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.
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 can't relate to this at all. AI models will surely get better at writing "enjoyable proofs," but for now the situation is what it is. You're passionate about this problem, right? But you don't want to do the work to understand the result? Fine. There's a new generation of younger, hungry mathematicians that are highly interested in figuring out why the result is true and I am sure they'd be happy to wade through it and spoon-feed you the answer instead. Maybe they should be running things.
Knowing a few PhD candidates and non-tenure track postdocs, the “younger, hungry mathematicians” are more worried about finding a damn job in the poorest job market - both academic and in industry - in a decade.
The problem here is that while you can call what OpenAI does "mathematics", I would hesitate to call it science. Science as a process of acquiring and developing knowledge within a domain involves a lot more than just dumping unfinished work on the scientific community. Among other things, it involves developing frameworks and understanding of the domain, formulating questions, creating results in a fashion suitable for verification/testing/replication, and relating these results to and integrating them with that edifice.
Have you looked around recently? Because there are plenty of mathematicians that are excited to read and learn about all of the new results. They've improved on the sub-n log n result and have even made a web site to track progress on it: https://beyond-n-log-n.netlify.app/
It looks like people are enjoying themselves, having fun with the new results, and generally doing all of the things you say "science" is supposed to be about. So what's the problem?
I didn't say it is useless. Consider Ramanujan, whose work gave rise to a lot of interesting math, even (and sometimes, especially) the parts that lacked proofs or had other gaps (probably because it was obvious to him). But a singular genius, whether a person or a machine, does not science make.
Kinda sounds like computer science vs developing - in the sense that people with a master's in CS and are dedicated to the craft will write wonderfully artistic software, while it doesn't actually take a love for the process to write code and get hired at some tech company (even less so now with agentic development).
Not what I am getting at. In fact, the problem I am getting at is the abolition of existing scientific and engineering principles and processes without a replacement and applies to programming with agents as well. This is not about artistry, but about building durable things.
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.
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".
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.
So OpenAI should be able to flood the world with AI pollution and ask scientists and mathematicians to wade through it all and tell us if there is any sense in it, then sit back and wait for them to report in?
OpenAI in fact didn't know what to do with results and didn't want to flood the world, so they asked mathematicians. Mathematicians recommended OpenAI to release them. My guess is it would have been better for OpenAI if they didn't release them. OpenAI is basically doing this as a goodwill.
People seem to have very misguided ideas about why OpenAI is doing this at all. It is not to brag or to torture mathematicians. It is an eval. OpenAI is known to be willing to pay large amount of money to get a good eval, think FrontierMath. FrontierMath is now saturated, so they need a replacement eval for math. Open math problems are actually a fairly good eval, although a proper eval is better (eg FrontierMath has known difficulty and have tiers from 1 to 4).
Mathematicians would prefer if OpenAI didn't use open math problems as an eval, but OpenAI is not obliged. I actually think OpenAI wouldn't point AI to open math problems if unsaturated FrontierMath Super Duper is available, as it just angers mathematicians, but such eval is not in fact available. Given OpenAI used open math problems as an eval, they could just throw out the result (this is in fact better as an eval since it will keep problems useful longer), but mathematicians preferred to see the result. So OpenAI released them.
Yes, they should. They have invented a magic button that can tell you the long-awaited answers to the burning mathematical questions that you've spent your life researching. The caveat is that the technology is still new, so the explanations "are not fun to read" like set theory papers usually are (lol). If you don't think that's a worthwhile tradeoff, that's your call, but it sure as hell isn't everyone's.
