> I believe in chasing fantastic scientific and mathematical progress with the help of LLMs, we risk imperiling our institutions, our professional norms, and human mathematical understanding
I don't think that defending institutions and professional status is a great image for a largely publicly funded academia. Academia should not be about reproducing itself firstmost. This may be a bit less pronounced in mathematical academic work ("which is already useless" as author says and def more honest about it) but broadly academia should care more about progress than its institutional status and professional norms (as in the status in which careering in academia is defined, not honesty, integrity, rigour and other such norms that are already not as greatly upheld anyway in many parts of it as it should).
The "human mathematical understanding" is indeed a valid concern imo.
Maintaining human understanding in the face of fast progress is a big unsolved problem. If you are worried about there being nothing left when LLMs tear their way through a topic then the presence of a big unsolved problem should be comforting!
And it seems legitimately like an important problem for mathematics (and other areas), one which is deeply academic in the best sense: mathematicians spend much more time transmitting understanding than doing novel math, because they mostly exist in academia and that’s the job.
The futures I predict, out of my ass, for when the LLM wildfire spreads enough:
1. We are in a situation that the pace crumbles, in which situation we are left with classes of problems LLMs simply cannot touch because they have exhausted the "low hanging fruits" that their training and architecture was optimised for solving. In this scenario there is still stuff for the mathematicians to do, but the way young research mathematicians get trained has to be adjusted.
2. Or we simply see some slowdown, but it is still fast enough that it overtakes human capacities and produces novel mathematics that are harder and harder to understand, as LLMs are adapting to solve more and more types of problems faster than humans, while more and more fields are transcribed into lean. I guess if that happens the main role would be to clean up the llms' work, trying to get some gist out of it to build theories, and guide the llms for those with access to them. But not sure how many mathematicians will have access to these advanced LLMs to work with, so this may create big issues. Until now funding of mathematical work was somewhat trivial, they would only have expenses for traveling, conferences, and phds and postdocs, compared to other fields that need labs, equipment, high compute and/or research assistants to function.
In the goal of the math problems to get the answers or think for years on a complicated topic? It’s the same Q developers have. Are they paid to type code or create programs?
As a not math person, seems strictly good that AI can solve more problems. If they were important, it can maybe unlock new science. If they had no useful purpose, why did we think about them for years?
The goal is more to understand why something is true than just whether it is true. To oversimplify a lot, it's the difference between industry versus academic motivation. In the former case you have a point, but not so much in the latter. We really need both modes of work going on.
> As a not math person, seems strictly good that AI can solve more problems.
As a math person I think that's probably true, though it's not that simple. We do still have to understand the solutions to the problems, and take time to explore. That's how we figure out what problems should be solved in the first place. Cognitive debt is bad enough in your codebase, but you don't really want it to overwhelm entire academic disciplines.
> If they had no useful purpose, why did we think about them for years?
I don't see a 'we' here. By your own admission you didn't spend years thinking about complicated math topics. So maybe you simply don't see the "purpose". Or maybe no one sees the purpose yet because for some math practical applications take years to discover.
The goal of math is perhaps the answer but also the understanding. One can't use the answers without understanding them, which is a fundamental difference between math and a program. Most modern math isn't applicable in the sense that you just take some result and it gives something practical. The value of math is in understanding it so that it can be properly applied which requires a deep knowledge of why it is so in the first place.
> If they had no useful purpose, why did we think about them for years?
A lot of mathematics is mostly useless, and probably will be for hundreds of years. Some of it ends up being useful, but it's unlikely that much of math like work on geometric langlands will have any applications whatsoever. Math is a service department and the way people teach math best is to be experts in it. In turn, the best way to do that is to develop new math, at least within the context of academia.
Yes, there is some pure math that is used eventually, but I'd say (as someone who worked in pure math for over a decade) that as the results become more specialized and abstract over time, fewer and fewer of them will ever be used.
Every once in a while you see a news article about some math related to physics or something but that's 1/1000 results, if that. The fact is, most modern math research is likely never to be "used".
That doesn't make it useless because maybe we just want to know, but we have to be realistic here...
> I am not a Luddite. I think that it is fine if human mathematicians decide that we want to use LLMs..
Luddites weren't technophobic. They were protesting against the industrialist drive to slash wages, release low quality goods and destroy their livelihoods in the process. Much like author.
They are remembered as the opposite because the industrialists won and the enshittification happened.
You may be interested in David Noble's work on this, see "Forces of Production: A Social History of Industrial Automation".
