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Hacker News
> “Even if AI can prove theorems and theory-craft more efficiently than humans, and even if these proofs and theories are beautiful and interesting, and even if they are presented with elegance and clarity of thought, mathematicians will still have a place in the appraisal, presentation, understanding and appreciation of this new abundance of pleasing non-human proofs. We can still practice mathematics, learn mathematics, teach mathematics and do mathematics together.”
I am not a mathematician, but this seems like an entirely non-problematic answer to me. Mathematics is ultimately the discovery of relations and their consequences, so of course large language models were eventually going to catch up. But precisely what they do lack is ability to appreciate these relations.
The author says mathematics is a spiritual pursuit.[1] I have asked LLMs about theological topics before and they have also been able to produce perfectly cogent answers (even heavy questions like “how did Aquinas view Pseudo-Dionysius’ negation-laden description of God”). I am not the least bit shaken by this, because it is still on me to evaluate and understand, and appreciate these answers.[2] The author seems to think LLM’s pattern recognition makes redundant human understanding and appreciation, which is a logical leap that doesn’t make sense to me. Maybe the author is conflating utility and purpose? I feel bad, and hope the author takes care of themself, but I really think the author is taking a massive leap here. It is not that deep.
[1] I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.
[2] I of course wouldn’t consult an LLM if I actually wanted to educate myself or reason about these topics. Not only do I want to reason through them myself, but when it comes to issues in philosophy/theology/heavy stuff, you need to take in to account the perspective and experiences of the human writing them. LLMs muddle everyone’s perspective together.
by yaqubroli
It should be a mandatory part of a technology-related degree to watch "The Man in the White Suit" (1951) https://youtu.be/RC8q1QSkE3M
When a new technology comes along, it diminishes some aspect of the human experience - because whoever had a talent for doing things the older, more difficult way becomes less important.
In that regard, AI is the extreme, because it threatens to make so many of our intellectual talents useless.
When I was in mathematics, reading other people's work was always more rewarding to me than doing my own. I would spend years on a question to get some progress, versus spending a few days or weeks reading a paper to enjoy something new. I understand not everyone is like me but I really welcome the omniscient mathematician machine people are predicting. I can't wait to ask all the questions I care about.
by Athanase000
One way to differentiate between an art or a craft and a science is that if a genie appeared and offered to trivialize all the discovery work of your career and simply give you the answers today, and you'd say "no", you're probably not doing science.
by tptacek
> For me, the affective quality of learning mathematics is empathetically tethered to an act of discovery and creation. It is social. We are conversant with another mathematician—perhaps long dead. If we follow the chain of communication we arrive at a mathematician who enjoyed some original discovery. Human mathematics is Talmudic. It is a lively discourse of philosophical and religious richness spanning thousands of years.
This is really beautiful. And no matter what happens, two things have to be true: some form of lively philosophic and religious richness will keep being a core part of our history and will touch every person in some way; and it will change enormously over time (maybe with math continuing to be a small part, maybe not).
There is a part of math that is like that. There's also another part (as Vladimir Arnold provocatively said):
> All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like) hydrodynamics (supported by manufacturers of atomic submarines) celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).
> Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
> Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.
> Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.
Those parts can just be delegated to AI the same way they used to be delegated to mathematicians. But Arnold continued:
> The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).
by ngriffiths
As a mathematics person, I find this at odds with my views. I know the current regime rewards new mathematical discoveries for professional advancement, but that is a job thing, one which can be altered by the powers that be. To me investigating mathematics is fun whether it is new to the world or not. The complaint is similar to lamenting how everywhere has already been visited and there is nothing to be done other than have your own personal experience of a place. I saw the redwoods recently for the first time and I thoroughly enjoyed the experience despite not being the first person to see them. Mathematical discovery is much the same except now we have tools that help us dramatically with the tedious stuff, the researching what others know. In the old days, I would spend a long time figuring something out and only at the end could I figure out where to find it in the literature. Very frustrating. Now, we have machines to guide us to many things and understandings and clarifications. They are guides that help us get to where we want to be and then let us wander as we desire. This is incredible. I am currently using them to develop the computational tools I want to use to explore stuff.
As for squeezing in the time to do mathematics if the paying jobs disappear, there is a good chance we will have a world of plenty very shortly. I have a belief that the Austrian economists are right that there will always be plenty for humans to do and get rewarded for, but I also think that the costs of living will be so low that someone who wants to do mathematics will have plenty of time to do so. I hope this person holds the faith long enough and tries to see how the AI's can help accelerate one's own understanding. I am no fan of AIs generating a bunch of papers that no one reads or cares about, but I could say the same about the immense number of papers made by humans as well. If anything, the AIs make all of that immense knowledge more valuable as it is now knowable and accessible through these tools. There is also the fact that the mathematics job market has been oversaturated for at least 20 years. What our new tools allow is for people to be able to do mathematics outside of having access to a research library and top mathematics department.
by jostylr
Grateful for this essay. Made me feel seen.
Someone said:
> No one is stopping you from doing what you enjoy.
But that's wrong. LLMs are creating an environment in which some things are no longer enjoyable.
For example there is less joy to be had in learning a programming language in 2026 than there was in 2016, because there is less utility in it now.
by marifjeren
Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output.
Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subfields of mathematics. Of course, you won't be doing the creation directly, in the way the mathematicians of old did; that's just not the name of the game anymore. But you will still be directing the research and involved in the creation.
by d_burfoot
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- Hacker News
- > “Even if AI can prove theorems and theory-craft more efficiently than humans, and even if these proofs and theories are beautiful and interesting, and even if they are presented with elegance and clarity of thought, mathematicians will still have a place in the appraisal, presentation, understanding and appreciation of this new abundance of pleasing non-human proofs. We can still practice mathematics, learn mathematics, teach mathematics and do mathematics together.”
I am not a mathematician, but this seems like an entirely non-problematic answer to me. Mathematics is ultimately the discovery of relations and their consequences, so of course large language models were eventually going to catch up. But precisely what they do lack is ability to appreciate these relations.
The author says mathematics is a spiritual pursuit.[1] I have asked LLMs about theological topics before and they have also been able to produce perfectly cogent answers (even heavy questions like “how did Aquinas view Pseudo-Dionysius’ negation-laden description of God”). I am not the least bit shaken by this, because it is still on me to evaluate and understand, and appreciate these answers.[2] The author seems to think LLM’s pattern recognition makes redundant human understanding and appreciation, which is a logical leap that doesn’t make sense to me. Maybe the author is conflating utility and purpose? I feel bad, and hope the author takes care of themself, but I really think the author is taking a massive leap here. It is not that deep.
[1] I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.
[2] I of course wouldn’t consult an LLM if I actually wanted to educate myself or reason about these topics. Not only do I want to reason through them myself, but when it comes to issues in philosophy/theology/heavy stuff, you need to take in to account the perspective and experiences of the human writing them. LLMs muddle everyone’s perspective together.
by yaqubroli - It should be a mandatory part of a technology-related degree to watch "The Man in the White Suit" (1951) https://youtu.be/RC8q1QSkE3M
When a new technology comes along, it diminishes some aspect of the human experience - because whoever had a talent for doing things the older, more difficult way becomes less important.
In that regard, AI is the extreme, because it threatens to make so many of our intellectual talents useless.
- When I was in mathematics, reading other people's work was always more rewarding to me than doing my own. I would spend years on a question to get some progress, versus spending a few days or weeks reading a paper to enjoy something new. I understand not everyone is like me but I really welcome the omniscient mathematician machine people are predicting. I can't wait to ask all the questions I care about.by Athanase000
- One way to differentiate between an art or a craft and a science is that if a genie appeared and offered to trivialize all the discovery work of your career and simply give you the answers today, and you'd say "no", you're probably not doing science.by tptacek
- > For me, the affective quality of learning mathematics is empathetically tethered to an act of discovery and creation. It is social. We are conversant with another mathematician—perhaps long dead. If we follow the chain of communication we arrive at a mathematician who enjoyed some original discovery. Human mathematics is Talmudic. It is a lively discourse of philosophical and religious richness spanning thousands of years.
This is really beautiful. And no matter what happens, two things have to be true: some form of lively philosophic and religious richness will keep being a core part of our history and will touch every person in some way; and it will change enormously over time (maybe with math continuing to be a small part, maybe not).
There is a part of math that is like that. There's also another part (as Vladimir Arnold provocatively said):
> All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like) hydrodynamics (supported by manufacturers of atomic submarines) celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).
> Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
> Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.
> Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.
Those parts can just be delegated to AI the same way they used to be delegated to mathematicians. But Arnold continued:
> The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).
by ngriffiths - As a mathematics person, I find this at odds with my views. I know the current regime rewards new mathematical discoveries for professional advancement, but that is a job thing, one which can be altered by the powers that be. To me investigating mathematics is fun whether it is new to the world or not. The complaint is similar to lamenting how everywhere has already been visited and there is nothing to be done other than have your own personal experience of a place. I saw the redwoods recently for the first time and I thoroughly enjoyed the experience despite not being the first person to see them. Mathematical discovery is much the same except now we have tools that help us dramatically with the tedious stuff, the researching what others know. In the old days, I would spend a long time figuring something out and only at the end could I figure out where to find it in the literature. Very frustrating. Now, we have machines to guide us to many things and understandings and clarifications. They are guides that help us get to where we want to be and then let us wander as we desire. This is incredible. I am currently using them to develop the computational tools I want to use to explore stuff.
As for squeezing in the time to do mathematics if the paying jobs disappear, there is a good chance we will have a world of plenty very shortly. I have a belief that the Austrian economists are right that there will always be plenty for humans to do and get rewarded for, but I also think that the costs of living will be so low that someone who wants to do mathematics will have plenty of time to do so. I hope this person holds the faith long enough and tries to see how the AI's can help accelerate one's own understanding. I am no fan of AIs generating a bunch of papers that no one reads or cares about, but I could say the same about the immense number of papers made by humans as well. If anything, the AIs make all of that immense knowledge more valuable as it is now knowable and accessible through these tools. There is also the fact that the mathematics job market has been oversaturated for at least 20 years. What our new tools allow is for people to be able to do mathematics outside of having access to a research library and top mathematics department.
by jostylr - Grateful for this essay. Made me feel seen.
Someone said:
> No one is stopping you from doing what you enjoy.
But that's wrong. LLMs are creating an environment in which some things are no longer enjoyable.
For example there is less joy to be had in learning a programming language in 2026 than there was in 2016, because there is less utility in it now.
by marifjeren - Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output.
Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subfields of mathematics. Of course, you won't be doing the creation directly, in the way the mathematicians of old did; that's just not the name of the game anymore. But you will still be directing the research and involved in the creation.
by d_burfoot