This is the best piece i have read on substack. As you said, some people like the progress, some not so much. A lot of people need purpose in their lives, and if we just allow AI to take over all the tasks in our society, whether its research or driving the busses, we are going to have a lot of people that are miserable. We have not solved much if people are not happy living their lives.
This is a good summary of the current state of math! I just finished a slightly different roundup (trying to talk to mathematicians directly) so this has been top of mind for me. (I hope you don't mind the link: https://www.understandingai.org/p/mathematicians-are-grappling-with)
One thing that surprised me when I talked with a bunch of mathematicians is that some of them believe that AI will eat the rest of the ladder of abstraction fairly quickly. Humans can jump up a level, but only so many times. AI may end up being better at digestion as well as problem solving and verification. This may seem unlikely today, but I think it's a possibility worth considering seriously. Especially as AI systems grow more autonomous.
Thanks Kai, I actually cited your post (as well as your earlier one). Super interesting stuff - changed my mind in a couple of ways and I ended up including the view that maybe there are no "safe harbors" within or outside mathematics. If Al eats the entire ladder anyway, then mathematicians - and all of us next - need to prepare even more (I agree saying "just go up" sounds exactly like "goalpost moving").
Sorry if I was being annoying with the link! Thanks for the citation.
I definitely did some grieving on Saturday with the Astra results (I long thought I was going to become a mathematician; Saturday might have been the day I decided for good not to go to math grad school), but the experience also felt like something that everyone will have to go through at some point.
Though I'm not sure that "just go up" is actually goalpost moving (in a pejorative sense). One of the beautiful things about moving goalposts is that we learn more about what we actually want. For many people, that may continue to be rising on the ladder of abstraction
First of all - what an amazing article. Thank you for summarising everything so well - I don’t know much about the mathematics field and your prose was so easy to follow.
Loved the part where you talked about receiver’s intelligence. I think that might be the most important part of this AI puzzle - AI can do all the amazing things in the world but if we don’t understand it on this side of the wall then what will we do with these life changing solutions.
First, excellent article on what I'd call "the near-death" of mathematicians (except for "brain development exercises" -- which are more useful than most people think. Indeed "logic" for humans is being able to piece together (often disparate, but at least tangentially related) facts that can be used to further an argument. Lawyers do this all the time. And despite their protestations, physicians doing "diagnostics," and even treatment regimens, based on their "learnings" and experience. . .are already on the road to obsolescence (unless they're a Dr House that can inject tangential and even non-logical observations). And we're just scratching the surface here.
BTW, as a (former) tech research director and senior executive (at META, Gartner, etc) for 40+ years, I think we're almost across "the Rubicon" on AI (Augmented Intelligence -- since it's no more "artificial" than most other human inventions/discoveries.
And to that end, I disagree with you about AI's "creativity," because creativity is more nuanced and linked to personal taste. I have had ChatGPT write haiku poems on quantum entanglement, entropy, etc (I've been writing haikus as a hobby for years) and I was blown away. I also had Midjourney create a "painting" with no more prompting than: "create a picture with the theme of Fahrenheit 451 in the style of Salvador Dali." Again, I was blown away (as was my daughter who is a user interface designer at Google). I have the "print" hanging on my office wall.
And last, I was especially impressed with your lengthy article (from last week) on Google's "tangential" AI strategy (and Hassabis's latest move seems to confirm) that seeks to better understand "world context."
One of the things that amused me about the story was its strong resonances with Minsky and Papert’s *Perceptrons* — their connectedness proof (featured with an illustration on the cover of the book) — since the “trick” the human go player exploited was basically a flaw in the model’s ability to detect the connectedness of its human opponent’s moves.
As you were talking about proof indigestion, and masterpieces littering the streets because publishers couldn’t snap them up, I found myself thinking of all the masterpieces that aren’t littering the streets because their creators were exhausted working three jobs to support their family, or died trying to cross a border seeking a different life. All the masterpieces forgotten in drawers in moldering buildings.
In a way, proof indigestion in the literary world is not a new problem at all.
As Stephen Jay Gould once remarked, “I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops.”
The $2,000 and the proof indigestion are the same fact. Generation got cheap and verification didn't, so the ratio between them collapsed, and everything in section VIII follows from that alone. Which also explains the counterexample bias you flag: a counterexample carries its own verification, a proof outsources it. The asymmetry isn't about abduction being hard. It's that AI is producing exactly the results whose checking cost stayed near zero, and stalling where the cost sits on us.
This is the best piece i have read on substack. As you said, some people like the progress, some not so much. A lot of people need purpose in their lives, and if we just allow AI to take over all the tasks in our society, whether its research or driving the busses, we are going to have a lot of people that are miserable. We have not solved much if people are not happy living their lives.