I don't think the claim is "they definitely have an oracle that solves the problem, and I reject it because it's hard to read". The claim is "OpenAI claims to have used an oracle to solve the problem. The proof is very difficult to read, and to even know if it does or not, we have to go through it with a fine-toothed comb, but they're going around claiming they definitely solved the problem (or at least getting press that claims that which they aren't pushing back against) and this might convince the people who sign grants even if it isn't true"
People who are invested in the idea that we've invented a general intelligence, now, which includes all these companies that are literally financially invested in this claim they are making, will tend to believe that its results can already be trusted in domains like this. Some mathematicians seem to believe some of the proofs written by their models, and some, like this one, don't. I do think it's valid for an expert to push back against the claim that the best use of their time right now is to verify the poorly written work of everyone who's claimed to solve the problem
Over the year, nothing they've released with a lean proof attached has turned out false (That's sort of the entire point. It's not impossible but it's really difficult). There's a reason most mathematicians, including the ones vehemently against OpenAI's dumping are not arguing the results are secretly false or have a high potential to be. And indeed, if that were the case, it would quickly become apparent and all this worry about grant signers would vanish into the wind. It's very easy to ignore nonsense. The problem is that it isn't nonsense.
I really don't know enough about it to know whether you're right or not, nor do I know whether or not you know enough to make the claim you're making, so I won't make an argument one way or another because it's non-sequitur to what I said anyway. The fact that you or I or Sam Altman or Terrence Tao believe the claim is irrelevant to whether this obligates the person who wrote the blog post to believe the claim, and it sounds like he's willing to consider the possibility that it is right, and would read the paper if it reached a threshold of comprehensibility expected of people making that kind of claim.
I don't understand. Why is this the onus of scientists and PhDs to review whatever results OpenAI had dumped out? If OpenAI had produced incomprehensible papers, surely any journals would just reject it, or demand the author to do a complete rewrite? Unless we are talking about a race to solve problems, which PhDs are afraid that they had been scooped up on?
The problem isn't just that the papers aren't fun to read. The problem is that a lot of the research that goes into solving these issues leads to other discovers, new fields to explore and people have to develop new approaches to solve them. The other part of it is, the quality and the enjoyment of working on these problems leads people to find new and other interest problems to work on.
If you just strip mine the answers and Sam Altmans magic button solves 100/100 problems, what's next? Who is left to come up with a new interesting question for the magic button to solve?
Lastly, life and the present moment is all there is, if there is no enjoyment in anything we do, then what's the point of all the "living for ever" Altman et al want to achieve.
We will live forever to read boring papers generated by LLMs? Literally sounds like an eternal hell.
Nuclear fusion is already proven by the universe to be a viable energy source by the fact that the sun exists but people still work on understanding and taking it and developing new approaches to accomplish it. People didn't stop experimenting with and developing programming languages because technically they're all turning complete and the first one was "enough." Y'all will be fine - every JavaScript framework that exists is someone looking at a theoretically correct and complete solution and deciding actually it sucks and they could do better. "I want to understand xyz but the proof is trash and I think it's ugly" will be plenty motivation for a lot of people to work on it.
He's tracking the community progress on sub-n log n multiplication. OpenAI started with 1 - 1.63e-55. The result has been now improved on 115 times, and the current record is "rohanarun"'s 1 - 9.87e-5. I'm sure by tomorrow it'll have improved again.
Does this look like people aren't having fun? Does it look like they aren't discovering stuff? It looks like it's spurred a cascade of interesting community activity. It doesn't really seem much different from what happened with the twin primes conjecture. Isn't that supposed to be the point of all this?
They should certainly be allowed to share their findings. No one is forcing scientists and mathematicians to review the findings in general. It’s just the case that the findings are of such such a quality that it would not make sense to ignore them wholesale
> No one is forcing scientists and mathematicians to review the findings in general.
This is like "no one is forcing software engineers to use AI tooling" or "no one is forcing you to show your ID in the airport" or "no one is forcing you to own a car in your small midwestern city" - there can be no law requiring something and the practical consequences of not doing so can be so painful that you're effectively forced anyway.
The best part is that when the academics fix OAI’s issues, the model gets better and OAI shareholders get richer and more powerful!
