth is, the value produced by their job just fell off a cliff. They need to find something else that provides value to replace it. That's it. Being upset about it isn't going to be productive.
Perhaps the value they can make is to rewrite the AI proofs to a more understandable format. Perhaps it is to go flip burgers at McDonalds. That's up to them, but i would suspect that calling releasing valuable information as "bad for science" is not very value accretive.
This part I don't understand. Not that anyone should read the entire Lean code of any proof, but if the statement of the theorem to be proven in lean seems to be correct, then I would think there would be at least some interest if in fact there was a formal proof (which might or might not correspond to the written proof) of something I was working on. That to me would be interesting. Or you are saying you doubt the validity of the formal proof, which would also be interesting. But saying it is of no consequence doesn't make any sense to me.
It would be like trying to look at a completed video game's assembly code, being told that it was call of duty, and then being asked questions about the high level code architecture.
AI models are perhaps unsurprisingly good at low level translation (see the progress being made for decomp games)
These models have surpassed human capabilities at math/machine code, but they can't "simplify" yet - in part because they don't have the same need to due to their comparative lack of cognitive constraints. AI Slop code is getting better, but it takes time. At the moment, its embarrassing frankly. It will come eventually, but right now OpenAI is not handling this with the care, respect, or concern that it deserves.
If you have a 20-40 IQ points gap with another developer, this happens a lot.
The baseline of "simplify" is wildly different based on your IQ points. That's precisely why exceptional students are usually bad in teaching. They try to break things down, simplify, but things still go over the head of normies.
However, we can intervene/train the models. So it should be possible to focus on the simplification, and as you said, it will come eventually.
Those who really understand a topic are usually also able (and great at) explaining it in very clear and "simple" terms. This may be part of my personal bias; I see theory builders as those who advance the field the most, and these are usually also amazing at explaining it. On the other hand, those who mostly "grind" through problems (approach them as complicated puzzles) with effort/time were often bad at explaining.
I observed the same for programming: the "architects" usually explain very well, the "debuggers" often don't. LLMs very much remind of the grind/puzzle approach. It does makes sense that RLVR, which in my understanding enables a lot of these results, would lead to a more mechanical approach.
Of course, I can't make any predictions on whether it will stay that way. But I strongly suspect that we need different ways of training for LLMs to write better text and explain better (I suspect the vagueness of LLM language is the result of RLHF as vague expression is less often incorrect).
Let's assume you have an IQ of 135. You are not that far from even the crazy smarts at 150 and as long as they have some social skills, it will work out. I, myself, never had issue with understanding the smart people.
Now let's assume you have an IQ of 110. Unless 140/150 IQ people are spending inordinate amount of time formulating how to simplify things for you, things will fly above your head.
This does not mean just because someone is 150, and someone is 110, the 110 is always the problem.
This also does not mean an 120 explaining something to 140, and failing is 120's fault or the other ones'.
Every combination is possible as we are talking about personalities/ability to articulate oneself.
However, I was talking about a specific scenario, which I have faced myself and saw it happen a lot of times (to other people), where someone's simplification level is still higher than someone's max understanding level simply because the deviation between their caliber is too great. In most cases, this can be worked around by the explainer spending inordinate amount of time.
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.
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
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.
If you did’t bother to write it, I shouldn’t be bothered to read it.
Perhaps AI agents can have their own publications and magazines where they are the chairs and associate editors and reviewers.
If AI can solve such grand, outstanding math problems, and mathematicians argue these pure math problems are important, what’s the problem with them needing to read the output if they want to understand it?
You don't think this changes when the thing in question is a proof of a STEM problem no human has ever been able to solve?
We'll see what the final slop rate is, but the three papers they retracted yesterday were for a trivial sign error. If they didn't catch that, that means OpenAI wants credit for solving problems, without the effort of sifting through their own garbage and making sense of it.
It's not like they needed to hurry out this release before carefully vetting. They're just "hacking" the math system and disrupting the work of thousands of researchers to create a gigantic RL dataset for themselves.
Really, what's the bloody hurry?
They could have released 1-5 papers, worked with researchers to understand what methods work and what don't, how to prompt the models better, how to build better guardrails for reasoning, etc. And give those researchers access to latest models and empower then to solve thousands of problems!
Instead OpenAI wants to piss all over the city to claim territory and now human mathematicians have to go around cleaning up that slop, only so that OpenAI can made some bullshit statement like: math is solved [mistakes are next].
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Imagine someone gave you a million line PR claiming to have vibecoded the operating system of the future (or whatever your application domain). Would you drop all your other work to focus on this?
And they generate enough PR that your manager and company leadership and public all start pressing you to accept it quickly?
If it verifiably works and solves important outstanding issues, then quite possibly yes.
