>The advent of AI was always going to be a seismic shock, but this huge dump of papers is a tsunami that we have no time to prepare for. It’s clear that OpenAI will happily wash away our community’s structures to further their financial interests.
What is the alternative?
1. Don't do the research internally (except someone else will do it once the model is public)?
2. Do the research internally but wait longer before telling anyone (this is what OpenAI did before, and mathematicians explicitly told them don't do it)?
3. Don't develop better models at all (except that Chinese models are only a few months behind)?
None of the options available to OpenAI would seem to solve the above concerns.
This is a very reductive take; there are so many other options available to OpenAI, many already suggested to them, here are a few of the many other options they have:
Spend the time (as mathematicians do) to cleanup, verify and explain properly any results they have found.
Pay mathematicians to spend their time doing the above with the results they do have.
Improve their LLMs so that they can do the work properly.
Dumping unverified results like this on the community and wasting other people's time with the gibberish their LLMs have produced is the height of hubris, but it leads to a good headline for the IPO.
Sure mathematicians can do that, and it’s probably the best response to irresponsible behaviour like this, but we’re talking about OpenAI’s behaviour here.
Let mathematicians do the AI-supported research on their own incentive at their own pace? What leaves a bad taste is that OpenAI doesn’t do this because they care about the actual math. Especially when they are leaving the necessary work of properly verifying, understanding, and writing up in an intelligible manner the proofs, up to the math community.
People would be more sympathetic if this was an alien race sharing their math results in not-quite-intelligible-to-us papers, because there at least we could assume that the aliens cared about the math and did their best to transmit their understanding to us.
>Let mathematicians do the AI-supported research on their own incentive at their own pace?
After they release a model, it only takes a handful of scrappy young math grads (incentivized to publish high-impact papers) to independently put in those exact same prompts, and more. The tsunami remains.
How is it worse if OpenAI hires those same grads internally (vs independently) to run the same prompts?
> leaving the necessary work... up to the math community
So now it's better if OpenAI hires the mathematicians internally (vs independently) to verify any results before release. I wish people would make up their mind!
Again, that's what the math community told OpenAI they don't want. They said do release any internal results early, rather than withhold them.
Or are you saying.... OpenAI should never run an internal test involving math proofs, for fear of this 'tsunami' of potential discoveries they'd be forced to release? Isn't that a bit like the scholars refusing to look through Galileo's telescope? :-/
Except they don't too the full work. If the prompt also verified that what was proven is what what asked for, and that the proof is correct, and then write it up in an understandable fashion, then the work is done. As it is now it is more like a spoiler for a movie than the actual movie.
I don’t blame OpenAI for that. There’s a ton of weirdly politically motivated denial of AI being useful for solving problems that require new answers. This is one of the very few possible ways to objectively prove that AI can do that.
What's more, it's quite possibly one of the best ways to improve AI, as math provides both a large corpus of training data and an objective way to measure capability. IMO this is likely why the AI companies are working on this, with improvement in math reasoning bleeding over into improvement in general reasoning.
Really, mathematicians should be thrilled about this, as this could be the biggest practical payoff of thousands of years of investment in math, bigger even than all the preceding science and engineering payoffs. We're told one of the benefits of a math education is learning how to think; was it really so unpredictable if that also applied to machines? This sort of payoff would justify wide open checkbooks for more math research, even by humans.
1) is probably phrased wrongly. I think it isn't even research for the AI labs, it's just an inevitable byproduct of how they train and verify their models. That goes perhaps to the heart of how the mathematicians feel about it: what they thought was a crowning achievement of the human intellect is now a byproduct of a mechanical-industrial process. But that also means the AI labs can't just stop, because they need ever harder puzzles to be part of the training.
I choose option 1. It's in the name! OpenAI should give mathematicians the chance to do at least some of this work themselves. It would be a lot easier for the community to adjust if they could use these same tools to explore how math research can adapt to the new circumstances. Instead, OpenAI is racing ahead to get as many results as possible with a proprietary model that the mathematical community cannot access. If these companies are building AI to benefit humanity as they assure us, then shouldn't they share their resources rather than vacuum up everything for themselves? Especially for something with as little direct monetary value as pure math.
I think there is way too much focus on how they released the results; it was going to be a huge shock no matter what. We should be talking about the massive concentration of "mathematical wealth" occurring here, and how it is a microscosm for what may happen on a much larger scale as AI outperforms humans on more and more domains.
I believe this whole AI vs. mathematicians story is only at the very beginning and that Mathematicians have an extremely narrow view of what's happening.
In particular, for Mathematicians worried about the inscrutability of AI-generated proofs and about the fact that Maths is first and foremost about understanding rather than proving for the sake of proving, they're vastly underestimating what AI will be able to deliver in years to come.
IMO, it's very likely that:
- AI will not just be able to prove theorems but more importantly *increase* the speed at which we *intuitively* understand the phenomenon under scrutiny. All these AI companies are busy using AIs to prove stuff, none of them has yet tried to point an AI in the direction of making an existing proof more understandable and intuitive to a human. My bet is there will be AIs trying to find the shortest path (where shorter = easier to understand) from an existing body of knowledge to a theorem proof, thereby iteratively slowly but surely "compressing" the whole universe of Mathematical knowledge over time (and making it easier for humans to digest).
- Same story for "discovering new mathematics", the other many-times-rehashed concern that AI-doing-math will impede that particular endeavor. Who's to say we can't define a bunch of criteria that quantify "interesting", point a bunch of AI's at it and press the button?
> none of them has yet tried to point an AI in the direction of making an existing proof more understandable and intuitive to a human
I'm absolutely certain they've tried that. The issue is this alien intelligence cannot do it. And there are no signs that it ever will. I think way more realistic scenario is this intelligence will go further away from ours and become incomprehensible when it grounds its alien math research on top of its own, not millenia of human's.
People still play chess and go and StarCraft. People do what people want to do. It's not clear whether this will reduce the number of working mathematicians or increase it. There will a lot to learn from the machine proofs that will open up new frontiers as well.
So, it's like the story, "We'll see."
There has been a shocking but not altogether surprising development, and all reactions are valid.
Those are activities where repeating the same experience yourself is still enjoyable, kind of like you might eat today even though you already ate yesterday.
Finding mathematical proofs is probably more like seeing the ending to a mystery novel. Once the ending has been spoiled for you, it's really hard for you to enjoy it the same way, and it might be more fun to move on to a different mystery.
Different people have different feeling and motivation and reasons for doing things. No doubt there are people thinking like you, but it's to early to tell how it will be for the majority.
> People still play chess and go and StarCraft
Because most people still find them enjoyable. You can't say those are less enjoyable than math. There is no universal scale for enjoyment.
> kind of like you might eat today even though you already ate yesterday
You'd die if you stop eating after yesterday's meals. That's survival.
Some people enjoy rewatching or rereading books and others dont.
Careers change and maybe we need a different type of mathematicians that does enjoy this work more than historical work?
No, people enjoy methematics for the inner journey and for the depth it offers that is orthogonal to everythibg in existance. Learning math is awesome, furthering the field is just paying your dues
Chess and StarCraft are games. For many other intellectual activities, part of the satisfaction comes from contributing something meaningful to a collective effort. If a machine can do that orders of magnitude faster, for many people these activities become effectively pointless.
The funny thing about people comparing mathematical research in the days of LLMs to playing chess in the days of Stockfish is that it identifies the competitive nature, and hence status seeking attitude, of the mathematical research community. Chess is, of course, a competitive game with a winner and a loser. You "win" mathematical research by solving a longstanding unsolved problem.
There is this idea of advancing human knowledge and adding to the record of what people know in mathematical research that breaks the analogy down, somewhat. But most people aren't Perelman. They would happily take the million dollar prize. And it is out of the question to do anything other than put your name on the published paper.
That is what I am gathering, too. I've been watching this from the sidelines, really confused by all the people moaning endlessly about how this revolution is somehow damaging to the community of mathematicians, which makes no sense to me no matter how many times I read their arguments.
But realizing that the primary driver was never actually proving the conjectures, nor understanding the proofs, sheds light into the issue. Many are not satisfied with the prospect of curating and preserving an ever growing collection of discoveries; what they wanted is being the discoverers themselves.
Which to me is mind boggling, because that is not what they have been saying aloud all along. Maybe it's my autism speaking, but I really thought they cared about the resulting knowledge rather than being recognized by their peers. How naïve of me to think that they were above that.
Meanwhile, people who simply enjoy having a tool that facilitates solving problems, because having a solution is their true goal rather than an excuse to obtain recognition or validation, are excited to use this new wonder.
