Isn't the whole point of the field of mathematics in a theoretical sense the pursuit of formal solutions?
So, why would they be advocating for limitations on arriving at solutions?
Mathematicians issue warning as AI rapidly gains ground
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Re: Mathematicians issue warning as AI rapidly gains ground
#112Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questio…
That's an interesting perspective and I wholly disagree with the conclusion You are saying that tough problems with no applicability are useful because people that you happen to respect got good by their curiosity and pursuit of trying to solve these kinds of problems and failing, but branching off into other cognitive areas as mathematicians Now if I know anything about math for the sake of math, and academics, thes…
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Re: Mathematicians issue warning as AI rapidly gains ground
#113Earlier quoted context omitted.
The most important part of math is advancing human understanding. A correct answer by itself is not as important as understanding why it is correct.
The value of human understanding just cratered because we have machines to understand for us now.
That seems about as shortsighted as claiming the value of human understanding has cratered after the invention of the electronic calculator.
Re: Mathematicians issue warning as AI rapidly gains ground
#114Earlier quoted context omitted.
The most important part of math is advancing human understanding. A correct answer by itself is not as important as understanding why it is correct.
The value of human understanding just cratered because we have machines to understand for us now.
Wonder what Frank Herbert would have to say about letting machines do the thinking for us.
Re: Mathematicians issue warning as AI rapidly gains ground
#115> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.
Culturally, mathematics is a jobs program for nerds. The field very explicitly takes pride in working on problems that have no obvious applications, and most practitioners are funded publicly or supported by private endowments, with zero pressure to deliver specific results.
Of course, this produces useful results every now and then, but it's not like we pursued ruthless efficiency / maximum rate of knowledge advancement before. We just let them do their thing, essentially treating them as artists and letting them pursue the craft for its own sake. If we weren't interested in maximum throughput before, why is that an objective now?
Re: Mathematicians issue warning as AI rapidly gains ground
#116Earlier quoted context omitted.
Works of Shinichi Mochizuki immediately come to mind. He is not AI but provides very good examples of math that is useless because it is incomprehensible by (other) humans.
Do AIs produce answers whose work is incomprehensible to humans? It seems like you could just have the AI elaborate multiple times until you were satisfied with the explanation and documentation of what went into figuring out the answer. It’s not like the AI is one shotting the answer in a single opaque query anyways.
It’s easy to imagine this being a problem both in quality and in volume. Verifiable work is less valuable than verified work. And noise is always costly.
Re: Mathematicians issue warning as AI rapidly gains ground
#117> “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University As a former physicist and current data scientist/engineer, I know for a fact that commercial utility drives math research and researchers. Math is a tool to solve problems. Some mathematicians might only love the process of using the tool,…
It's also a way to model the world and produce new useful abstractions. It's not just about solving problems.
Re: Mathematicians issue warning as AI rapidly gains ground
#118Isn't the whole point of the field of mathematics in a theoretical sense the pursuit of formal solutions? So, why would they be advocating for limitations on arriving at solutions?
It's more nuanced than this. Peter Scholze said in response to this declaration:
> The goal of mathematical research is human understanding of mathematics, and so mathematics can only thrive in a community of human mathematicians. It is crucial to preserve this communal spirit. [0]
Terence Tao has also talked about the requirement for a mathematical proof: along with generation and formal verification, there is an important step of "proof digestion"
> understanding the essence of a solution, placing it in context with previous literature, summarizing and explaining it effectively, and gaining insights on other related problems and topics [1]
[0]: https://siliconreckoner.substack.com/p/the-leiden-declaratio...
Re: Mathematicians issue warning as AI rapidly gains ground
#119Isn't the whole point of the field of mathematics in a theoretical sense the pursuit of formal solutions? So, why would they be advocating for limitations on arriving at solutions?
You will find your answer in the article
Re: Mathematicians issue warning as AI rapidly gains ground
#120Isn't the whole point of the field of mathematics in a theoretical sense the pursuit of formal solutions? So, why would they be advocating for limitations on arriving at solutions?
It's more nuanced than this. Peter Scholze said in response to this declaration: > The goal of mathematical research is human understanding of mathematics, and so mathematics can only thrive in a community of human mathematicians. It is crucial to preserve this communal spirit. [0] Terence Tao has also talked about the requirement for a mathematical proof: along with generation and formal verification, there is an im…
Solve it and understand it; seems intuitive to me.
I don't understand how that contradicts my question.