If a human published 700 papers and only 3 (or 30) ended up having significant errors, I'd call that a pretty good batting average, considering that the typical rate of errors may be around a third (https://lamport.azurewebsites.net/pubs/statistics.pdf). But for some reason people hold AI output to an absurd standard where if it's not 100% perfect then it's useless.
You're basically asking them to turn off their immune system
I'm not asking "them" to do anything. They can do whatever they want, including rejecting obviously useful tools. But then they shouldn't be surprised when they're quickly surpassed by others who don't share their ideological blinders.
The math peer review process can take months/years to decide on the correctness of a solution -- especially those written as sloppily as these AI proofs. Let's see what the numbers are once the dust settles -- how many of the 700 are correct, and how many of those are valuable.
I don't think you have a consistent argument or stance.
It seems your argument is that nobody should be reading the "AI slop" proofs, because if they were seriously studied, a lot of them will turn out to contain errors, and you know this because people have checked and found 1% of them to be wrong, which you knew even before anyone checked them, because nobody should be reading those proofs in the first place.
At least you'd be consistent if you keep arguing that it's going to be a waste of time to check them. You knew it right? Why even bother to see what the numbers turned out to be?
...
>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?
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.
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
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.
> 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.
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.
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.
How would you know that the new paper contained the same content as the original (let alone the actual Lean code)?
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.
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.
I can't speak for the rest of the world, but I think it's amazing that multiplication and 3SUM are sub-quadratic despite that being "obviously" impossible.
I wonder what this means long term.
Long term, stronger models than what OpenAI used will be available to everyone. Some mathematicians will take advantage of those tools and do great things; others will continue their whiny gatekeeping and become irrelevant.
Strong and cheap enough to make solving these problems by this approach less than a million-dollar venture?
(Pedantry: We already knew that integer multiplication, at least, was O(n log n). which is subquadratic.)
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-...)
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?
Yes, the situation sucks overall and mathematics as a whole is in a turbulent time now.
But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem. #2 above is still true regardless of where it came from or how hard it can be to absorb.
While reading "The Mathocalypse" post [0] by Scott Aaronson, Scott described his wife Dana's reaction to one of the newly solved results in her primary domain of expertise, on which she'd been working for decades.
After her initial shock, and annoyance with the format/style, she decided to start using Astra - for the first time - to help her understand the new result. And he reported in the comments that she had made a lot of progress understanding it in one day, and may be even excited to give a talk about it!
That seems like a much healthier attitude towards these new results.
Yes, everything else sucks about this messy period. But there are still diamonds (in the rough) in this drop that perhaps should be looked into. If the author is too busy, perhaps one of their students can take a look? Someone will, eventually.
[0] https://scottaaronson.blog/?p=10169
If some mathematicians complain about OpenAI sucking, that is fine actually, and if others are more “mature” about it, that that is fine too. Neither of these reactions should be at put as an equivalence to the blame OpenAI deserves for this stunt.
I don't believe this myself. But I do believe that if you've formed your very ideas about what is good and desirable on the basis of a culture that has held certain values dear for hundreds of years, and have fought against every doubt and difficulty in life for decades to mold yourself into that image, that it does not 'suck' that you are unable to adapt to a new reality overnight.
Very few people that would love to be craftsmen would love to be factory foremen. It is far too insensitive to the human experience to expect people to just deal.
Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.
Some people told themselves they were the pinnacle, the first-rate mind, as opposed to all the second-rater. Well guess what, now your first-rate mind is a commodity and exposition is more valuable. They'd better learn to live with it.
Thankfully, very few mathematicians share Hardy's opinion, just as very few share his opinion that "mathematics is a young man's game" (and indeed we now have prizes like the Abel Prize with no age limit).
In fact, many of the greatest mathematicians throughout history have taken exposition very seriously, e.g. Euclid, Euler, Lagrange, Cauchy, Dirichlet, Kolmogorov etc. all wrote textbooks. Many mathematicians today carry on that tradition of taking exposition seriously and write books and freely share their lecture notes.
So we should not take Hardy's opinion as representing the opinion of all mathematicians or even most mathematicians. In fact, Hardy's statement is somewhat self-contradictory since he himself wrote several expository books (e.g. "A Course of Pure Mathematics").
Wait, who are those people? Who is that Hardy and what did he really say? What did he really mean? Who else said or meant the same things?
Who are you criticising, exactly?
A first rate mind communes with mathematics not matter terrestrial. An Uber-Erdos entering to lecture is indifferent to the auditorium as well as it's contents. He's at the board silently communicating new mathematics. Not for himself, not for you, but for mathematics.
It might be a shock for you but they are very few in numbers. Most of researchers I know are always busy with something. They cannot just drop other responsibilities for something like this. They will take their own time getting through the proofs (if they want to).