Please don't pretend that you've somehow been deceived. Hasn't everyone heard quips like "theoretical physics is like sex: it has some useful results, but that's not why we do it"? How hard is it to understand that doing something is what gives pleasure, rather than the outcome?
Having AI tools does not remove the ability to do anything, other than being the first. I genuinely don't get that viewpoint, it is alien to me. It is equivalent to saying that the existence of bicycles removes the pleasure of running.
Pro tip: life is pointless. So the machines are better at thinking about certain classes of things. So what? Either you enjoy thinking or you don't. Deciding whether you enjoy it or not based on a global scorecard is silly. Surely there are aliens out there somewhere that already figured out any given problem. Does that make finding the solution yourself any less satisfying?
I think what people actually want when they say this is to be the hero. They want the admiration. Which is fine, but at least he honest.
Yes! If their true goal was expanding the field, they would be excited. But if, instead, they saw this as some sort of a race to be the first to prove a conjecture, then their frustration is understandable. But it would be good if they had been honest about it from the get go; possibly they did not even realize it themselves.
I bet lots of them, who are in it for the love of the game, are truly excited by what is going on.
> People still play chess and go and StarCraft. People do what people want to do.
Poor analogy. Because math is one of those job-hobby type hybrids where the job may be enjoyable but you still need the academic infrastructure to do it on a modern level, both because you need funding and you need others to motivate you to keep to a certain standard.
Job-hobby hybrids like this are not the same as running and Starcraft where you can do it by yourself and still reap a lot of benefit from it in the same way. Hobbyists might still do math but if it were just up to the hobbyists, we wouldn't have the level of discovery we have today.
I think the whole point is that we are no longer at the top of the totem pole, cognition-wise. At least not in certain areas. Better get used to your goals being self-driven. If your sense of self relies on being the best you've got a problem.
All the “it’s not clear if there will be fewer jobs in the future” rhetoric is frankly mind boggling. It’s pretty clear the goal of LLMs in a capital sense is to reduce operational budgets as much as possible. If it doesn’t happen naturally it will happen by execs forcing that decision.
Academic mathematics isn't an operational institution.
Though its funding does move with the number of major projects academia is tasked with that rely on mathematics to advance, it's a fundamental knowledge area that has no operational requirements to exist.
Have you not already heard others make this analogy a million times by now? It seems like I read it multiple times a day at this point.
Mathematics can be enjoyed recreationally as a puzzle like any other, but it isn’t just an arbitrary puzzle. It’s a science where one discovers truth and seeks an understanding of, and dreams up, new phenomena. It’s not chess, or go, or StarCraft. There’s no fixed rule set and the goal isn’t to ‘win’ or beat your opponents.
Let’s stop repeating this nonsense as if it’s a profound observation.
I think human mathematicians would be more enthusiastic if these frontier labs were putting out new interesting open problems. As some of them are pointing out in the responses, the purpose of having big open questions is often more about the tools and techniques used in solving them. If some can be gleaned from the AI proofs then great but, if not, the only real outcome for some (not all) of these results is that humans won't be able to develop those techniques.
If OpenAI were coming up with interesting problems that everyone could explore as they foreclosed all these existing ones, I don't think the response would be as critical. Obviously, that's much more difficult and doesn't tie into the only telos of these companies (having a huge IPO to make all their investors and equity holding employees rich).
As usual (at least, as of recently), Terry Tao's assessment is measured but trenchant. Mathematical research has been a human process of improving understanding, to an extent that if you go far back enough in time, it was not distinguished from "philosophy". Part of that involves (involved?) ac academic engagement with the pursuit of knowledge, which means that results are discussed, presented, picked apart, etc., in a community of other people in pursuit of knowledge. The end result being the sum knowledge that humanity possesses grows. The way these results were dumped unceremoniously bypasses all of that. And, because we have all seen what regard the tech leadership class have shown for humanity, even in much more concrete and significant ethical questions than "is it ok to destroy the academic community", such as "is it ok to lower the friction to surveilling and/or enacting violence on society to the extent that it's all encompassing", I think it's pretty reasonable that their complicity in the latter will extend to the former.
I should point out that this is not a categorical treatment of AI results. I think about outcomes. Would I be angry if OpenAI dropped full contents of all the Vesuvius Challenge scrolls? Obviously not.
they would be treated the same: "we dont have time for your slop questions and conjectures, they do not even come from a place of struggle and curiosity, we will not engage with your PR attempts, we already have problems to solve and things to think about for the next 200 years"
I think this response makes unwarranted assumptions about the ideologies and goals of the people you're talking about, which is not even supported by most of these quotes in the linked page.
All of these reactions from Mathematicians keep reminding me of - true or urban legend, doesn't matter - the ballad of John Henry [1] who, according to the lore, died trying to compete with a steam powered drill.
I think that this specific blog post is an important one for history.
The stunned responses indicate a set of some of humanity's brightest struggling to comprehend the emergence of such an incomprehensibly creative and powerful intelligence.
AI has come for coding.
AI has come for mathematics.
AI will come for everything else if we don't do something NOW.
I don't really understand these takes if we speak of the long-term. You're speaking of a world where there'd be widespread access to high quality cognitive work for a price approaching $0. The possibilities this would open are endless. We need to ensure that we don't neglect our own personal development, and fall into the sci-fi trope of an ignorant civilization relying on an machine built by their ancestors, but I don't think that's much of a practical concern.
In the short-run I think concern is much more merited because it will obviously cause some instability as the economy settles into a new equilibrium, but that's always the case with any sort of revolutionary technology. And this would almost certainly just be short-term stuff. As the value of one thing goes down, the value of other things would go up, and new things would emerge.
"a set of some of humanity's brightest struggling to comprehend the emergence of such an incomprehensibly creative and powerful intelligence"
Where do you get this from? There is exactly one comment that even mentions creativity, and none of them speak about intelligence. All seem to agree it's slop.
> To be fair, my first reaction was almost boredom. Yes, the AI has “proved” (really? Are we sure? Can we even understand what is written there?) a bunch of interesting results in my field. Not even a Millennium Problem. Pff. [..] If a paper or thesis is so badly written that I cannot get past the first page without considerable effort, I reject it and ask for a new, readable version. With these AI-generated papers, I feel that we, as a community, are not applying the same standards of quality and rigour. They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with redundant arguments, unclear logical structure, multiple dead ends, and strange or unsettling terminology — in other words, slop.
why assume that because LLMs are strong in a narrow set of fields it will be strong in everything? we don't make that assumption about other forms of intelligence. i.e nobody thinks Stockfish is good at product management, and people generally don't think that a genius composer will be equally good at botany.
In 1904, Psychologist Charles Spearman noticed something interesting about school children's academic performance. Students who excelled in one subject tended to do well in others even when those subjects appeared quite different. He proposed that a common underlying ability, which he called the general intelligence factor, or g, could explain these correlations. [1]
Today, g is one of the most robust findings in differential psychology. The tendency for different cognitive abilities to correlate positively has been replicated across numerous studies. g typically accounts for around 40 to 60% of the variance in cognitive test performance and is predictive of numerous life outcomes, including educational achievement and occupational performance. [2]
Evidence of g isn't confined to humans either. Studies of mice have identified a general cognitive factor explaining roughly 30 to 40% of the variation in performance across different learning tasks [3]. We have similar results for primates and birds.
To put it simply, intelligence tends to generalize. Humans who tend to have higher verbal skills also tend to have higher spatial skills, better memories, and faster processing speed. Someone with the cognitive ability to become an exceptional chemist might just as easily have become an exceptional mathematician or software engineer. The knowledge and skills required are obviously different, but the underlying cognitive abilities that make someone successful in one intellectually demanding field often transfer to others.
cognitive abilities correlate across a particular set of measured tasks but it's not established that high performance in those tasks generalises to arbitrary domains
theres a difference between having a general capacity to learn, possessing domain-specific expertise, and being able to reliably apply that expertise in the real world.
even in humans, a genius mathematician isn't necessarily an exceptional manager, composer, or biologist. general intelligence might make it easier to acquire those skills but it doesn't substitute for them.
the question isn't whether LLMs exhibit "g" but if the abilities being measured are representative of the broader capabilities we're predicting. that's not something g settles.
>The knowledge and skills required are obviously different, but the underlying cognitive abilities that make someone successful in one intellectually demanding field often transfer to others.
The fact of the matter is that If you have a good general capacity to learn then becoming a competent x is generally only a matter of time and interest. For LLMs, it's the same except with data and compute. Naturally, all work done on a computer is in danger.
because that's what's filling this role right now. the stated goal of these companies is ""agi"", exactly what you're talking about. if LLMs fail to take them there, they'll look for something else to do so. that's their whole thing. and then the guy's association will resolve different accordingly.
it's like recognizing that when most people talk about the os they're using, they're really discussing their de. great, their mistake, but at the same time they're not actually making any mistakes either, you're the one taking them there, then beating them with experience. what a de can pull off can heavily depend on how the underlying os works, and some os have a fixed de they ship with that's almost never replaced cause it's not really intended to be. going off about specifics when they did not talk in terms of specifics is obnoxious. which is probably no coincidence, given your username of choice.
