So random lurker #3 here. I am of the "somewhat mathematically inclined weirdo/idiot" demographic and spend abnormally large amounts of time trying to teach myself math . Basically all the mathematics I missed at school and was afraid an elderly Soviet Professor would teach me...
Mathematics education in public schools tends to be poorly motivated apart for being utilitarian and ruthless "filtering mechanism" for children that are otherwise cast aside as "future manual laborers". This seems like it is pervasive across many modern cultures.
I sometimes find myself wondering what the point of me learning mathematics is ... how do I justify to other people that what I do is worthwhile and interesting? Why is mathematics important? Is mathematics more like an art? In the "Age of AI" is math more like art and music: a set of digital artifacts that can just be generated on demand and thus lose their meaning? Is math a social and cultural activity?
Also, do the people at google actually understand what math is for? It seems like a lot of the engineering brained people at Google (and I went to school with a lot of those kids) mostly look at life as a increasingly difficult set of tests/prompts to pass. When they want to "automate mathematics to benefit humanity" how exactly what they are doing benefiting humanity? Perhaps these people have some mistaken belief -from their schooling no doubt- that "math equals intelligence"?
That I even have to ask these questions betrays my privilege and maybe "material concerns" of the average worker would increase if there was an "abundance" of math ... but we will instead get a paucity of meaning with no abundance of anything material.
I do understand that this is a common conceit in your posts. But thought I would write a lament. FWIW I am not a mathematician of any type: but always made time to grapple with weird and mind bending concepts.
Michael: I read through once through the five documents. If I had more time, I would read them more carefully a second time and have more substantial suggestions. So, this is a very brief suggestion: I propose that there should be a clear distinction between two aspects/levels re: AI and mathematics. (1) The mutual impact (the impact is in both directions) between AI and the practice of mathematicians, and (2) the responsibility of mathematicians as an academic community vis-a-vis ominous implications (e.g. some are threatening to the human species) of AI's increasing penetration in the conduct of public institutions (e.g. some government's increased surveillance of citizens).
1- instead of mere speculation, we have many historical examples of technology changing the way in which mathematicians work, and the types of questions they are able to ask—and answer. This might be better left to a historian of math, or an anthropologist, but I find this dimension largely absent from much of the discourse. If we can understand technological impact in a historical context, it might help us gain traction at forming better questions in the present.
2- another commenter here mentions that AI is math. Essentially, this is true. It obviously requires other technologies, such as computing architectures, but if you subtract the math there is no more "AI." We must develop better definitions of AI (by 'we' I mean mathematicians) that are rooted in math, information theory, physics. This will help us understand the physics of the situation better, and we can potentially begin to corral wild speculation.
Regarding your point 2): "what these things are" and by "things" I mean Generative Pre-trained Transformers and LLMs. The first link is interesting, because the original author has an academic interest in the interplay of math, information theory (algorithmic and otherwise), and "computation" broadly in "physical systems". He compares LLMs to other artificial systems such as bureaucracies etc. that are designed but have "complex dynamics". Worth a read.
Dear Michael, I'm surprised that the document "Questions Artificial Intelligence Raises for the Mathematics Profession" doesn't talk about the fact that Math is at the heart of LLMs and that mathematicians can play key roles in advancing the mathematics of AI, explaining the mathematical underpinnings to the public, and using mathematical tools to explain the inner workings of AI systems and improving them. AI is mathematics - the models and the fitting of the models is all mathematics. Mathematics need to evolve to keep up with AI. For example, what new mathematics needs to be invented to better analyze the functions that AI learns? Conversely, what mathematical techniques from AI can be adopted in mathematics (randomized analysis is one example). Thanks for all you do and hope you can have some influence here. -Tammy Kolda
It looks like Google is interested in providing access to AlphaEvolve for academics in the coming months. It seems to me that this is the only AI system currently in existence that might assist in genuine mathematical research. Should there be some initial guidance from your committee about its use, given how soon it might become available?
Long time reader, first time call--- I mean, commenter.