As someone who uses LLM tech occasionally, this is why I prefer using open local models. If I’m making myself obsolete, at least I’m not making some asshole richer and their closed model better.
You know, I kinda relate to the feeling of not wanting look at those outputs if I think of it from a layman's perspective.
I just imagined that instead of math papers, they released 700+ feature length films, and the only way to tell if one of them is any good is to watch it in its entirety.
That feels pretty unappealing to me.
I know it's the same for human made films, so what's the difference right? But those are good enough most of the time that it's a decent bet, and the people that made them had real skin in the game.
Contrast that with something made by a nondeterministic slop machine with no skin in the game where small details can be off in a way that's jarring. Right out the gate I have an aversion to committing that much time to something that very well may waste it.
That's actually a really interesting thought. Given Sora, and the amount of funding they have, they could have created started their own film festival and dropped 700+ feature length films, had they wanted to go in that direction. But they didn't. Hmm.
What else should they do? See these models get smarter and smarter, somewhat-solve things but only to the tune of 90% what mathematicians (or experts in any other field) would deem acceptable, and then gate keep the findings for the next few years going through peer review and paywalled journals? I for one welcome the flood, bring on more in every possible industry and see where all that progress lands up. Sure it will upset a lot. A lot of things also upset the luddites.
> this is an opportunity for people to pick up where the model left off and run with it
Like people enjoy racing in front of a stopped train? As soon as they turn on the engine again, they will run you over. The questions that remain will be only the low value ones, not worth the effort to vacuum up.
So no, the smarter, hungrier people are not the ones that are going to swoop in. It will be the most desperate.
> Some output is going to be wrong or incomplete
This is a very human take on the situation. No, the Lean proof is not going to be wrong, and it will be incomplete only in the sense that OpenAI didn’t try to push the results further.
Are you going to be doing the work to verify the results ? Will you just expecting other people to wade through the flood and reap the benefits later on?
Nobody is forced to verify the results. I am honestly not expecting anything other than AI to get smarter and smarter and people who are motivated and interested enough to pick up after it; and potentially reap all the long term benefits ahead of those who aren’t (seeing this happening with software development in my own field). But in the end; if you don’t like it, you’re not forced to do anything.
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?
"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.
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.
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.
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.
At first I thought this was going to be more Luddite babble, but it makes a good point. OpenAI isn't contributing if they are make unreadable papers. They should use a little more of their compute to nail interpretability. The difficulty will only get worse as AI plow deeper into the frontier and produce increasingly alien looking output. I suspect it's a workflow issue. If not, it's a bad oversight if the current generation of models are capable of making mathematical breakthroughs but can't explain how they build on existing frameworks.
Work this abstract almost certainly has no value outside the community that is (was) interested in the result. OpenAI should engage with the community to realize the value (beyond PR).
> 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?
>OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why?
...
>So, no, I will not be sending Sam Altman a bottle of whisky anytime soon, nor I am planning on spending my time reading through that paper and trying to make sense of it.
Think about a hypothetical circumstance where we get radio communication with some aliens on another planet. They send over tons of math to help us advance our tech, we know the math they're sending us is correct, but their explanations are really hard to work through because they aren't humans and the math is so different from anything we've done. Should we whine about the results they sent to us and refuse to engage with it?
Love your metaphor here. I guess there will always be people who try to keep going and follow their current projects and say that only human math is real math and we should only use alien technology for proofreading mails and such but not their highly established and esteemed professions.
Or just keep your hubris low, update your priors, work towards progress.
In this hypothetical case funding agencies would probably happily pay for “alien maths translation grants” and you could write papers about advances in that field and get jobs etc. So arguably for better or worse it would create a specialised academic cottage industry that somehow interfaces with the rest of maths.
I would admit seeing more mathematicians irritated is a good popcorn show.