We are doing something now. We're making it so the AI does it all better, so we don't have to do it anymore. Gotta break a few eggs to make an omelet, but it's going to be a delicious fucking omelet when it's ready. I don't understand why people are pushing back so hard on making the world a better place. I personally can't wait until it's clankers all the way down.
Yes, the humans who control this system will surely evenly distribute the spoils of this new revolution among the people who have no stake in it. Certainly it will not lead to a kind of hyper-poverty not seen in recent human history where near demigods and subhumans are technically the same species, but only until the AI starts working on genetics.
Who controls anything? That's one reason I'm highly optimistic here. You can already performantly run frontier level models on systems with $1600 tier video cards. A couple of years ago it required supercomputing clusters. At this rate frontier tier models will be running on any plain old computer in a couple of years.
If LLM's reach their potential we're speaking of access to generalizable high quality cognitive labor for something approaching $0, for everybody.
>You can already performantly run frontier level models on systems with $1600 tier video cards.
Quanted out Qwen 3.8 models are not frontier level. Have you used them for real work? They suck. They are so unsure of themselves due to the quant-lobotomy. They just endlessly loop in thinking even when they have the right decision and then output it when they get to the thinking cap. They score close in benchmarks because most benchmarks don't measure time to complete a task.
I use Qwen quants in production for fast inference but I disable thinking and have them fine tuned for the task. My realtime transcription + translation stack right now is running 5 streams at 380 tok/s.
Running DeepSeek 4.1 Flash at FP4 is going to need at least a 10-15k machine. I'd consider that near frontier level.
However much compute you can buy, the big boys will always be able to buy orders of magnitude more. Orders of magnitude more compute means orders of magnitude more political and economic power.
The price will never be zero, since there is a finite amount of compute possible.
There is zero reason to believe we're barrelling toward utopia and plenty of examples that illustrate exactly where we are headed.
That's fine, because you don't need infinite compute to run or train current models. If the "big boys" are buying more compute that's because they hope to provide a better service.
I misspoke when I said "zero". I should have said "down to marginal cost". It's fine for AI to be priced at the cost of its compute! That's the efficient outcome.
What reason do you expect to provide a moat for a monopoly? Training on existing customer interactions? That might get you an oligopoly, but there are already two serious competitors in the US alone and several potential Chinese rivals.
Whether you agree or not, if you seriously can’t understand why people might be existentially (or economically!) anxious about the thinking machines, you may have already outsourced too much of your thinking to them.
> you may have already outsourced too much of your thinking to them
i'd think that instead of just giving in and reacting with a cheap insult, highlighting the unreasonable leap in rhetoric might be a bit more persuasive. to be specific:
> I don't understand why people are pushing back so hard on making the world a better place.
"making the world a better place" is not what's receiving the pushback. on the contrary, kind of the whole argument is that the current developments are short sighted, and that they will leave leave the world in a worse place on the long term.
and then one can agree or disagree about that, but at least then we'd not be arguing strawmans anymore, nor approaching increasingly childish insults
Many of the reactions are some version of 'pissed off', which I totally understand. This reaction stands out and resonates with me:
> With these AI-generated papers, I feel that we, as a community, are not applying the same standards of quality and rigour. They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with redundant arguments, unclear logical structure, multiple dead ends, and strange or unsettling terminology — in other words, slop. And we are then expected to go through it, check it, clean it up, simplify it, and explain what is actually going on. This comes at a considerable cost to us in terms of time and effort, while they can simply move on and slop-bulldoze the next conjecture. And, of course, the credit remains theirs. In some sense, we are willingly contributing to our own demise.
I'm not a mathematician, so I didn't even try to read it. But if it is unreadable slop -- then why should we (humans) believe it is correct? And why should professional mathematicians labor through reading it?
I was really quite surprised that they'd parade around 722 manuscripts with only less than half (or really, close to only a third) of it being machine-checked. It's genuinely equivalent to the overconfident and blind drive-by PRs in software that people here should be well familiar with, and those are not exactly the hallmark of quality usually. Quite the curiously dangerous game to play when you're trying to scoop an entire field of study on an industrial scale as powerplay.
Or it's a touching show of openness. They're not in this for the ego-boost, they're sharing data on how things are working. Naive of them to expect gratitude, I guess.
It's only any of these things to the extent their unverified proofs end up correct. Otherwise, not only is it naive indeed, it is out of touch, an insulting waste of time, and mistaken. Hence why I find this a curiously dangerous game to play. Nobody treats this as the "scientific process" they're trying to frame this as, where manuscripts can just be redacted. If they genuinely believe in that framing, they're even more naive and out of touch than one can possibly imagine.
It really pains me to read the responses here to this and the AHM statements. It feels like HN people here are talking with such... privilege. These are the smartest people on the planet saying "hey, please don't do this, it's seriously hampering our work in this field". And then people on here say that mathematicians are... gate keeping? Not embracing progress? Who are you to say that? How do you know? What happened to empathy for others? I don't understand you all...
Part of it is probably because we've already been through this? The SWE field has seen exactly these reactions over the past 4+ years.
Some people saw "the spark" before LLMs were mainstream. We had code autocomplete models based on GPT2 that ran on your machine and provided line-based autocomplete. Then we had gpt3.5 (chatgpt launch) where it almost looked like it could write python, then we had gpt4 and saw the first glimpses of actual code writing, then opus4 / gpt5, and today we have sol/fable etc. At every step we had people in this field write the same kinds of takes. And at every step the tech evolved, improved, and got better. To a point where the vast majority learned to accept it, and the denialists (there are still some) are now in a minority.
And the acceptance phase was not "we are now useless as SWE", nor was it "hah, it's only for the juniors, we are safe. It was, mainly, "we can now work at a higher level of abstraction, and use our experience to guide these tools and work faster / broader / deeper in a topic. Basically understand the tools, learn their pros and cons, and adapt at using them.
Also part of it could be that the message seems to complain about the situation without providing alternatives. What are the alternatives? What are they proposing? "Please don't do this" does seem like gate keeping if you don't offer an alternative. What exactly do they want these labs to do? Don't try to solve the problems? (stop the count?) Don't publish the results? It's not clear to me.
I guess a lot of people are unclear on the messaging. Is this purely ideological, or is it something more? (It doesn't help that AHM also has a section where they highlight their members who pledge to do research "without AI assistance". Whatever that means. Yeah, that's cute, but can signal denial, which again we've already seen in SWE, and hopefully most people have dismissed it already) Are these statements part of the 7 stages of grief, or is there more? When taken at face value, the statements seem rushed, unprepared and "in denial". At least when compared to writing on the same topic from other people in the field (Tao et all).
> "hey, please don't do this, it's seriously hampering our work in this field"
I don't think that that's really a fair summary of the linked article though. By my reading, I'd say that a quarter of the responses were overall positive on the announcement, a quarter were overall negative, and the rest were mixed/neutral. I agree that there are many mathematicians saying something similar to "please don't do this", but that's not a consensus (or even a plurality) view.
(I agree with your broader point though, that lots of the other replies to this article are way too dismissive of mathematicians' concerns.)
OpenAI dropped a slop bomb on mathematics the same way people will drop slop bombs in codebases and the people here are saying “well drop everything and review it of course!”
I think it’s very reasonable to expect the people that are dropping this on other people for review to have reviewed it first, closely, made adjustments, etc, the same way I do before dumping my Claude/ChatGPT assisted PRs onto other people.
The reviewers shouldn’t be exerting more effort than the person that set the prompt.
So why are these models more successful than mathematicians at solving these problems? Is it because of the computational power they bring to the problem? Is it because they use new techniques not thought of before? Or is it because human mathematicians have been approaching these problems in the wrong way?
A bit part of it is that no one human mathematical genius can hold all of math in their mind at once. The surface area is enormous. Humans specialize. The model has the luxury of finding obvious interactions in widely disconnected fields that no human would have found.
This seems like a like a huge advantage, the models can view everything. I wonder if they're being used to look at problems in physics like quantum gravity.
But they aren't more successful. They can solve this because of standing on a huge body of work made by working mathematicians. Without it AI would get nowhere. Now AI are burning the minds that fed it for short term gain.
When AI has exhausted the existing math literature (and found a bunch of errors, I'm sure) it will have to start producing its own conjectures. Millions of them, even billions. And using all the experience from trying to prove them to improve.