> That seems like a much healthier attitude towards these new results.
Another thing to consider is not all mathematicians are from US or with good funding. The PI or graduate students cannot afford to pay 200/month.
TFA was about a niche topic that OpenAI doesn't have in-house expertise in.
Otoh Aaronson is the co-author on Lijie Chen's (reasoning lead at OAI) top cited paper. OAI have deployed their resources more effectively against UGC that some of their staff are already familiar with
https://scholar.google.com/citations?user=T_OhvOsAAAAJ
https://finance.biggo.com/news/B0eMxZsBy4YEFZDUVPWh
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 this TCS problem that some of the staff are already familiar with
https://scholar.google.com/citations?user=T_OhvOsAAAAJ
https://finance.biggo.com/news/B0eMxZsBy4YEFZDUVPWh
For me the problem is that rigth now the structure of incentives that has been built (e.g. you publish more = you get a grant; good exposition < solving a conjecture) is now broken. So, for instance, you would be very irresponsible if you throw your student into one of those AI papers, it's too much the risk. This part is mathematician's responsability, they need to change this incentives structure.
In any case, OpenAI is being a dickhead here. They throw millions of dollars at these problems, but they can't afford basic literature reviews (the drafts barely cite previous work)? Or checking that Lean's formalizations really correspond to what they claim to prove (even for Navier-Stokes they made this mistake)? It's obvious that for them this is just a PR stunt.
There's also the case of ethical violations, straight up scientific misconduct, as when OpenAI steals results of others (their customers) and present them as their own.
One particularly bad one came yesterday: https://arxiv.org/abs/2610.10072
> The result is also contained in a paper [8] released by OpenAI on October 6, 2026, in which the proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.
Of course it's hard to say what to make of that without knowing what exactly went into the machine, but it certainly looks bad. And there's obviously a non-zero probability that it is indeed another instance of plagiarism, given that that's how they operate.
In this case, the author is a grad student, so what we're looking at is a company willing to steal from a student, ignoring whatever impact that could have on their career prospects, for a tiny piece of marketing material.
But this is even worse, because there is no way that OpenAI "trained" on this data between September 8, 2026, the date Chenglong Ma uploaded the paper to ChatGPT; and October 6, 2026, the date that OpenAI released a paper with "identical proof strategy and specific choices of notation" (Ma). That's one month, that's not the timescale for model training.
So this implies _not_ that OpenAI is training on user input, in the conventional sense of adjusting weights; but rather that they are *straight-up channeling ideas from user input*, and with a very short lag. You would think there would be about a million controls to prevent this.
This is next-level alarming. I would be very interested in knowing whether Chenlong activated the privacy (do not train, etc) options in ChatGPT, and any other details of their setup (which plan, etc). Also, note that "do not train" might be, in a lawyerly sense, considered by OpenAI to be strictly about weights, and not covering "we hoover up your results and regurgitate them".
I don't see how it's related to quality at that point. Call your technique "the banana method" and wait to see OpenAI invent "the banana method"
No it doesn't. Hundreds of open problems in a STEM field getting solved at once does not suck at all.
You would have to be deeply jaded and cynical to conclude that.
https://dakshitakhurana.substack.com/p/classical-at-heart
I actually think it would be very smart for the big AI labs to get together to fund an independent organization to manage such a thing, and hire mathematicians to run it.
What is happening now is that some aspects of mathematics are turning into essentially an exercise in software engineering. It is well known that proofs and computer programs have an isomorphism, and I think the eventual merger is more or less inevitable.
That's not to say that there isn't an infinite amount of work remaining for mathematicians to do. There are only so many problems that are going to be amenable to this approach.
Right, and for some reason that "trillion dollar" company with mathematicians on staff didn't "look into" their own results. Almost like they don't care about engaging with the actual community they're dumping on.
You speak of this as if the default is to engage.
To make an analogy: math is like OSS. You are free to fork and create your own feature, maintainer has no obligation to look at your PR and improve it to a state that’s worth merging. Eg This happened to Zig where the Bun team maintained a fork for a while. And I’m sure there’re countless examples. An instance of a maintainer finding a PR so interesting and keep digesting it and eventually even give a talk about it, is irrelevant. It is entirely their free will to do so.
These aren't results yet. They're potential results, but to find out we'd have to get a human mathematician to sift through a metric shitload of LLM hallucinations to see if there's a nugget of truth somewhere in there.
Academics have always been required to engage with hacks and cranks to some extent; the deluge of AI proof writing has only exacerbated the problem.
English speakers generally use this word in a very broad sense “and now Netflix is forcing ads on paying users”, “because there was no sink, I was forced to drink the whole thing”. It is only when you are literally describing a crime where this word has this strict meaning you are alluding to.