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.
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.
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.
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.
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.
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.
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.
> 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.
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.
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.
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.