You're acting like math is some sort of infinite game of automating unit tests. There is no shortage of conjectures and generating them is cheap. The struggle is finding the ones that are actually interesting. They only have value when they can unify disparate domains or reveal something that was previously hidden, or (the thing that I see most Mathematicians lamenting today) if they force the creation of new abstractions to solve.
Insight in mathematics doesn't emerge from brute-forcing conjectures. There is a recognized aesthetic economy that exists and without a semantic filter to detect the significance in any of these proofs we just end up with a lot of noise.
Oh, I'm sure most of those millions or billions of automated theorems will be uninteresting to us. But they will, in aggregate, be useful for the AIs, in improving the models and identifying lemmas and abstractions.
Yes, it would be very much like automatically generated tests. These are not worth much by themselves, but in massive bulk they can do interesting things.
Why on earth would open AI pay for that though? There is no value in it anymore. The pointlessness of this destruction of math really is depressing to me.
I feel it would be effective and prudent to protest the current use of AI in mathematics and to effectively unionize and ostracize AI use until many of these demands are met. The companies that own the models and the infrastructure will never be more vulnerable.
They have fired a salvo. Fire Back.
The companies are bending over backwards to accommodate. If they decide mathematicians are true enemies, they will bring out the knives. For example, pushing for cutting off of funding and setting up a competing Math 2.0, replacing Math 1.0 like chemistry replaced alchemy.
> One thing to keep in mind about this drop of papers is that they were not created by OpenAI with the main goal of making progress in mathematical research, or even primarily for PR (there were some PR posts, but e.g. the final announcement was comparatively restrained). The main reason these papers exist is that OpenAI used unsolved math problems to evaluate their internal models for the purpose of improving their capabilities. They had to use hard open problems because these are the only ones still posing a challenge to frontier AI models. I believe that, from OpenAI’s point of view, the papers are essentially a byproduct of their internal development.
> And I mourn the path not taken, and the opportunities lost in the frantic race to develop this technology. Labs submitting their frontier models to independent researchers for proper scientific evaluation. Coordination with the research community to ensure these tools are applied to complement and enhance the abilities and activities of human researchers, rather than compete with them. Use of these tools to foster collaboration and sharing, rather than competition and secrecy. Opening new doors, without closing old ones.
But that is not the path we now find ourselves in. Instead, the community needs to come together more than ever. To clearly declare our own standards and values, to build our own tools and practices, to support our most vulnerable members, and to chart our own path forward. Let’s get to work.
We should remember that we are all in this together; mathematics is a marathon, not a sprint; and the goal is and always will be the human understanding of mathematics, which will invariably take time.
What is worrying me the most, at the moment, is actually the (in)security of cryptography. Finding algorithms breaking standard cryptographic protocols is a number theory problem whose difficulty does, to my non-expert eyes, not significantly exceed what these systems are now capable of. And it would have disastrous consequences on society if such an algorithm is found.
I sympathise with a lot of the details of mathematicians' complaints, but at the same time I still see very few people stepping beyond "what will this do for the discipline" to think "what will this do for social welfare". It's like hearing scribes complaining about the printing press. Yes, I'm sorry that you won't get paid to do beautiful illuminated manuscripts, but I think the benefit to society outweighs that, and if it didn't, then why were you being paid to do the illumination in the first place?
It's not that there aren't possible arguments here (AI is destroying the basis for further progress). But this perspective is hardly even being addressed by most of the reactions.
Were these problems just beautiful but useless? If so why did we pay people to work on them? My impression was that many mathematicians receive large research grants.
...
I think the paradigm has to shift. We should apply to AI-generated mathematical announcements the same standards of rigour, clarity, and exposition that we demand from human-generated papers. Do you want the approval of the mathematical community? A badge of legitimacy? Then give us something that is actually readable and verifiable. If not, we should simply ignore it.
In other words, I do not think that we, as a community, should spend our time cleaning up their mess in order to increase someone else’s commercial revenues.
...
It’s always frustrating to listen to people on HN and X, the everything app, talk about this with that characteristic smugness. “It’s totally understandable that they feel this way” “oh people still play chess!” As if what mathematicians are upset at “losing” an arbitrary strategy game. It’s a very childish way to interact with it but you can’t expect much I guess.
I like this website though because it collects a lot of the important frustrations from the mathematical community, these open problems were curated in order to organize a field around, most to all of them only have/had value in so far as they promoted study of the subject. The claim that AI proofs will open new frontiers for mathematics research could probably be true but misses the point that the manner OpenAI has gone about their “contribution” does more to cauterize the field than promote anything productive. OpenAI is functionally reducing the communities ability to ask real questions. Math is ultimately a very different field from the rest of the natural sciences, and I suspect a lot of the more simple discussion on this subject misses the objections because of those differences. All this to say, I don’t know that OpenAI is doing these haphazard releases cynically, with the assurance that all that matters is the headline, but it really does feel that way right now.
1. "...these open problems were curated in order to organize a field around, most to all of them only have/had value in so far as they promoted study of the subject" - I don't understand, how were the open problems curated? Do you mean that mathematicians put a lot of work into coming up with the problems and now all that work is somehow worthless now?
2. "OpenAI is functionally reducing the communities ability to ask real questions." How? Let's assume all the remaining proofs are correct (big assumption): how does resolving conjectures reduce the ability to pose new problems? This only makes sense to me if the assumption is that there are a relatively small number of possible problems to solve and so it's like a game that's coming to an end with no more interesting areas to explore. Surely math is bigger than these?
Sure,
1. Yes, a lot of effort is put into problem curation. Some parts of math are very problem list oriented while others are more program oriented. The work put into formulating the “correct” or “meaningful” (both of these adjectives should be taken in context) questions is not “somehow worthless” now, but the problems themselves now can/will no longer serve the same purpose they did. A significant part of their purpose was to organize the fields. If a solved problem could still provide a reference point for a field to organize around is a question I don’t really have the answer to.
2. Yes, math is bigger than the solved problems, of course. There is a plausibly infinite number of problems and theorems to work on. That being said, the ability to ask new questions which are of some “mathematical use” requires skills built from working on and solving prior problems. It might have happened to you in college at an advanced class where the professor would turn to the class and ask if there were any question, but everyone is so past their depth that despite being confused, no questions are asked. I’m not saying math is coming to an end but rather that one part of it, the question asking part, has become harder while the question answering part has become much easier.
The above depends on some understanding of what makes something useful in mathematics, which is not something I trust myself to relay the nuances of. Anyways, I hope I elucidated my opinions workably enough.
An interesting split in reactions by people who work in mathematics to the OpenAI release:
1. Reacting from the POV of the individual person: disappointment, disillusionment, and/or grief from those who've worked on some problem for years and now don't have something to work on; it's been a part of their identity. As well as those whose career tracks and plans were thrown in disarray.
I wholeheartedly sympathize with the above.
2. Reacting from the POV of the entirety of mathematics as a field of study/research:
"If OpenAI wanted to destroy the mathematical community, this would be a great way to go about it."
"...it will create conflict in the mathematical community;"
"I feel that solving so many problems in such a short time may damage the math community and profession"
"They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with redundant arguments, ... — in other words, slop. And we are then expected to go through it, check it, clean it up, simplify it, and explain what is actually going on. This comes at a considerable cost to us ...And, of course, the credit remains theirs."
This second type of reaction... is confusing. No one is forced to read any of the papers. Ignore them if you want. But also, isn't reading papers a lot of the job?
"Open problems are a resource that the mathematical community developed over decades or even centuries"
I doubt mathematicians have intentionally not solved problems just so that they can remain unsolved? Build on these advancements (or disprove them - wouldn't that be an amazing result!) and pose new problems?
What if a human dropped all of these without AI? I suspect there wouldn't be the same reaction for some reason.
1. Don't do the research internally (except someone else will do it once the model is public)?
2. Do the research internally but wait longer before telling anyone (this is what OpenAI did before, and mathematicians explicitly told them don't do it)?
3. Don't develop better models at all (except that Chinese models are only a few months behind)?
None of the options available to OpenAI would seem to solve the above concerns.
This is a very reductive take; there are so many other options available to OpenAI, many already suggested to them, here are a few of the many other options they have:
Spend the time (as mathematicians do) to cleanup, verify and explain properly any results they have found.
Pay mathematicians to spend their time doing the above with the results they do have.
Improve their LLMs so that they can do the work properly.
Dumping unverified results like this on the community and wasting other people's time with the gibberish their LLMs have produced is the height of hubris, but it leads to a good headline for the IPO.
What’s to stop people from ignoring these altogether and continuing their own work?