For what's worth it, this batch of results are not very tight intentionally by OpenAI and promising mathematicians already started to consume them and improve the results, while someone is still complaining on it.
openai 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
Very well written summary of the current situation
Imagine being someone who is working on one of these problems. You have no good guarantee that the problem was solved, but you will have the horrible homework of reading the AI slop. Also, if you do have something interesting to say about the problem, people will have less enthusiasm about it now
I am no mathematician, but I can definitely relate to the "horrible homework of reading AI slop". We've started allowing a non-developer to submit AI generated code into our codebase (in droves).
When I am tasked with reviewing that code. First, I don't know if it's valid. The person who wrote it doesn't know if it's valid. In order to validate it I must step back and understand the full problem space. Then, when I ask for revisions or clarifications, it's seen as either
A - Slowing progress, being resistant to change... or...
B - Thanks for catching that (Claude fix PR 532 with the review comments)
It's 100% removed the enthusiasm.
Perhaps, there is a point where we just "give up" the understanding and accept AI output as the ground truth, because the sheer amount of generation is too much for our puny human minds to comprehend, and a lot of the times it IS right, even if a little wonky.
The gradient into formalisms is steep and the bottom is deep. These are the worst results anyone will ever see again. The bottom of the internet is also deep, but won't be around much longer.
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'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
Most software developers (or people in any field, working for anyone) rarely own anything they do at work.
And the entrepreneurs running their own companies (which there's an explosion of atm largely because of AI) do indeed "own" the higher-level products and things they're producing, even if AI writes the code.
> 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.
> 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.
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.
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.
I think it can both true that 1) OpenAI is being inconsiderate/harmful/<pick-whatever-adjective> with their math releases, and 2) there is now a treasure trove of mathematical results ready for the taking.
Yes, the situation sucks overall and mathematics as a whole is in a turbulent time now.
But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem. #2 above is still true regardless of where it came from or how hard it can be to absorb.
While reading "The Mathocalypse" post [0] by Scott Aaronson, Scott described his wife Dana's reaction to one of the newly solved results in her primary domain of expertise, on which she'd been working for decades.
After her initial shock, and annoyance with the format/style, she decided to start using Astra - for the first time - to help her understand the new result. And he reported in the comments that she had made a lot of progress understanding it in one day, and may be even excited to give a talk about it!
That seems like a much healthier attitude towards these new results.
Yes, everything else sucks about this messy period. But there are still diamonds (in the rough) in this drop that perhaps should be looked into. If the author is too busy, perhaps one of their students can take a look? Someone will, eventually.
[0] https://scottaaronson.blog/?p=10169
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 can't relate to this at all. AI models will surely get better at writing "enjoyable proofs," but for now the situation is what it is. You're passionate about this problem, right? But you don't want to do the work to understand the result? Fine. There's a new generation of younger, hungry mathematicians that are highly interested in figuring out why the result is true and I am sure they'd be happy to wade through it and spoon-feed you the answer instead. Maybe they should be running things.
Knowing a few PhD candidates and non-tenure track postdocs, the “younger, hungry mathematicians” are more worried about finding a damn job in the poorest job market - both academic and in industry - in a decade.
They don’t have any more patience for this.
The problem here is that while you can call what OpenAI does "mathematics", I would hesitate to call it science. Science as a process of acquiring and developing knowledge within a domain involves a lot more than just dumping unfinished work on the scientific community. Among other things, it involves developing frameworks and understanding of the domain, formulating questions, creating results in a fashion suitable for verification/testing/replication, and relating these results to and integrating them with that edifice.
Have you looked around recently? Because there are plenty of mathematicians that are excited to read and learn about all of the new results. They've improved on the sub-n log n result and have even made a web site to track progress on it: https://beyond-n-log-n.netlify.app/
It looks like people are enjoying themselves, having fun with the new results, and generally doing all of the things you say "science" is supposed to be about. So what's the problem?
I didn't say it is useless. Consider Ramanujan, whose work gave rise to a lot of interesting math, even (and sometimes, especially) the parts that lacked proofs or had other gaps (probably because it was obvious to him). But a singular genius, whether a person or a machine, does not science make.
