| ▲ | 100+ reactions to 100+ solutions(proofsandprompts.com) |
| 76 points by jacobedawson a day ago | 68 comments |
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| ▲ | schiffern 15 hours ago | parent | next [-] |
| >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. |
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| ▲ | layer8 14 hours ago | parent | next [-] | | 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. | | |
| ▲ | schiffern 2 hours ago | parent | next [-] | | >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? :-/ | | |
| ▲ | nxpnsv 2 hours ago | parent [-] | | 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. |
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| ▲ | ncruces 14 hours ago | parent | prev [-] | | 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. | | |
| ▲ | Robotbeat 7 hours ago | parent | next [-] | | 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. | |
| ▲ | famouswaffles 7 hours ago | parent | prev [-] | | Well yeah, their ultimate goal is to develop "highly autonomous systems that outperform humans at most economically valuable work" |
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| ▲ | boredhedgehog 4 hours ago | parent | prev [-] | | 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. |
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| ▲ | sunir 20 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | omoikane 19 hours ago | parent | next [-] | | > 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. | | |
| ▲ | tobbe2064 3 hours ago | parent | next [-] | | 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 | |
| ▲ | jryle70 18 hours ago | parent | prev | next [-] | | 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. | |
| ▲ | namrog84 13 hours ago | parent | prev | next [-] | | 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? | |
| ▲ | ur-whale 17 hours ago | parent | prev | next [-] | | > 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. | |
| ▲ | vadansky 16 hours ago | parent | prev | next [-] | | > is probably more like seeing the ending to a mystery novel So math should switch to a Columbo methodology? | |
| ▲ | slopinthebag 16 hours ago | parent | prev [-] | | some people eat the same bland things every day and others spend a considerable amount of time learning and preparing new recipes. |
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| ▲ | lf88 19 hours ago | parent | prev | next [-] | | 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. | | |
| ▲ | abnry 19 hours ago | parent | next [-] | | 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. | | |
| ▲ | david-gpu 15 minutes ago | parent [-] | | 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. |
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| ▲ | elicash 19 hours ago | parent | prev | next [-] | | 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.) | |
| ▲ | idiotsecant 7 hours ago | parent | prev [-] | | 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. | | |
| ▲ | david-gpu 10 minutes ago | parent [-] | | 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. |
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| ▲ | vouaobrasil 18 hours ago | parent | prev | next [-] | | > 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. | | |
| ▲ | idiotsecant 7 hours ago | parent [-] | | 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. |
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| ▲ | dist-epoch 20 hours ago | parent | prev | next [-] | | > People still play chess and go and StarCraft but very few get paid to do that | | |
| ▲ | esafak 6 hours ago | parent [-] | | And now it's everybody else's turn! At least starving artists are safe! |
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| ▲ | xanderlewis 19 hours ago | parent | prev | next [-] | | 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. | | |
| ▲ | sunir 15 hours ago | parent [-] | | 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. |
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| ▲ | righthand 18 hours ago | parent | prev [-] | | 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. | | |
| ▲ | sunir 15 hours ago | parent [-] | | 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. |
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| ▲ | guy_named_matt 17 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | somenameforme 3 hours ago | parent | next [-] | | 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. | |
| ▲ | thelastgallon 5 hours ago | parent | prev | next [-] | | 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. | |
| ▲ | customguy 3 hours ago | parent | prev | next [-] | | "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. | |
| ▲ | stronglikedan 17 hours ago | parent | prev | next [-] | | > 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. | | |
| ▲ | wk_end 12 hours ago | parent | next [-] | | 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. | | |
| ▲ | perching_aix 9 hours ago | parent [-] | | > 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 |
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| ▲ | idiotsecant 7 hours ago | parent | prev [-] | | 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. | | |
| ▲ | somenameforme 2 hours ago | parent | next [-] | | 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. | |
| ▲ | dash2 3 hours ago | parent | prev [-] | | Competition will drive down prices to zero, so we'll all be demigods. |
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| ▲ | slopinthebag 16 hours ago | parent | prev [-] | | 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. | | |
| ▲ | famouswaffles 6 hours ago | parent | next [-] | | 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... | | |
| ▲ | slopinthebag 5 hours ago | parent [-] | | 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. |
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| ▲ | perching_aix 9 hours ago | parent | prev [-] | | they did not specify LLMs | | |
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| ▲ | drumhead 13 hours ago | parent | prev | next [-] |
| 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? |
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| ▲ | nxpnsv an hour ago | parent | next [-] | | 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. | |
| ▲ | idiotsecant 7 hours ago | parent | prev [-] | | 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. |
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| ▲ | smath 15 hours ago | parent | prev | next [-] |
| 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? |
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| ▲ | perching_aix 10 hours ago | parent [-] | | 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. |
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| ▲ | antonly 16 hours ago | parent | prev | next [-] |
| 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... |
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| ▲ | NitpickLawyer 4 hours ago | parent | next [-] | | 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). | |
| ▲ | gucci-on-fleek 3 hours ago | parent | prev | next [-] | | > "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.) | |
| ▲ | Espressosaurus 16 hours ago | parent | prev [-] | | 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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| ▲ | dash2 3 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | markvdb 6 hours ago | parent | prev | next [-] |
| The bittersweet irony of an explosion of scientific progress under anti-intellectual political leadership. |
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| ▲ | djoldman 14 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | ur-whale 16 hours ago | parent | prev | next [-] |
| 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?
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| ▲ | AlienRobot 2 hours ago | parent | next [-] | | >they're vastly underestimating what AI will be able to deliver in years to come Will it be able to, though? | |
| ▲ | esafak 6 hours ago | parent | prev [-] | | Don't rub it in; they're depressed enough as it is! |
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| ▲ | TripolitianFish 18 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | djoldman 14 hours ago | parent [-] | | 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? |
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| ▲ | ur-whale 17 hours ago | parent | prev | next [-] |
| 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) |
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| ▲ | viccis 18 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | githubnuoo 18 hours ago | parent [-] | | 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" | | |
| ▲ | viccis 18 hours ago | parent [-] | | 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. |
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| ▲ | weard_beard 17 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | thereisnospork 9 hours ago | parent | prev [-] |
| I read a bunch of carpenters bemoaning the invention of the table saw. |