“Dumping unverified results” seems to imply that those results come with an obligation of some kind.
Sure mathematicians can do that, and it’s probably the best response to irresponsible behaviour like this, but we’re talking about OpenAI’s behaviour here.
Let mathematicians do the AI-supported research on their own incentive at their own pace? What leaves a bad taste is that OpenAI doesn’t do this because they care about the actual math. Especially when they are leaving the necessary work of properly verifying, understanding, and writing up in an intelligible manner the proofs, up to the math community.
People would be more sympathetic if this was an alien race sharing their math results in not-quite-intelligible-to-us papers, because there at least we could assume that the aliens cared about the math and did their best to transmit their understanding to us.
How is it worse if OpenAI hires those same grads internally (vs independently) to run the same prompts?
So now it's better if OpenAI hires the mathematicians internally (vs independently) to verify any results before release. I wish people would make up their mind!Again, that's what the math community told OpenAI they don't want. They said do release any internal results early, rather than withhold them.
Or are you saying.... OpenAI should never run an internal test involving math proofs, for fear of this 'tsunami' of potential discoveries they'd be forced to release? Isn't that a bit like the scholars refusing to look through Galileo's telescope? :-/
Except they don't too the full work. If the prompt also verified that what was proven is what what asked for, and that the proof is correct, and then write it up in an understandable fashion, then the work is done. As it is now it is more like a spoiler for a movie than the actual movie.
For OpenAI/Anthropic/etc it's apparently not enough to be the tool that helped a mathematician with a discovery/proof/etc.
They need to state it was entirely autonomous.
I don’t blame OpenAI for that. There’s a ton of weirdly politically motivated denial of AI being useful for solving problems that require new answers. This is one of the very few possible ways to objectively prove that AI can do that.
What's more, it's quite possibly one of the best ways to improve AI, as math provides both a large corpus of training data and an objective way to measure capability. IMO this is likely why the AI companies are working on this, with improvement in math reasoning bleeding over into improvement in general reasoning.
Really, mathematicians should be thrilled about this, as this could be the biggest practical payoff of thousands of years of investment in math, bigger even than all the preceding science and engineering payoffs. We're told one of the benefits of a math education is learning how to think; was it really so unpredictable if that also applied to machines? This sort of payoff would justify wide open checkbooks for more math research, even by humans.
Well yeah, their ultimate goal is to develop "highly autonomous systems that outperform humans at most economically valuable work"
1) is probably phrased wrongly. I think it isn't even research for the AI labs, it's just an inevitable byproduct of how they train and verify their models. That goes perhaps to the heart of how the mathematicians feel about it: what they thought was a crowning achievement of the human intellect is now a byproduct of a mechanical-industrial process. But that also means the AI labs can't just stop, because they need ever harder puzzles to be part of the training.
I choose option 1. It's in the name! OpenAI should give mathematicians the chance to do at least some of this work themselves. It would be a lot easier for the community to adjust if they could use these same tools to explore how math research can adapt to the new circumstances. Instead, OpenAI is racing ahead to get as many results as possible with a proprietary model that the mathematical community cannot access. If these companies are building AI to benefit humanity as they assure us, then shouldn't they share their resources rather than vacuum up everything for themselves? Especially for something with as little direct monetary value as pure math.
I think there is way too much focus on how they released the results; it was going to be a huge shock no matter what. We should be talking about the massive concentration of "mathematical wealth" occurring here, and how it is a microscosm for what may happen on a much larger scale as AI outperforms humans on more and more domains.
I believe this whole AI vs. mathematicians story is only at the very beginning and that Mathematicians have an extremely narrow view of what's happening.
In particular, for Mathematicians worried about the inscrutability of AI-generated proofs and about the fact that Maths is first and foremost about understanding rather than proving for the sake of proving, they're vastly underestimating what AI will be able to deliver in years to come.
IMO, it's very likely that:
> none of them has yet tried to point an AI in the direction of making an existing proof more understandable and intuitive to a human
I'm absolutely certain they've tried that. The issue is this alien intelligence cannot do it. And there are no signs that it ever will. I think way more realistic scenario is this intelligence will go further away from ours and become incomprehensible when it grounds its alien math research on top of its own, not millenia of human's.
>they're vastly underestimating what AI will be able to deliver in years to come
Will it be able to, though?
Don't rub it in; they're depressed enough as it is!
People still play chess and go and StarCraft. People do what people want to do. It's not clear whether this will reduce the number of working mathematicians or increase it. There will a lot to learn from the machine proofs that will open up new frontiers as well.
So, it's like the story, "We'll see."
There has been a shocking but not altogether surprising development, and all reactions are valid.
> People still play chess and go and StarCraft
Those are activities where repeating the same experience yourself is still enjoyable, kind of like you might eat today even though you already ate yesterday.
Finding mathematical proofs is probably more like seeing the ending to a mystery novel. Once the ending has been spoiled for you, it's really hard for you to enjoy it the same way, and it might be more fun to move on to a different mystery.
Different people have different feeling and motivation and reasons for doing things. No doubt there are people thinking like you, but it's to early to tell how it will be for the majority.
> People still play chess and go and StarCraft
Because most people still find them enjoyable. You can't say those are less enjoyable than math. There is no universal scale for enjoyment.
> kind of like you might eat today even though you already ate yesterday
You'd die if you stop eating after yesterday's meals. That's survival.
Some people enjoy rewatching or rereading books and others dont. Careers change and maybe we need a different type of mathematicians that does enjoy this work more than historical work?
> is probably more like seeing the ending to a mystery novel
lots of people enjoy knowing the end of the story as they start a book, and it does not prevent them from enjoying the book in the slightest.
Something that always comes as a great surprise to those who don't.
No, people enjoy methematics for the inner journey and for the depth it offers that is orthogonal to everythibg in existance. Learning math is awesome, furthering the field is just paying your dues
> is probably more like seeing the ending to a mystery novel
So math should switch to a Columbo methodology?
some people eat the same bland things every day and others spend a considerable amount of time learning and preparing new recipes.
Chess and StarCraft are games. For many other intellectual activities, part of the satisfaction comes from contributing something meaningful to a collective effort. If a machine can do that orders of magnitude faster, for many people these activities become effectively pointless.
The funny thing about people comparing mathematical research in the days of LLMs to playing chess in the days of Stockfish is that it identifies the competitive nature, and hence status seeking attitude, of the mathematical research community. Chess is, of course, a competitive game with a winner and a loser. You "win" mathematical research by solving a longstanding unsolved problem.
There is this idea of advancing human knowledge and adding to the record of what people know in mathematical research that breaks the analogy down, somewhat. But most people aren't Perelman. They would happily take the million dollar prize. And it is out of the question to do anything other than put your name on the published paper.
That is what I am gathering, too. I've been watching this from the sidelines, really confused by all the people moaning endlessly about how this revolution is somehow damaging to the community of mathematicians, which makes no sense to me no matter how many times I read their arguments.
But realizing that the primary driver was never actually proving the conjectures, nor understanding the proofs, sheds light into the issue. Many are not satisfied with the prospect of curating and preserving an ever growing collection of discoveries; what they wanted is being the discoverers themselves.
Which to me is mind boggling, because that is not what they have been saying aloud all along. Maybe it's my autism speaking, but I really thought they cared about the resulting knowledge rather than being recognized by their peers. How naïve of me to think that they were above that.
Meanwhile, people who simply enjoy having a tool that facilitates solving problems, because having a solution is their true goal rather than an excuse to obtain recognition or validation, are excited to use this new wonder.
Please don't pretend that you've somehow been deceived. Hasn't everyone heard quips like "theoretical physics is like sex: it has some useful results, but that's not why we do it"? How hard is it to understand that doing something is what gives pleasure, rather than the outcome?
Having AI tools does not remove the ability to do anything, other than being the first. I genuinely don't get that viewpoint, it is alien to me. It is equivalent to saying that the existence of bicycles removes the pleasure of running.
As for the personal swipe: please do better.
[dead]
This comment reminds me of the "run for fun" guy in Back to the Future Part III.
https://www.youtube.com/watch?v=ouCVJIpSmEE
(This isn't to say I disagree with you.)
Pro tip: life is pointless. So the machines are better at thinking about certain classes of things. So what? Either you enjoy thinking or you don't. Deciding whether you enjoy it or not based on a global scorecard is silly. Surely there are aliens out there somewhere that already figured out any given problem. Does that make finding the solution yourself any less satisfying?
I think what people actually want when they say this is to be the hero. They want the admiration. Which is fine, but at least he honest.
Yes! If their true goal was expanding the field, they would be excited. But if, instead, they saw this as some sort of a race to be the first to prove a conjecture, then their frustration is understandable. But it would be good if they had been honest about it from the get go; possibly they did not even realize it themselves.