Kinda sounds like computer science vs developing - in the sense that people with a master's in CS and are dedicated to the craft will write wonderfully artistic software, while it doesn't actually take a love for the process to write code and get hired at some tech company (even less so now with agentic development).
Not what I am getting at. In fact, the problem I am getting at is the abolition of existing scientific and engineering principles and processes without a replacement and applies to programming with agents as well. This is not about artistry, but about building durable things.
How about the scenario where they are already better if you give them more time/tokens/…? Would it be a more relatable concern in that case?
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.
You're passionate about this problem, right?
There's a "Silicon Valley-ism" for you. We offer a thing in whatever form we want and people "who are passionate" will gobble it up, should gobble it up, 'cause they're "passionate".
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.
So OpenAI should be able to flood the world with AI pollution and ask scientists and mathematicians to wade through it all and tell us if there is any sense in it, then sit back and wait for them to report in?
Nice idea.
OpenAI in fact didn't know what to do with results and didn't want to flood the world, so they asked mathematicians. Mathematicians recommended OpenAI to release them. My guess is it would have been better for OpenAI if they didn't release them. OpenAI is basically doing this as a goodwill.
(See https://agmai.org/general-sep29/ for the recommendation in question.)
People seem to have very misguided ideas about why OpenAI is doing this at all. It is not to brag or to torture mathematicians. It is an eval. OpenAI is known to be willing to pay large amount of money to get a good eval, think FrontierMath. FrontierMath is now saturated, so they need a replacement eval for math. Open math problems are actually a fairly good eval, although a proper eval is better (eg FrontierMath has known difficulty and have tiers from 1 to 4).
Mathematicians would prefer if OpenAI didn't use open math problems as an eval, but OpenAI is not obliged. I actually think OpenAI wouldn't point AI to open math problems if unsaturated FrontierMath Super Duper is available, as it just angers mathematicians, but such eval is not in fact available. Given OpenAI used open math problems as an eval, they could just throw out the result (this is in fact better as an eval since it will keep problems useful longer), but mathematicians preferred to see the result. So OpenAI released them.
Yes, they should. They have invented a magic button that can tell you the long-awaited answers to the burning mathematical questions that you've spent your life researching. The caveat is that the technology is still new, so the explanations "are not fun to read" like set theory papers usually are (lol). If you don't think that's a worthwhile tradeoff, that's your call, but it sure as hell isn't everyone's.
I don't think the claim is "they definitely have an oracle that solves the problem, and I reject it because it's hard to read". The claim is "OpenAI claims to have used an oracle to solve the problem. The proof is very difficult to read, and to even know if it does or not, we have to go through it with a fine-toothed comb, but they're going around claiming they definitely solved the problem (or at least getting press that claims that which they aren't pushing back against) and this might convince the people who sign grants even if it isn't true"
People who are invested in the idea that we've invented a general intelligence, now, which includes all these companies that are literally financially invested in this claim they are making, will tend to believe that its results can already be trusted in domains like this. Some mathematicians seem to believe some of the proofs written by their models, and some, like this one, don't. I do think it's valid for an expert to push back against the claim that the best use of their time right now is to verify the poorly written work of everyone who's claimed to solve the problem
Over the year, nothing they've released with a lean proof attached has turned out false (That's sort of the entire point. It's not impossible but it's really difficult). There's a reason most mathematicians, including the ones vehemently against OpenAI's dumping are not arguing the results are secretly false or have a high potential to be. And indeed, if that were the case, it would quickly become apparent and all this worry about grant signers would vanish into the wind. It's very easy to ignore nonsense. The problem is that it isn't nonsense.
