I think the focus of mathematical AI criticism needs to be narrower. Is the concern that AI has limitations, or that it's too good? Nuance allows for both of these angles of attack to coexist, but it's sufficiently bleak to speculate about AI making mathematicians obsolete. Suppose AI progresses to the point where all new conjectures and proofs were developed by AI's before humans - e.g., the Riemann hypothesis gets proven by AI before humans prove it, as does the twin prime conjecture, Goldbach, and every conjectured and as-yet unconjectured mathematical result. Before that point I would start filling out applications to the nearest Luddite cells, and I likely wouldn't be alone.
I notice that people struggle, generally, to show why generative AI is so poisonous. "Oh, what's the big deal? It's just like spellcheck. It's just like a graphing calculator. It's just like a search engine. It's just like Photoshop", etc. It's always analogous to some harmless thing - but it's not! If you're creatively inclined, if you have a mathematics background, you just know in your bones it's not the same. There's a clip of Andrew Wiles describing what proving Fermat meant to him, and he gets so overwhelmed with emotion that he - a grown man in his forties - starts tearing up and has to turn away from the camera. To show what we're in danger of losing, maybe mathematicians - uncharacteristically - need to introduce more emotion to this discussion.
FYI the Chat comment on Paul Feyerabend is confabulation. He and Imre Lakatos were to write a book together just when Lakatos died, they were close friends and PF wrote on IL but not much vice versa. Their texts are correlated. Then unlike Proofs & Refutations Against Method (PK’s 1/2 of planned book) is not at all about math and only indirectly human creativity (vs scientific progress). The comment about ‘results’ for P&R is also off: the point of P&R is the unity of proofs, theorems (‘results’) and concepts essential to both formed through their interaction in historical time. No ‘understanding’ here!
Wonderful article, I saw a great insight into AI. Thank you.
Isn't passive consumption the real goal of AI? Just accept what you are given by the overally rational machine (which is godlike with its inputs, processings of inputs, and outputs) so you continually accept more until you no longer believe you can do without its outputs and then pay rents for its use (which seems to be the consumer side of a tech cycle).
I think the focus of mathematical AI criticism needs to be narrower. Is the concern that AI has limitations, or that it's too good? Nuance allows for both of these angles of attack to coexist, but it's sufficiently bleak to speculate about AI making mathematicians obsolete. Suppose AI progresses to the point where all new conjectures and proofs were developed by AI's before humans - e.g., the Riemann hypothesis gets proven by AI before humans prove it, as does the twin prime conjecture, Goldbach, and every conjectured and as-yet unconjectured mathematical result. Before that point I would start filling out applications to the nearest Luddite cells, and I likely wouldn't be alone.
I notice that people struggle, generally, to show why generative AI is so poisonous. "Oh, what's the big deal? It's just like spellcheck. It's just like a graphing calculator. It's just like a search engine. It's just like Photoshop", etc. It's always analogous to some harmless thing - but it's not! If you're creatively inclined, if you have a mathematics background, you just know in your bones it's not the same. There's a clip of Andrew Wiles describing what proving Fermat meant to him, and he gets so overwhelmed with emotion that he - a grown man in his forties - starts tearing up and has to turn away from the camera. To show what we're in danger of losing, maybe mathematicians - uncharacteristically - need to introduce more emotion to this discussion.
FYI the Chat comment on Paul Feyerabend is confabulation. He and Imre Lakatos were to write a book together just when Lakatos died, they were close friends and PF wrote on IL but not much vice versa. Their texts are correlated. Then unlike Proofs & Refutations Against Method (PK’s 1/2 of planned book) is not at all about math and only indirectly human creativity (vs scientific progress). The comment about ‘results’ for P&R is also off: the point of P&R is the unity of proofs, theorems (‘results’) and concepts essential to both formed through their interaction in historical time. No ‘understanding’ here!
Wonderful article, I saw a great insight into AI. Thank you.
Isn't passive consumption the real goal of AI? Just accept what you are given by the overally rational machine (which is godlike with its inputs, processings of inputs, and outputs) so you continually accept more until you no longer believe you can do without its outputs and then pay rents for its use (which seems to be the consumer side of a tech cycle).