I bet lots of them, who are in it for the love of the game, are truly excited by what is going on.
> I bet lots of them, who are in it for the love of the game, are truly excited by what is going on.
The noise from AHM and the like can be seen as a drive to intimidate these people into silence.
> People still play chess and go and StarCraft. People do what people want to do.
Poor analogy. Because math is one of those job-hobby type hybrids where the job may be enjoyable but you still need the academic infrastructure to do it on a modern level, both because you need funding and you need others to motivate you to keep to a certain standard.
Job-hobby hybrids like this are not the same as running and Starcraft where you can do it by yourself and still reap a lot of benefit from it in the same way. Hobbyists might still do math but if it were just up to the hobbyists, we wouldn't have the level of discovery we have today.
I think the whole point is that we are no longer at the top of the totem pole, cognition-wise. At least not in certain areas. Better get used to your goals being self-driven. If your sense of self relies on being the best you've got a problem.
> People still play chess and go and StarCraft
but very few get paid to do that
And now it's everybody else's turn!
At least starving artists are safe!
All the “it’s not clear if there will be fewer jobs in the future” rhetoric is frankly mind boggling. It’s pretty clear the goal of LLMs in a capital sense is to reduce operational budgets as much as possible. If it doesn’t happen naturally it will happen by execs forcing that decision.
Academic mathematics isn't an operational institution.
Though its funding does move with the number of major projects academia is tasked with that rely on mathematics to advance, it's a fundamental knowledge area that has no operational requirements to exist.
Have you not already heard others make this analogy a million times by now? It seems like I read it multiple times a day at this point.
Mathematics can be enjoyed recreationally as a puzzle like any other, but it isn’t just an arbitrary puzzle. It’s a science where one discovers truth and seeks an understanding of, and dreams up, new phenomena. It’s not chess, or go, or StarCraft. There’s no fixed rule set and the goal isn’t to ‘win’ or beat your opponents.
Let’s stop repeating this nonsense as if it’s a profound observation.
I didn't say that. I just pointed out that computers are better at these mental activities than humans, and humans still do them. More in fact.
It's an unbelievably unoriginal statement, and an irrelevant one too.
AI isn't going to stop hobbyists doing anything; no one ever suggested so. We're not talking about hobbyists.
I think human mathematicians would be more enthusiastic if these frontier labs were putting out new interesting open problems. As some of them are pointing out in the responses, the purpose of having big open questions is often more about the tools and techniques used in solving them. If some can be gleaned from the AI proofs then great but, if not, the only real outcome for some (not all) of these results is that humans won't be able to develop those techniques.
If OpenAI were coming up with interesting problems that everyone could explore as they foreclosed all these existing ones, I don't think the response would be as critical. Obviously, that's much more difficult and doesn't tie into the only telos of these companies (having a huge IPO to make all their investors and equity holding employees rich).
As usual (at least, as of recently), Terry Tao's assessment is measured but trenchant. Mathematical research has been a human process of improving understanding, to an extent that if you go far back enough in time, it was not distinguished from "philosophy". Part of that involves (involved?) ac academic engagement with the pursuit of knowledge, which means that results are discussed, presented, picked apart, etc., in a community of other people in pursuit of knowledge. The end result being the sum knowledge that humanity possesses grows. The way these results were dumped unceremoniously bypasses all of that. And, because we have all seen what regard the tech leadership class have shown for humanity, even in much more concrete and significant ethical questions than "is it ok to destroy the academic community", such as "is it ok to lower the friction to surveilling and/or enacting violence on society to the extent that it's all encompassing", I think it's pretty reasonable that their complicity in the latter will extend to the former.
I should point out that this is not a categorical treatment of AI results. I think about outcomes. Would I be angry if OpenAI dropped full contents of all the Vesuvius Challenge scrolls? Obviously not.
they would be treated the same: "we dont have time for your slop questions and conjectures, they do not even come from a place of struggle and curiosity, we will not engage with your PR attempts, we already have problems to solve and things to think about for the next 200 years"
I think this response makes unwarranted assumptions about the ideologies and goals of the people you're talking about, which is not even supported by most of these quotes in the linked page.
All of these reactions from Mathematicians keep reminding me of - true or urban legend, doesn't matter - the ballad of John Henry [1] who, according to the lore, died trying to compete with a steam powered drill.
[1] https://en.wikipedia.org/wiki/John_Henry_(folklore)
I think that this specific blog post is an important one for history.
The stunned responses indicate a set of some of humanity's brightest struggling to comprehend the emergence of such an incomprehensibly creative and powerful intelligence.
AI has come for coding.
AI has come for mathematics.
AI will come for everything else if we don't do something NOW.
I don't really understand these takes if we speak of the long-term. You're speaking of a world where there'd be widespread access to high quality cognitive work for a price approaching $0. The possibilities this would open are endless. We need to ensure that we don't neglect our own personal development, and fall into the sci-fi trope of an ignorant civilization relying on an machine built by their ancestors, but I don't think that's much of a practical concern.
In the short-run I think concern is much more merited because it will obviously cause some instability as the economy settles into a new equilibrium, but that's always the case with any sort of revolutionary technology. And this would almost certainly just be short-term stuff. As the value of one thing goes down, the value of other things would go up, and new things would emerge.
"a set of some of humanity's brightest struggling to comprehend the emergence of such an incomprehensibly creative and powerful intelligence"
Where do you get this from? There is exactly one comment that even mentions creativity, and none of them speak about intelligence. All seem to agree it's slop.
> To be fair, my first reaction was almost boredom. Yes, the AI has “proved” (really? Are we sure? Can we even understand what is written there?) a bunch of interesting results in my field. Not even a Millennium Problem. Pff. [..] If a paper or thesis is so badly written that I cannot get past the first page without considerable effort, I reject it and ask for a new, readable version. With these AI-generated papers, I feel that we, as a community, are not applying the same standards of quality and rigour. They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with redundant arguments, unclear logical structure, multiple dead ends, and strange or unsettling terminology — in other words, slop.
why assume that because LLMs are strong in a narrow set of fields it will be strong in everything? we don't make that assumption about other forms of intelligence. i.e nobody thinks Stockfish is good at product management, and people generally don't think that a genius composer will be equally good at botany.
In 1904, Psychologist Charles Spearman noticed something interesting about school children's academic performance. Students who excelled in one subject tended to do well in others even when those subjects appeared quite different. He proposed that a common underlying ability, which he called the general intelligence factor, or g, could explain these correlations. [1]
Today, g is one of the most robust findings in differential psychology. The tendency for different cognitive abilities to correlate positively has been replicated across numerous studies. g typically accounts for around 40 to 60% of the variance in cognitive test performance and is predictive of numerous life outcomes, including educational achievement and occupational performance. [2]
Evidence of g isn't confined to humans either. Studies of mice have identified a general cognitive factor explaining roughly 30 to 40% of the variation in performance across different learning tasks [3]. We have similar results for primates and birds.
To put it simply, intelligence tends to generalize. Humans who tend to have higher verbal skills also tend to have higher spatial skills, better memories, and faster processing speed. Someone with the cognitive ability to become an exceptional chemist might just as easily have become an exceptional mathematician or software engineer. The knowledge and skills required are obviously different, but the underlying cognitive abilities that make someone successful in one intellectually demanding field often transfer to others.
And yes, there is also evidence of g in LLMs [4].
[1] https://www.jstor.org/stable/1412107
[2] https://pmc.ncbi.nlm.nih.gov/articles/PMC8293439/
[3] https://pmc.ncbi.nlm.nih.gov/articles/PMC2614349/
[4] https://www.sciencedirect.com/science/article/pii/S016028962...
cognitive abilities correlate across a particular set of measured tasks but it's not established that high performance in those tasks generalises to arbitrary domains
theres a difference between having a general capacity to learn, possessing domain-specific expertise, and being able to reliably apply that expertise in the real world.
even in humans, a genius mathematician isn't necessarily an exceptional manager, composer, or biologist. general intelligence might make it easier to acquire those skills but it doesn't substitute for them.
the question isn't whether LLMs exhibit "g" but if the abilities being measured are representative of the broader capabilities we're predicting. that's not something g settles.
You are just restating what I already said.
>The knowledge and skills required are obviously different, but the underlying cognitive abilities that make someone successful in one intellectually demanding field often transfer to others.