I'm no mathematician, but have been an avid reader of your substack for a couple years now. I just recently started a Ph.D. in Philosophy and will likely be working AI into my dissertation on Philosophy of Technology to some degree (it would be academically irresponsible if I didn't).
The one thing that has most frustrated me, honestly, has been the lack of investigation regarding what it is that these things (programs? algorithms? perhaps just a new/novel method of data storage?) actually are and how we should conceive of them. Hopefully this isn't an unhelpful suggestion, but I think opening some sort of dialogue on that front is the most helpful thing for the discourse at this point. Everyone simply takes the name 'AI', or 'Artificial Intelligence', or 'Automatic Proof Checker' (or whatever the equivalent is within the mathematical discourse)--which are brands more than anything else--and runs with it as though it sufficiently describes what these things do, what they are, and how we should conceive of them.
I realize it's not directly related to mathematics, but I've found you to have one of the most balanced and reasonable perspectives on the topic. Even the title of your substack, "Silicon Reckoner", is to me such an incredible way to refuse the push to integrate this single technique into every possible social sphere imaginable. Simply changing *what these things are called*--'silicon reckoners' instead of 'digital computers'--to me touches at the heart of the issue. This goes back to the initial days of computational theory (Turing Machines even being described as 'symbol manipulators' is even something that I don't think should be taken for granted).
Anyway, this has been more rant than helpful advice, but that would be what I would say if I were to be in the meeting. Perhaps I would be labeled an unhelpful, uncooperative derailer. But I think that's sort of what we need right now, since the train we're all currently on seems to me to be more similar to those Germany ran in the middle of the 20th century than those which enabled the industrial revolution to scale up to the extent that it did.
So random lurker #3 here. I am of the "somewhat mathematically inclined weirdo/idiot" demographic and spend abnormally large amounts of time trying to teach myself math . Basically all the mathematics I missed at school and was afraid an elderly Soviet Professor would teach me...
Mathematics education in public schools tends to be poorly motivated apart for being utilitarian and ruthless "filtering mechanism" for children that are otherwise cast aside as "future manual laborers". This seems like it is pervasive across many modern cultures.
I sometimes find myself wondering what the point of me learning mathematics is ... how do I justify to other people that what I do is worthwhile and interesting? Why is mathematics important? Is mathematics more like an art? In the "Age of AI" is math more like art and music: a set of digital artifacts that can just be generated on demand and thus lose their meaning? Is math a social and cultural activity?
Also, do the people at google actually understand what math is for? It seems like a lot of the engineering brained people at Google (and I went to school with a lot of those kids) mostly look at life as a increasingly difficult set of tests/prompts to pass. When they want to "automate mathematics to benefit humanity" how exactly what they are doing benefiting humanity? Perhaps these people have some mistaken belief -from their schooling no doubt- that "math equals intelligence"?
That I even have to ask these questions betrays my privilege and maybe "material concerns" of the average worker would increase if there was an "abundance" of math ... but we will instead get a paucity of meaning with no abundance of anything material.
I do understand that this is a common conceit in your posts. But thought I would write a lament. FWIW I am not a mathematician of any type: but always made time to grapple with weird and mind bending concepts.
Michael: I read through once through the five documents. If I had more time, I would read them more carefully a second time and have more substantial suggestions. So, this is a very brief suggestion: I propose that there should be a clear distinction between two aspects/levels re: AI and mathematics. (1) The mutual impact (the impact is in both directions) between AI and the practice of mathematicians, and (2) the responsibility of mathematicians as an academic community vis-a-vis ominous implications (e.g. some are threatening to the human species) of AI's increasing penetration in the conduct of public institutions (e.g. some government's increased surveillance of citizens).
Two fundamental issues might be addressed:
1- instead of mere speculation, we have many historical examples of technology changing the way in which mathematicians work, and the types of questions they are able to ask—and answer. This might be better left to a historian of math, or an anthropologist, but I find this dimension largely absent from much of the discourse. If we can understand technological impact in a historical context, it might help us gain traction at forming better questions in the present.
