100+ reactions to 100+ solutions
proofsandprompts.com
proofsandprompts.com
>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.
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.
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.
They need to state it was entirely autonomous.
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.
>Let mathematicians do the AI-supported research on their own incentive at their own pace?
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
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? :-/
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.
“Dumping unverified results” seems to imply that those results come with an obligation of some kind.
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.
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?Will it be able to, though?
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.
So, it's like the story, "We'll see."
There has been a shocking but not altogether surprising development, and all reactions are valid.
but very few get paid to do that
At least starving artists are safe!
https://www.youtube.com/watch?v=ouCVJIpSmEE
(This isn't to say I disagree with you.)
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.
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.
As for the personal swipe: please do better.
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.
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.
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.
AI isn't going to stop hobbyists doing anything; no one ever suggested so. We're not talking about hobbyists.
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.
> 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.
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.
So math should switch to a Columbo methodology?
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.
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.
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.
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.
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.
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
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.
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.
If LLM's reach their potential we're speaking of access to generalizable high quality cognitive labor for something approaching $0, for everybody.
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.
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.
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...
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.
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.
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.
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.
> 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 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.
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).
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.)
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.
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.
> 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.
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.
> 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.
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.
I bet more money was spent on the tokens than the mathematicians.
... 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
I don't think that's why the AI companies are doing this.
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?
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.
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."
"Open problems are a resource that the mathematical community developed over decades or even centuries"
What if a human dropped all of these without AI? I suspect there wouldn't be the same reaction for some reason.