The fact of the matter is that If you have a good general capacity to learn then becoming a competent x is generally only a matter of time and interest. For LLMs, it's the same except with data and compute. Naturally, all work done on a computer is in danger.
they did not specify LLMs
they are clearly talking about llms
because that's what's filling this role right now. the stated goal of these companies is ""agi"", exactly what you're talking about. if LLMs fail to take them there, they'll look for something else to do so. that's their whole thing. and then the guy's association will resolve different accordingly.
it's like recognizing that when most people talk about the os they're using, they're really discussing their de. great, their mistake, but at the same time they're not actually making any mistakes either, you're the one taking them there, then beating them with experience. what a de can pull off can heavily depend on how the underlying os works, and some os have a fixed de they ship with that's almost never replaced cause it's not really intended to be. going off about specifics when they did not talk in terms of specifics is obnoxious. which is probably no coincidence, given your username of choice.
> if we don't do something NOW
We are doing something now. We're making it so the AI does it all better, so we don't have to do it anymore. Gotta break a few eggs to make an omelet, but it's going to be a delicious fucking omelet when it's ready. I don't understand why people are pushing back so hard on making the world a better place. I personally can't wait until it's clankers all the way down.
Yes, the humans who control this system will surely evenly distribute the spoils of this new revolution among the people who have no stake in it. Certainly it will not lead to a kind of hyper-poverty not seen in recent human history where near demigods and subhumans are technically the same species, but only until the AI starts working on genetics.
Who controls anything? That's one reason I'm highly optimistic here. You can already performantly run frontier level models on systems with $1600 tier video cards. A couple of years ago it required supercomputing clusters. At this rate frontier tier models will be running on any plain old computer in a couple of years.
If LLM's reach their potential we're speaking of access to generalizable high quality cognitive labor for something approaching $0, for everybody.
>You can already performantly run frontier level models on systems with $1600 tier video cards.
Quanted out Qwen 3.8 models are not frontier level. Have you used them for real work? They suck. They are so unsure of themselves due to the quant-lobotomy. They just endlessly loop in thinking even when they have the right decision and then output it when they get to the thinking cap. They score close in benchmarks because most benchmarks don't measure time to complete a task.
I use Qwen quants in production for fast inference but I disable thinking and have them fine tuned for the task. My realtime transcription + translation stack right now is running 5 streams at 380 tok/s.
Running DeepSeek 4.1 Flash at FP4 is going to need at least a 10-15k machine. I'd consider that near frontier level.
Competition will drive down prices to zero, so we'll all be demigods.
However much compute you can buy, the big boys will always be able to buy orders of magnitude more. Orders of magnitude more compute means orders of magnitude more political and economic power.
The price will never be zero, since there is a finite amount of compute possible.
There is zero reason to believe we're barrelling toward utopia and plenty of examples that illustrate exactly where we are headed.
That's fine, because you don't need infinite compute to run or train current models. If the "big boys" are buying more compute that's because they hope to provide a better service.
I misspoke when I said "zero". I should have said "down to marginal cost". It's fine for AI to be priced at the cost of its compute! That's the efficient outcome.
What reason do you expect to provide a moat for a monopoly? Training on existing customer interactions? That might get you an oligopoly, but there are already two serious competitors in the US alone and several potential Chinese rivals.
Whether you agree or not, if you seriously can’t understand why people might be existentially (or economically!) anxious about the thinking machines, you may have already outsourced too much of your thinking to them.
> you may have already outsourced too much of your thinking to them
i'd think that instead of just giving in and reacting with a cheap insult, highlighting the unreasonable leap in rhetoric might be a bit more persuasive. to be specific:
> I don't understand why people are pushing back so hard on making the world a better place.
"making the world a better place" is not what's receiving the pushback. on the contrary, kind of the whole argument is that the current developments are short sighted, and that they will leave leave the world in a worse place on the long term.
and then one can agree or disagree about that, but at least then we'd not be arguing strawmans anymore, nor approaching increasingly childish insults
AI has to come for politicians, CEOs, executive leadership and management in all kinds of organizations first.
We can find a robot that will play golf instead of CEOs.
AI can generate keynotes and meet with other AI agents, pat itself on the back for success stories and give itself promotions and empire building.
Many of the reactions are some version of 'pissed off', which I totally understand. This reaction stands out and resonates with me:
> With these AI-generated papers, I feel that we, as a community, are not applying the same standards of quality and rigour. They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with redundant arguments, unclear logical structure, multiple dead ends, and strange or unsettling terminology — in other words, slop. And we are then expected to go through it, check it, clean it up, simplify it, and explain what is actually going on. This comes at a considerable cost to us in terms of time and effort, while they can simply move on and slop-bulldoze the next conjecture. And, of course, the credit remains theirs. In some sense, we are willingly contributing to our own demise.
I'm not a mathematician, so I didn't even try to read it. But if it is unreadable slop -- then why should we (humans) believe it is correct? And why should professional mathematicians labor through reading it?
I was really quite surprised that they'd parade around 722 manuscripts with only less than half (or really, close to only a third) of it being machine-checked. It's genuinely equivalent to the overconfident and blind drive-by PRs in software that people here should be well familiar with, and those are not exactly the hallmark of quality usually. Quite the curiously dangerous game to play when you're trying to scoop an entire field of study on an industrial scale as powerplay.
Or it's a touching show of openness. They're not in this for the ego-boost, they're sharing data on how things are working. Naive of them to expect gratitude, I guess.
It's only any of these things to the extent their unverified proofs end up correct. Otherwise, not only is it naive indeed, it is out of touch, an insulting waste of time, and mistaken. Hence why I find this a curiously dangerous game to play. Nobody treats this as the "scientific process" they're trying to frame this as, where manuscripts can just be redacted. If they genuinely believe in that framing, they're even more naive and out of touch than one can possibly imagine.
It really pains me to read the responses here to this and the AHM statements. It feels like HN people here are talking with such... privilege. These are the smartest people on the planet saying "hey, please don't do this, it's seriously hampering our work in this field". And then people on here say that mathematicians are... gate keeping? Not embracing progress? Who are you to say that? How do you know? What happened to empathy for others? I don't understand you all...
Part of it is probably because we've already been through this? The SWE field has seen exactly these reactions over the past 4+ years.
Some people saw "the spark" before LLMs were mainstream. We had code autocomplete models based on GPT2 that ran on your machine and provided line-based autocomplete. Then we had gpt3.5 (chatgpt launch) where it almost looked like it could write python, then we had gpt4 and saw the first glimpses of actual code writing, then opus4 / gpt5, and today we have sol/fable etc. At every step we had people in this field write the same kinds of takes. And at every step the tech evolved, improved, and got better. To a point where the vast majority learned to accept it, and the denialists (there are still some) are now in a minority.
And the acceptance phase was not "we are now useless as SWE", nor was it "hah, it's only for the juniors, we are safe. It was, mainly, "we can now work at a higher level of abstraction, and use our experience to guide these tools and work faster / broader / deeper in a topic. Basically understand the tools, learn their pros and cons, and adapt at using them.
Also part of it could be that the message seems to complain about the situation without providing alternatives. What are the alternatives? What are they proposing? "Please don't do this" does seem like gate keeping if you don't offer an alternative. What exactly do they want these labs to do? Don't try to solve the problems? (stop the count?) Don't publish the results? It's not clear to me.
I guess a lot of people are unclear on the messaging. Is this purely ideological, or is it something more? (It doesn't help that AHM also has a section where they highlight their members who pledge to do research "without AI assistance". Whatever that means. Yeah, that's cute, but can signal denial, which again we've already seen in SWE, and hopefully most people have dismissed it already) Are these statements part of the 7 stages of grief, or is there more? When taken at face value, the statements seem rushed, unprepared and "in denial". At least when compared to writing on the same topic from other people in the field (Tao et all).
> "hey, please don't do this, it's seriously hampering our work in this field"
I don't think that that's really a fair summary of the linked article though. By my reading, I'd say that a quarter of the responses were overall positive on the announcement, a quarter were overall negative, and the rest were mixed/neutral. I agree that there are many mathematicians saying something similar to "please don't do this", but that's not a consensus (or even a plurality) view.
(I agree with your broader point though, that lots of the other replies to this article are way too dismissive of mathematicians' concerns.)
OpenAI dropped a slop bomb on mathematics the same way people will drop slop bombs in codebases and the people here are saying “well drop everything and review it of course!”
I think it’s very reasonable to expect the people that are dropping this on other people for review to have reviewed it first, closely, made adjustments, etc, the same way I do before dumping my Claude/ChatGPT assisted PRs onto other people.
The reviewers shouldn’t be exerting more effort than the person that set the prompt.
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So why are these models more successful than mathematicians at solving these problems? Is it because of the computational power they bring to the problem? Is it because they use new techniques not thought of before? Or is it because human mathematicians have been approaching these problems in the wrong way?
A bit part of it is that no one human mathematical genius can hold all of math in their mind at once. The surface area is enormous. Humans specialize. The model has the luxury of finding obvious interactions in widely disconnected fields that no human would have found.
