The cultural divide between mathematics and AI
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Re: The cultural divide between mathematics and AI
#2> Throughout the conference, I noticed a subtle pressure on presenters to incorporate AI themes into their talks, regardless of relevance.
This is well-studied and not unique to AI, the USA in English, or even Western traditions. Here is what I mean: a book called Diffusion of Innovations by Rogers explains a history of technology introduction.. if the results are tallied in population, money or other prosperity, the civilizations and their language groups that have systematic ways to explore and apply new technology are "winners" in the global context.
AI is a powerful lever. The meta-conversation here might be around concepts of cancer, imbalance and chairs on the deck of the Titanic.. but this is getting off-topic for maths.
Re: The cultural divide between mathematics and AI
#3Nice article. I didn't read every section in detail but I think it makes a good point that AI researchers maybe focus too much on the thought of creating new mathematics while being able to repdroduce, index or formalize existing mathematics is really they key goal imo. This will then also lead to new mathematics. I think the more you advance in mathematical maturity the bigger the "brush" becomes with which you make your strokes. As an undergrad a stroke can be a single argument in a proof, or a simple Lemma. As a professor it can be a good guess for a well-posedness strategy for a PDE. I think AI will help humans find new mathematics with much bigger brush strokes. If you need to generalize a specific inequality on the whole space to Lipschitz domains, perhaps AI will give you a dozen pages, perhaps even of formalized Lean, in a single stroke. If you are a scientist and consider an ODE model, perhaps AI can give you formally verified error and convergence bounds using your specific constants. You switch to a probabilistic setting? Do not worry. All of these are examples of not very deep but tedious and non-trivial mathematical busywork that can take days or weeks. The mathematical ability necessary to do this has in my opinion already been demonstrated by o3 in rare cases. It can not piece things together yet though. But GPT-4 could not piece together proofs to undergrad homework problems while o3 now can. So I believe improvement is quite possible.
Re: The cultural divide between mathematics and AI
#4> Throughout the conference, I noticed a subtle pressure on presenters to incorporate AI themes into their talks, regardless of relevance. This is well-studied and not unique to AI, the USA in English, or even Western traditions. Here is what I mean: a book called Diffusion of Innovations by Rogers explains a history of technology introduction.. if the results are tallied in population, money or other prosperity, the…
I think another way to think about this is that subtly trying to consider AI in your AI-unrelated research is just respecting the bitter lesson. You need to at least consider how a data-driven approach might work for your problem. It could totally wipe you out - make your approach pointless. That's the bitter lesson.
Re: The cultural divide between mathematics and AI
#5AI is young, and at the center of the industry spotlight, so it attracts a lot of people who are not in it to understand anything. It's like when the whole world got on the Internet, and the culture suddenly shifted. It's a good thing; you just have to dress up your work in the right language, and you can get funding, like when Richard Bellman coined the term "dynamic programming" to make it palatable to the Secretary of Defense, Charles Wilson.
Re: The cultural divide between mathematics and AI
#6[flagged]
Re: The cultural divide between mathematics and AI
#7AI is young, and at the center of the industry spotlight, so it attracts a lot of people who are not in it to understand anything. It's like when the whole world got on the Internet, and the culture suddenly shifted. It's a good thing; you just have to dress up your work in the right language, and you can get funding, like when Richard Bellman coined the term "dynamic programming" to make it palatable to the Secretar…
AI has been around since at least the 1970s.
Re: The cultural divide between mathematics and AI
#8I'm a former research mathematician who worked for a little while in AI research, and this article matched up very well with my own experience with this particular cultural divide. Since I've spent a lot more time in the math world than the AI world, it's very natural for me to see this divide from the mathematicians' perspective, and I definitely agree that a lot of the people I've talked to on the other side of this divide don't seem to quite get what it is that mathematicians want from math: that the primary aim isn't really to find out whether a result is true but why it's true.
To be honest, it's hard for me not to get kind of emotional about this. Obviously I don't know what's going to happen, but I can imagine a future where some future model is better at proving theorems than any human mathematician, like the situation, say, chess has been in for some time now. In that future, I would still care a lot about learning why theorems are true --- the process of answering those questions is one of the things I find the most beautiful and fulfilling in the world --- and it makes me really sad to hear people talk about math being "solved", as though all we're doing is checking theorems off of a to-do list. I often find the conversation pretty demoralizing, especially because I think a lot of the people I have it with would probably really enjoy the thing mathematics actually is much more than the thing they seem to think it is.
Re: The cultural divide between mathematics and AI
#9AI is young, and at the center of the industry spotlight, so it attracts a lot of people who are not in it to understand anything. It's like when the whole world got on the Internet, and the culture suddenly shifted. It's a good thing; you just have to dress up your work in the right language, and you can get funding, like when Richard Bellman coined the term "dynamic programming" to make it palatable to the Secretar…
AI has been around since at least the 1970s.
Or 1949 if you consider the Turing Test, or 1912 if you consider Torres Quevedo's machine El Ajedrecista that plays rook endings. The illusion of AI dates back to 1770's The Turk.
Re: The cultural divide between mathematics and AI
#10AI is young, and at the center of the industry spotlight, so it attracts a lot of people who are not in it to understand anything. It's like when the whole world got on the Internet, and the culture suddenly shifted. It's a good thing; you just have to dress up your work in the right language, and you can get funding, like when Richard Bellman coined the term "dynamic programming" to make it palatable to the Secretar…
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