People do indeed slur the luddites, and I have to say, emotionally they are very sympathetic.
At the same time, they slur the industrialists, who are also caricatured. What we need to acknowledge, is that the cheaper mass produced goods allow more people to have those goods, even if they are not as good as the artisanal goods.
That is why, for example, when you have projects like trying to create a laptop for the third world, they use cheap components and make a lot of sacrifices, because a shitty laptop that you can use is better than a nice laptop you can't afford.
But it is absolutely true, that progress is not just an arrow pointing up. Progress generally means a reduction in quality and durability and often it means a reduction in beauty as well. And progress also often means replacing artisinal work with mind numbing drudgery or even unhealthy office work that humans were not meant to do, physically and psychologically. There is a real cost to progress, and people on both sides of this debate understand this cost and come to different conclusions. There is no villain here.
Another work I'd recommend is "On the Nature of the Gothic" by Ruskin. It is part of a series on Venetian Architecture Ruskin wrote, called "The Stones of Venice", and he focuses on the amazing variety, gratuitousness, and somewhat poor execution of the countless gargoyles and other flourishes that he saw when visiting Venice:
https://archive.org/details/natureofgothicch00rusk/page/n9/m...
It's hard to say what the optimum is. We have cheap disposable clothes when in the past, people might own only a single suit, but it was a beautiful, handmade suit that fit them well and they could even pass onto their children. We have cheap Ikea furniture but in the past people had handmade gorgeous heirlooms they could have as family inheritances. But those were heavy and hard to move around and you were stuck with them. There are real trade offs. And when most people choose the mass produced stuff, the artisanal stuff gets more expensive also. At the same time, it can truly be soulless to be surrounded by cheap junk that you feel was made in a hostile manner to human nature. Where you fall on this depends a lot on your disposable income.
> while “Luddite” may be a pejorative today, the textile workers who destroyed mechanized looms were not behaving so irrationally from an economic standpoint.
So when the author says she is not a Luddite, she does so knowing full well what that word means.
Exactly. Luddites are not necessarily completely anti-tool. They were against large scale applications of complex technology to replace human beings en-masse. Personally I'd consider myself a Luddite but I'm not against a hammer or even a calculator but I am against AI completely, and I think more and more people should be Luddites...
> I believe in chasing fantastic scientific and mathematical progress with the help of LLMs, we risk imperiling our institutions, our professional norms, and human mathematical understanding
I don't think that defending institutions and professional status is a great image for a largely publicly funded academia. Academia should not be about reproducing itself firstmost. This may be a bit less pronounced in mathematical academic work ("which is already useless" as author says and def more honest about it) but broadly academia should care more about progress than its institutional status and professional norms (as in the status in which careering in academia is defined, not honesty, integrity, rigour and other such norms that are already not as greatly upheld anyway in many parts of it as it should).
The "human mathematical understanding" is indeed a valid concern imo.
Maintaining human understanding in the face of fast progress is a big unsolved problem. If you are worried about there being nothing left when LLMs tear their way through a topic then the presence of a big unsolved problem should be comforting!
And it seems legitimately like an important problem for mathematics (and other areas), one which is deeply academic in the best sense: mathematicians spend much more time transmitting understanding than doing novel math, because they mostly exist in academia and that’s the job.
The futures I predict, out of my ass, for when the LLM wildfire spreads enough:
1. We are in a situation that the pace crumbles, in which situation we are left with classes of problems LLMs simply cannot touch because they have exhausted the "low hanging fruits" that their training and architecture was optimised for solving. In this scenario there is still stuff for the mathematicians to do, but the way young research mathematicians get trained has to be adjusted.
2. Or we simply see some slowdown, but it is still fast enough that it overtakes human capacities and produces novel mathematics that are harder and harder to understand, as LLMs are adapting to solve more and more types of problems faster than humans, while more and more fields are transcribed into lean. I guess if that happens the main role would be to clean up the llms' work, trying to get some gist out of it to build theories, and guide the llms for those with access to them. But not sure how many mathematicians will have access to these advanced LLMs to work with, so this may create big issues. Until now funding of mathematical work was somewhat trivial, they would only have expenses for traveling, conferences, and phds and postdocs, compared to other fields that need labs, equipment, high compute and/or research assistants to function.
In the goal of the math problems to get the answers or think for years on a complicated topic? It’s the same Q developers have. Are they paid to type code or create programs?
As a not math person, seems strictly good that AI can solve more problems. If they were important, it can maybe unlock new science. If they had no useful purpose, why did we think about them for years?