I really don't know enough about it to know whether you're right or not, nor do I know whether or not you know enough to make the claim you're making, so I won't make an argument one way or another because it's non-sequitur to what I said anyway. The fact that you or I or Sam Altman or Terrence Tao believe the claim is irrelevant to whether this obligates the person who wrote the blog post to believe the claim, and it sounds like he's willing to consider the possibility that it is right, and would read the paper if it reached a threshold of comprehensibility expected of people making that kind of claim.
I don't understand. Why is this the onus of scientists and PhDs to review whatever results OpenAI had dumped out? If OpenAI had produced incomprehensible papers, surely any journals would just reject it, or demand the author to do a complete rewrite? Unless we are talking about a race to solve problems, which PhDs are afraid that they had been scooped up on?
The problem isn't just that the papers aren't fun to read. The problem is that a lot of the research that goes into solving these issues leads to other discovers, new fields to explore and people have to develop new approaches to solve them. The other part of it is, the quality and the enjoyment of working on these problems leads people to find new and other interest problems to work on.
If you just strip mine the answers and Sam Altmans magic button solves 100/100 problems, what's next? Who is left to come up with a new interesting question for the magic button to solve?
Lastly, life and the present moment is all there is, if there is no enjoyment in anything we do, then what's the point of all the "living for ever" Altman et al want to achieve.
We will live forever to read boring papers generated by LLMs? Literally sounds like an eternal hell.
Nuclear fusion is already proven by the universe to be a viable energy source by the fact that the sun exists but people still work on understanding and taking it and developing new approaches to accomplish it. People didn't stop experimenting with and developing programming languages because technically they're all turning complete and the first one was "enough." Y'all will be fine - every JavaScript framework that exists is someone looking at a theoretically correct and complete solution and deciding actually it sucks and they could do better. "I want to understand xyz but the proof is trash and I think it's ugly" will be plenty motivation for a lot of people to work on it.
How is the journey to understand fusion related to not wanting to spent your limited time on earth wading through AI slop?
Here's a guy who's made a "beyond n log n" tracker: https://x.com/aurel_pr/status/2108214135179944096
He's tracking the community progress on sub-n log n multiplication. OpenAI started with 1 - 1.63e-55. The result has been now improved on 115 times, and the current record is "rohanarun"'s 1 - 9.87e-5. I'm sure by tomorrow it'll have improved again.
Does this look like people aren't having fun? Does it look like they aren't discovering stuff? It looks like it's spurred a cascade of interesting community activity. It doesn't really seem much different from what happened with the twin primes conjecture. Isn't that supposed to be the point of all this?
They should certainly be allowed to share their findings. No one is forcing scientists and mathematicians to review the findings in general. It’s just the case that the findings are of such such a quality that it would not make sense to ignore them wholesale
> No one is forcing scientists and mathematicians to review the findings in general.
This is like "no one is forcing software engineers to use AI tooling" or "no one is forcing you to show your ID in the airport" or "no one is forcing you to own a car in your small midwestern city" - there can be no law requiring something and the practical consequences of not doing so can be so painful that you're effectively forced anyway.
The best part is that when the academics fix OAI’s issues, the model gets better and OAI shareholders get richer and more powerful!
As someone who uses LLM tech occasionally, this is why I prefer using open local models. If I’m making myself obsolete, at least I’m not making some asshole richer and their closed model better.
No, they don't have to ask. Those interested enough will jump at the opportunity, even if it's just to be "one of the first to get it".
You know, I kinda relate to the feeling of not wanting look at those outputs if I think of it from a layman's perspective.
I just imagined that instead of math papers, they released 700+ feature length films, and the only way to tell if one of them is any good is to watch it in its entirety.
That feels pretty unappealing to me.
I know it's the same for human made films, so what's the difference right? But those are good enough most of the time that it's a decent bet, and the people that made them had real skin in the game.
Contrast that with something made by a nondeterministic slop machine with no skin in the game where small details can be off in a way that's jarring. Right out the gate I have an aversion to committing that much time to something that very well may waste it.
