>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.
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.
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.
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?
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.
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.
> 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.
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.
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...
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.
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.
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.
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
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.
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?
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.
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.
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?
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?
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 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.
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.
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.
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.
Well yeah, their ultimate goal is to develop "highly autonomous systems that outperform humans at most economically valuable work"
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.
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
So math should switch to a Columbo methodology?
> 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.
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.
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.)
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.
> 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.
> People still play chess and go and StarCraft
but very few get paid to do that
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.
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...
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.
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.
> 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.
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
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.
they did not specify LLMs
they are clearly talking about llms
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?
I read a bunch of carpenters bemoaning the invention of the table saw.
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.
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.
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:
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?
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 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.