This seems like a like a huge advantage, the models can view everything. I wonder if they're being used to look at problems in physics like quantum gravity.
I am seeing a lot of high energy physics preprints on arxiv coming with AI acknowledgement recently https://arxiv.org/abs/2610.10673 https://arxiv.org/abs/2610.09093
But they aren't more successful. They can solve this because of standing on a huge body of work made by working mathematicians. Without it AI would get nowhere. Now AI are burning the minds that fed it for short term gain.
When AI has exhausted the existing math literature (and found a bunch of errors, I'm sure) it will have to start producing its own conjectures. Millions of them, even billions. And using all the experience from trying to prove them to improve.
You're acting like math is some sort of infinite game of automating unit tests. There is no shortage of conjectures and generating them is cheap. The struggle is finding the ones that are actually interesting. They only have value when they can unify disparate domains or reveal something that was previously hidden, or (the thing that I see most Mathematicians lamenting today) if they force the creation of new abstractions to solve.
Insight in mathematics doesn't emerge from brute-forcing conjectures. There is a recognized aesthetic economy that exists and without a semantic filter to detect the significance in any of these proofs we just end up with a lot of noise.
Oh, I'm sure most of those millions or billions of automated theorems will be uninteresting to us. But they will, in aggregate, be useful for the AIs, in improving the models and identifying lemmas and abstractions.
Yes, it would be very much like automatically generated tests. These are not worth much by themselves, but in massive bulk they can do interesting things.
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Why on earth would open AI pay for that though? There is no value in it anymore. The pointlessness of this destruction of math really is depressing to me.
They would do it if it would improve the general intelligence of their model(s).
I feel it would be effective and prudent to protest the current use of AI in mathematics and to effectively unionize and ostracize AI use until many of these demands are met. The companies that own the models and the infrastructure will never be more vulnerable. They have fired a salvo. Fire Back.
The companies are bending over backwards to accommodate. If they decide mathematicians are true enemies, they will bring out the knives. For example, pushing for cutting off of funding and setting up a competing Math 2.0, replacing Math 1.0 like chemistry replaced alchemy.
This is pretty insightful:
> One thing to keep in mind about this drop of papers is that they were not created by OpenAI with the main goal of making progress in mathematical research, or even primarily for PR (there were some PR posts, but e.g. the final announcement was comparatively restrained). The main reason these papers exist is that OpenAI used unsolved math problems to evaluate their internal models for the purpose of improving their capabilities. They had to use hard open problems because these are the only ones still posing a challenge to frontier AI models. I believe that, from OpenAI’s point of view, the papers are essentially a byproduct of their internal development.
Terence Tao:
> And I mourn the path not taken, and the opportunities lost in the frantic race to develop this technology. Labs submitting their frontier models to independent researchers for proper scientific evaluation. Coordination with the research community to ensure these tools are applied to complement and enhance the abilities and activities of human researchers, rather than compete with them. Use of these tools to foster collaboration and sharing, rather than competition and secrecy. Opening new doors, without closing old ones.
But that is not the path we now find ourselves in. Instead, the community needs to come together more than ever. To clearly declare our own standards and values, to build our own tools and practices, to support our most vulnerable members, and to chart our own path forward. Let’s get to work.
Also this, from Peter Scholze:
We should remember that we are all in this together; mathematics is a marathon, not a sprint; and the goal is and always will be the human understanding of mathematics, which will invariably take time.
What is worrying me the most, at the moment, is actually the (in)security of cryptography. Finding algorithms breaking standard cryptographic protocols is a number theory problem whose difficulty does, to my non-expert eyes, not significantly exceed what these systems are now capable of. And it would have disastrous consequences on society if such an algorithm is found.
I sympathise with a lot of the details of mathematicians' complaints, but at the same time I still see very few people stepping beyond "what will this do for the discipline" to think "what will this do for social welfare". It's like hearing scribes complaining about the printing press. Yes, I'm sorry that you won't get paid to do beautiful illuminated manuscripts, but I think the benefit to society outweighs that, and if it didn't, then why were you being paid to do the illumination in the first place?
It's not that there aren't possible arguments here (AI is destroying the basis for further progress). But this perspective is hardly even being addressed by most of the reactions.
What social welfare has this brought?
I bet more money was spent on the tokens than the mathematicians.
Were these problems just beautiful but useless? If so why did we pay people to work on them? My impression was that many mathematicians receive large research grants.
It feels like I’m reading a historical document from the industrial revolution
I like this one and find it easily actionable
... I think the paradigm has to shift. We should apply to AI-generated mathematical announcements the same standards of rigour, clarity, and exposition that we demand from human-generated papers. Do you want the approval of the mathematical community? A badge of legitimacy? Then give us something that is actually readable and verifiable. If not, we should simply ignore it.
In other words, I do not think that we, as a community, should spend our time cleaning up their mess in order to increase someone else’s commercial revenues. ...
Enrico Fatighenti
> Do you want the approval of the mathematical community? A badge of legitimacy?
I don't think that's why the AI companies are doing this.
It’s always frustrating to listen to people on HN and X, the everything app, talk about this with that characteristic smugness. “It’s totally understandable that they feel this way” “oh people still play chess!” As if what mathematicians are upset at “losing” an arbitrary strategy game. It’s a very childish way to interact with it but you can’t expect much I guess.
I like this website though because it collects a lot of the important frustrations from the mathematical community, these open problems were curated in order to organize a field around, most to all of them only have/had value in so far as they promoted study of the subject. The claim that AI proofs will open new frontiers for mathematics research could probably be true but misses the point that the manner OpenAI has gone about their “contribution” does more to cauterize the field than promote anything productive. OpenAI is functionally reducing the communities ability to ask real questions. Math is ultimately a very different field from the rest of the natural sciences, and I suspect a lot of the more simple discussion on this subject misses the objections because of those differences. All this to say, I don’t know that OpenAI is doing these haphazard releases cynically, with the assurance that all that matters is the headline, but it really does feel that way right now.
Please explain 2 things:
1. "...these open problems were curated in order to organize a field around, most to all of them only have/had value in so far as they promoted study of the subject" - I don't understand, how were the open problems curated? Do you mean that mathematicians put a lot of work into coming up with the problems and now all that work is somehow worthless now?
2. "OpenAI is functionally reducing the communities ability to ask real questions." How? Let's assume all the remaining proofs are correct (big assumption): how does resolving conjectures reduce the ability to pose new problems? This only makes sense to me if the assumption is that there are a relatively small number of possible problems to solve and so it's like a game that's coming to an end with no more interesting areas to explore. Surely math is bigger than these?
Sure, 1. Yes, a lot of effort is put into problem curation. Some parts of math are very problem list oriented while others are more program oriented. The work put into formulating the “correct” or “meaningful” (both of these adjectives should be taken in context) questions is not “somehow worthless” now, but the problems themselves now can/will no longer serve the same purpose they did. A significant part of their purpose was to organize the fields. If a solved problem could still provide a reference point for a field to organize around is a question I don’t really have the answer to.
2. Yes, math is bigger than the solved problems, of course. There is a plausibly infinite number of problems and theorems to work on. That being said, the ability to ask new questions which are of some “mathematical use” requires skills built from working on and solving prior problems. It might have happened to you in college at an advanced class where the professor would turn to the class and ask if there were any question, but everyone is so past their depth that despite being confused, no questions are asked. I’m not saying math is coming to an end but rather that one part of it, the question asking part, has become harder while the question answering part has become much easier.
The above depends on some understanding of what makes something useful in mathematics, which is not something I trust myself to relay the nuances of. Anyways, I hope I elucidated my opinions workably enough.
Thank you!
An interesting split in reactions by people who work in mathematics to the OpenAI release:
1. Reacting from the POV of the individual person: disappointment, disillusionment, and/or grief from those who've worked on some problem for years and now don't have something to work on; it's been a part of their identity. As well as those whose career tracks and plans were thrown in disarray.
I wholeheartedly sympathize with the above.
2. Reacting from the POV of the entirety of mathematics as a field of study/research:
This second type of reaction... is confusing. No one is forced to read any of the papers. Ignore them if you want. But also, isn't reading papers a lot of the job? I doubt mathematicians have intentionally not solved problems just so that they can remain unsolved? Build on these advancements (or disprove them - wouldn't that be an amazing result!) and pose new problems?What if a human dropped all of these without AI? I suspect there wouldn't be the same reaction for some reason.
The bittersweet irony of an explosion of scientific progress under anti-intellectual political leadership.
Is denying human biodiversity or heritability of IQ considered intellectual?
I read a bunch of carpenters bemoaning the invention of the table saw.