That's actually a really interesting thought. Given Sora, and the amount of funding they have, they could have created started their own film festival and dropped 700+ feature length films, had they wanted to go in that direction. But they didn't. Hmm.
What else should they do? See these models get smarter and smarter, somewhat-solve things but only to the tune of 90% what mathematicians (or experts in any other field) would deem acceptable, and then gate keep the findings for the next few years going through peer review and paywalled journals? I for one welcome the flood, bring on more in every possible industry and see where all that progress lands up. Sure it will upset a lot. A lot of things also upset the luddites.
Exactly.. this is an opportunity for people to pick up where the model left off and run with it. Like you don't have to, nobody is forcing you to.
However, there are always smarter, hungrier people out there and this is a buffet.
Some output is going to be wrong or incomplete. I am willing to bet even those have nuggets that can be used elsewhere.
> this is an opportunity for people to pick up where the model left off and run with it
Like people enjoy racing in front of a stopped train? As soon as they turn on the engine again, they will run you over. The questions that remain will be only the low value ones, not worth the effort to vacuum up.
So no, the smarter, hungrier people are not the ones that are going to swoop in. It will be the most desperate.
> Some output is going to be wrong or incomplete
This is a very human take on the situation. No, the Lean proof is not going to be wrong, and it will be incomplete only in the sense that OpenAI didn’t try to push the results further.
Are you going to be doing the work to verify the results ? Will you just expecting other people to wade through the flood and reap the benefits later on?
Nobody is forced to verify the results. I am honestly not expecting anything other than AI to get smarter and smarter and people who are motivated and interested enough to pick up after it; and potentially reap all the long term benefits ahead of those who aren’t (seeing this happening with software development in my own field). But in the end; if you don’t like it, you’re not forced to do anything.
Very sensible comments. It is along the lines of the fury I get when I am confronted with an 11 page dump of an issue analysis created by an AI agent that makes no sense but I have to go through because customer shared it.
If you did’t bother to write it, I shouldn’t be bothered to read it.
Perhaps AI agents can have their own publications and magazines where they are the chairs and associate editors and reviewers.
Nobody came to him and forced him to read it, just like nobody is forcing you to read code I had chatgpt write.
If AI can solve such grand, outstanding math problems, and mathematicians argue these pure math problems are important, what’s the problem with them needing to read the output if they want to understand it?
Can't you read the article and understand how he kind is obligated to engage with it ?
"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.
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.
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.
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.
At first I thought this was going to be more Luddite babble, but it makes a good point. OpenAI isn't contributing if they are make unreadable papers. They should use a little more of their compute to nail interpretability. The difficulty will only get worse as AI plow deeper into the frontier and produce increasingly alien looking output. I suspect it's a workflow issue. If not, it's a bad oversight if the current generation of models are capable of making mathematical breakthroughs but can't explain how they build on existing frameworks.
If you don't think they have contributed anything then you can safely ignore them.
Exactly what the author is doing.
Work this abstract almost certainly has no value outside the community that is (was) interested in the result. OpenAI should engage with the community to realize the value (beyond PR).
If he doesn’t like the paper’s structure he can just prompt gpt pro to review and amend.
I know the model that produced these proofs is still private, but it’s worth a shot tackling the proofs with the current consumer-available frontier.
In short, we’ve reinvented cranks sending unsolicited, poorly written putative proofs
> OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why? I am trying to finish several papers, I am supervising a number of Ph.D. students, and I have a lot of active research of my own to do. When am I supposed to sift through a badly written paper? Why should I bother, when they don't bother to communicate better?
Excellent point.
I don't blame the AI for this - I blame OpenAI.
Literal slop grenade (see https://fortune.com/2026/09/17/shopify-tobias-lutke-ai-slop-...)
>OpenAI drops some hundreds of "solutions", incomprehensibly written "solutions", and we are all expected to jump on them and what? Appreciate their contributions? Why?
...