Thank you Rune, deeply appreciate it 🙏🏻
This is a good summary of the current state of math! I just finished a slightly different roundup (trying to talk to mathematicians directly) so this has been top of mind for me. (I hope you don't mind the link: https://www.understandingai.org/p/mathematicians-are-grappling-with)
One thing that surprised me when I talked with a bunch of mathematicians is that some of them believe that AI will eat the rest of the ladder of abstraction fairly quickly. Humans can jump up a level, but only so many times. AI may end up being better at digestion as well as problem solving and verification. This may seem unlikely today, but I think it's a possibility worth considering seriously. Especially as AI systems grow more autonomous.
Thanks Kai, I actually cited your post (as well as your earlier one). Super interesting stuff - changed my mind in a couple of ways and I ended up including the view that maybe there are no "safe harbors" within or outside mathematics. If Al eats the entire ladder anyway, then mathematicians - and all of us next - need to prepare even more (I agree saying "just go up" sounds exactly like "goalpost moving").
Sorry if I was being annoying with the link! Thanks for the citation.
I definitely did some grieving on Saturday with the Astra results (I long thought I was going to become a mathematician; Saturday might have been the day I decided for good not to go to math grad school), but the experience also felt like something that everyone will have to go through at some point.
Though I'm not sure that "just go up" is actually goalpost moving (in a pejorative sense). One of the beautiful things about moving goalposts is that we learn more about what we actually want. For many people, that may continue to be rising on the ladder of abstraction
First of all - what an amazing article. Thank you for summarising everything so well - I don’t know much about the mathematics field and your prose was so easy to follow.
Loved the part where you talked about receiver’s intelligence. I think that might be the most important part of this AI puzzle - AI can do all the amazing things in the world but if we don’t understand it on this side of the wall then what will we do with these life changing solutions.
Thank you for sharing this wonderful article!
🙏🏻🙏🏻🙏🏻
Hey Alberto,
First, excellent article on what I'd call "the near-death" of mathematicians (except for "brain development exercises" -- which are more useful than most people think. Indeed "logic" for humans is being able to piece together (often disparate, but at least tangentially related) facts that can be used to further an argument. Lawyers do this all the time. And despite their protestations, physicians doing "diagnostics," and even treatment regimens, based on their "learnings" and experience. . .are already on the road to obsolescence (unless they're a Dr House that can inject tangential and even non-logical observations). And we're just scratching the surface here.
BTW, as a (former) tech research director and senior executive (at META, Gartner, etc) for 40+ years, I think we're almost across "the Rubicon" on AI (Augmented Intelligence -- since it's no more "artificial" than most other human inventions/discoveries.
And to that end, I disagree with you about AI's "creativity," because creativity is more nuanced and linked to personal taste. I have had ChatGPT write haiku poems on quantum entanglement, entropy, etc (I've been writing haikus as a hobby for years) and I was blown away. I also had Midjourney create a "painting" with no more prompting than: "create a picture with the theme of Fahrenheit 451 in the style of Salvador Dali." Again, I was blown away (as was my daughter who is a user interface designer at Google). I have the "print" hanging on my office wall.
And last, I was especially impressed with your lengthy article (from last week) on Google's "tangential" AI strategy (and Hassabis's latest move seems to confirm) that seeks to better understand "world context."
Keep up the great work
Be well,
dale
I thought this story: https://www.vice.com/en/article/a-human-amateur-beat-a-top-go-playing-ai-using-a-simple-trick/ about a human defeating computerized Go was about Alpha Go, but I see it was about a lesser, open-source model.
One of the things that amused me about the story was its strong resonances with Minsky and Papert’s *Perceptrons* — their connectedness proof (featured with an illustration on the cover of the book) — since the “trick” the human go player exploited was basically a flaw in the model’s ability to detect the connectedness of its human opponent’s moves.
As you were talking about proof indigestion, and masterpieces littering the streets because publishers couldn’t snap them up, I found myself thinking of all the masterpieces that aren’t littering the streets because their creators were exhausted working three jobs to support their family, or died trying to cross a border seeking a different life. All the masterpieces forgotten in drawers in moldering buildings.
In a way, proof indigestion in the literary world is not a new problem at all.
As Stephen Jay Gould once remarked, “I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops.”
The $2,000 and the proof indigestion are the same fact. Generation got cheap and verification didn't, so the ratio between them collapsed, and everything in section VIII follows from that alone. Which also explains the counterexample bias you flag: a counterexample carries its own verification, a proof outsources it. The asymmetry isn't about abduction being hard. It's that AI is producing exactly the results whose checking cost stayed near zero, and stalling where the cost sits on us.
Very true, if you didn’t get to the UC Berkeley Agentic AI Summit you may benefit from my summary: https://substack.com/@thefirewall/note/c-307976585?r=5dv35z&utm_source=notes-share-action&utm_medium=web