> Are they paid to type code or create programs?
The goal is more to understand why something is true than just whether it is true. To oversimplify a lot, it's the difference between industry versus academic motivation. In the former case you have a point, but not so much in the latter. We really need both modes of work going on.
> As a not math person, seems strictly good that AI can solve more problems.
As a math person I think that's probably true, though it's not that simple. We do still have to understand the solutions to the problems, and take time to explore. That's how we figure out what problems should be solved in the first place. Cognitive debt is bad enough in your codebase, but you don't really want it to overwhelm entire academic disciplines.
> If they had no useful purpose, why did we think about them for years?
I don't see a 'we' here. By your own admission you didn't spend years thinking about complicated math topics. So maybe you simply don't see the "purpose". Or maybe no one sees the purpose yet because for some math practical applications take years to discover.
The goal of math is perhaps the answer but also the understanding. One can't use the answers without understanding them, which is a fundamental difference between math and a program. Most modern math isn't applicable in the sense that you just take some result and it gives something practical. The value of math is in understanding it so that it can be properly applied which requires a deep knowledge of why it is so in the first place.
> If they had no useful purpose, why did we think about them for years?
A lot of mathematics is mostly useless, and probably will be for hundreds of years. Some of it ends up being useful, but it's unlikely that much of math like work on geometric langlands will have any applications whatsoever. Math is a service department and the way people teach math best is to be experts in it. In turn, the best way to do that is to develop new math, at least within the context of academia.
Yes, there is some pure math that is used eventually, but I'd say (as someone who worked in pure math for over a decade) that as the results become more specialized and abstract over time, fewer and fewer of them will ever be used.
Every once in a while you see a news article about some math related to physics or something but that's 1/1000 results, if that. The fact is, most modern math research is likely never to be "used".
That doesn't make it useless because maybe we just want to know, but we have to be realistic here...
> I am not a Luddite. I think that it is fine if human mathematicians decide that we want to use LLMs..
Luddites weren't technophobic. They were protesting against the industrialist drive to slash wages, release low quality goods and destroy their livelihoods in the process. Much like author.
They are remembered as the opposite because the industrialists won and the enshittification happened.
You may be interested in David Noble's work on this, see "Forces of Production: A Social History of Industrial Automation".
People do indeed slur the luddites, and I have to say, emotionally they are very sympathetic.
At the same time, they slur the industrialists, who are also caricatured. What we need to acknowledge, is that the cheaper mass produced goods allow more people to have those goods, even if they are not as good as the artisanal goods.
That is why, for example, when you have projects like trying to create a laptop for the third world, they use cheap components and make a lot of sacrifices, because a shitty laptop that you can use is better than a nice laptop you can't afford.
But it is absolutely true, that progress is not just an arrow pointing up. Progress generally means a reduction in quality and durability and often it means a reduction in beauty as well. And progress also often means replacing artisinal work with mind numbing drudgery or even unhealthy office work that humans were not meant to do, physically and psychologically. There is a real cost to progress, and people on both sides of this debate understand this cost and come to different conclusions. There is no villain here.
Another work I'd recommend is "On the Nature of the Gothic" by Ruskin. It is part of a series on Venetian Architecture Ruskin wrote, called "The Stones of Venice", and he focuses on the amazing variety, gratuitousness, and somewhat poor execution of the countless gargoyles and other flourishes that he saw when visiting Venice: https://archive.org/details/natureofgothicch00rusk/page/n9/m...
It's hard to say what the optimum is. We have cheap disposable clothes when in the past, people might own only a single suit, but it was a beautiful, handmade suit that fit them well and they could even pass onto their children. We have cheap Ikea furniture but in the past people had handmade gorgeous heirlooms they could have as family inheritances. But those were heavy and hard to move around and you were stuck with them. There are real trade offs. And when most people choose the mass produced stuff, the artisanal stuff gets more expensive also. At the same time, it can truly be soulless to be surrounded by cheap junk that you feel was made in a hostile manner to human nature. Where you fall on this depends a lot on your disposable income.
The author mentions this in the article:
> while “Luddite” may be a pejorative today, the textile workers who destroyed mechanized looms were not behaving so irrationally from an economic standpoint.
So when the author says she is not a Luddite, she does so knowing full well what that word means.
Exactly. Luddites are not necessarily completely anti-tool. They were against large scale applications of complex technology to replace human beings en-masse. Personally I'd consider myself a Luddite but I'm not against a hammer or even a calculator but I am against AI completely, and I think more and more people should be Luddites...