>So, no, I will not be sending Sam Altman a bottle of whisky anytime soon, nor I am planning on spending my time reading through that paper and trying to make sense of it.
Think about a hypothetical circumstance where we get radio communication with some aliens on another planet. They send over tons of math to help us advance our tech, we know the math they're sending us is correct, but their explanations are really hard to work through because they aren't humans and the math is so different from anything we've done. Should we whine about the results they sent to us and refuse to engage with it?
Love your metaphor here. I guess there will always be people who try to keep going and follow their current projects and say that only human math is real math and we should only use alien technology for proofreading mails and such but not their highly established and esteemed professions. Or just keep your hubris low, update your priors, work towards progress.
> to help us advance our tech
The major discussion is about whether this will in fact advance our tech.
In the Three Body Problem, the alien race shows us “miracles” in an attempt to discourage us from the pursuit of science. Consider that possibility.
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.
I would admit seeing more mathematicians irritated is a good popcorn show.
For what's worth it, this batch of results are not very tight intentionally by OpenAI and promising mathematicians already started to consume them and improve the results, while someone is still complaining on it.
Reading though these comments I truly understand why the hardest part of my career in "IT" has been personalities.
The lack of emotional maturity and empathy is very on par with my experience thus far.
openai will take expert responses like this and improve the next set of papers
it won't be long before there's no more low hanging fruit like this to complain about, and the writing / explanations of the results are superhuman as well
separately, i really liked the author's denial-of-service analogy. super useful practical framing
Look forward to seeing an LLM write something well, that will truly be a breakthrough in the field.
Very well written summary of the current situation
Imagine being someone who is working on one of these problems. You have no good guarantee that the problem was solved, but you will have the horrible homework of reading the AI slop. Also, if you do have something interesting to say about the problem, people will have less enthusiasm about it now
I am no mathematician, but I can definitely relate to the "horrible homework of reading AI slop". We've started allowing a non-developer to submit AI generated code into our codebase (in droves).
When I am tasked with reviewing that code. First, I don't know if it's valid. The person who wrote it doesn't know if it's valid. In order to validate it I must step back and understand the full problem space. Then, when I ask for revisions or clarifications, it's seen as either
A - Slowing progress, being resistant to change... or... B - Thanks for catching that (Claude fix PR 532 with the review comments)
It's 100% removed the enthusiasm.
Perhaps, there is a point where we just "give up" the understanding and accept AI output as the ground truth, because the sheer amount of generation is too much for our puny human minds to comprehend, and a lot of the times it IS right, even if a little wonky.
The gradient into formalisms is steep and the bottom is deep. These are the worst results anyone will ever see again. The bottom of the internet is also deep, but won't be around much longer.
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'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 mathematicians are so upset
Their field is at the stage where the humans are “debugging” the AI slop.
They are still imagining how to escape from having to read the generated code. Hopefully they find a way.
You will own nothing and you will be happy.
I don't see how this quote is relevant here.
Most software developers (or people in any field, working for anyone) rarely own anything they do at work.
And the entrepreneurs running their own companies (which there's an explosion of atm largely because of AI) do indeed "own" the higher-level products and things they're producing, even if AI writes the code.
What is supposed to have changed?
Love this!
> This is why I generally avoid using AI for mathematics (I am happy to ask LLMs to consolidate information for me, or to generate a useful infographic, or to proof read an email, etc.)
In other words, the author is OK with using LLMs to replace data analysts (that could consolidate information), to replace graphic designers (that could generate infographics), and to replace editors (that could proofread an email). But don't you dare use LLMs in their mathematics.
I don't know about this person, but for me and I'm guessing the average professional in basically any field, before LLMs, they simply ignored information that needed summarizing, made their own crappy slides, and didn't proofread their emails.
> 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.
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.
Wow talk about sour grapes! No one is forcing you or any other mathematician at gun point to engage with this release at all. Ridiculous drivel.
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.