2- another commenter here mentions that AI is math. Essentially, this is true. It obviously requires other technologies, such as computing architectures, but if you subtract the math there is no more "AI." We must develop better definitions of AI (by 'we' I mean mathematicians) that are rooted in math, information theory, physics. This will help us understand the physics of the situation better, and we can potentially begin to corral wild speculation.
I'm perhaps going to start spamming this ... but I submit for your consideration:
https://www.programmablemutter.com/p/on-feral-library-card-catalogs-or
https://leon.bottou.org/news/two_lessons_from_iclr_2025
Regarding your point 2): "what these things are" and by "things" I mean Generative Pre-trained Transformers and LLMs. The first link is interesting, because the original author has an academic interest in the interplay of math, information theory (algorithmic and otherwise), and "computation" broadly in "physical systems". He compares LLMs to other artificial systems such as bureaucracies etc. that are designed but have "complex dynamics". Worth a read.
Thank you for this. I'll be forwarding the references to the committee.
Dear Michael, I'm surprised that the document "Questions Artificial Intelligence Raises for the Mathematics Profession" doesn't talk about the fact that Math is at the heart of LLMs and that mathematicians can play key roles in advancing the mathematics of AI, explaining the mathematical underpinnings to the public, and using mathematical tools to explain the inner workings of AI systems and improving them. AI is mathematics - the models and the fitting of the models is all mathematics. Mathematics need to evolve to keep up with AI. For example, what new mathematics needs to be invented to better analyze the functions that AI learns? Conversely, what mathematical techniques from AI can be adopted in mathematics (randomized analysis is one example). Thanks for all you do and hope you can have some influence here. -Tammy Kolda
Thank you for all your timely reflections: The following paper by M. Atiyah (I believe) is highly relevant: https://iopscience.iop.org/article/10.1070/IM8512/pdf
Kind regards,
EC
It looks like Google is interested in providing access to AlphaEvolve for academics in the coming months. It seems to me that this is the only AI system currently in existence that might assist in genuine mathematical research. Should there be some initial guidance from your committee about its use, given how soon it might become available?
I'll mention this; it's possible that someone on the committee knows more about this system.
Howdy,
Long time reader, first time call--- I mean, commenter.
I'm no mathematician, but have been an avid reader of your substack for a couple years now. I just recently started a Ph.D. in Philosophy and will likely be working AI into my dissertation on Philosophy of Technology to some degree (it would be academically irresponsible if I didn't).
The one thing that has most frustrated me, honestly, has been the lack of investigation regarding what it is that these things (programs? algorithms? perhaps just a new/novel method of data storage?) actually are and how we should conceive of them. Hopefully this isn't an unhelpful suggestion, but I think opening some sort of dialogue on that front is the most helpful thing for the discourse at this point. Everyone simply takes the name 'AI', or 'Artificial Intelligence', or 'Automatic Proof Checker' (or whatever the equivalent is within the mathematical discourse)--which are brands more than anything else--and runs with it as though it sufficiently describes what these things do, what they are, and how we should conceive of them.
I realize it's not directly related to mathematics, but I've found you to have one of the most balanced and reasonable perspectives on the topic. Even the title of your substack, "Silicon Reckoner", is to me such an incredible way to refuse the push to integrate this single technique into every possible social sphere imaginable. Simply changing *what these things are called*--'silicon reckoners' instead of 'digital computers'--to me touches at the heart of the issue. This goes back to the initial days of computational theory (Turing Machines even being described as 'symbol manipulators' is even something that I don't think should be taken for granted).
Anyway, this has been more rant than helpful advice, but that would be what I would say if I were to be in the meeting. Perhaps I would be labeled an unhelpful, uncooperative derailer. But I think that's sort of what we need right now, since the train we're all currently on seems to me to be more similar to those Germany ran in the middle of the 20th century than those which enabled the industrial revolution to scale up to the extent that it did.
I submit for your consideration:
https://www.programmablemutter.com/p/on-feral-library-card-catalogs-or
https://leon.bottou.org/news/two_lessons_from_iclr_2025
Regarding "what these things are" and by "things" I mean Generative Pre-trained Transformers and LLMs