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somesortofthing 48 minutes ago [-]
Taken on its premises at least, I think this piece inadvertently fails to make a case for why "pure mathematics" should persist as a field of human or machine activity. A real-world system with the abilities of a robustly superintelligent mathematician can, when some practical problem requires it, formulate a problem statement, churn for a bit, spit out a formalized answer, and continue whatever outer-loop task it was doing without a human even finding out.
If you have a system that gives you arbitrary on-demand math results, dedicating any resources, be they human labor or compute, to producing them for their own sake just seems like a waste. Why catalog the Library of Babel?
traes 31 minutes ago [-]
There's a substantial gap between "the machine is better than human mathematicians" and "the machine can formalize a solution to any problem immediately." Much of the important mathematical theory behind modern science was mapped out in advance by mathematicians, and scientists were able to find and take advantage of this mathematics where applicable. Mapping out our understanding of e.g. physics and our understanding of mathematics in parallel and finding connections later has historically been a highly successful approach, and I see no reason to believe the same would not be true for advanced machines. Would Einstein have been able to formulate GR without the existing theory of differential geometry? Maybe, but maybe not. Would an advanced machine be able to develop the theory of differential geometry in response to gravitational measurements? Maybe, but maybe not.
Edit: Perhaps I could have been terser here. Really the idea is that small jumps are easier to make than big jumps. Continually developing pure mathematics is a way to make small jumps in logic and intuition add up to big jumps in applications.
amurthy1 7 minutes ago [-]
There are some parallels here to AI coding where even if the AI can write all the code, it's still valuable to have a human who can read and understand the code to verify correctness. The same is true of AI generated math proofs that humans will want to verify are around before they feed them back into the AI and build new insights.
roenxi 56 minutes ago [-]
> What I find striking here is that there are both fewer questions and fewer answers.
Assuming the ratio of answers per question remains the same (or drops because the answer quality raises) this is the sort of thing I would suspect.
It wouldn't even be theoretically surprising if the number of Qs & As on MathOverflow trend down purely because all the easy questions get answered. Wouldn't necessarily expect that, but because we can't really anticipate whether questions should trend up/down/sideways I don't think analysing MathOverflow is really all that interesting. Like the writer observes, kids these days are probably all over on Discord.
1 hours ago [-]
anArbitraryOne 1 hours ago [-]
Seems like clickbait so I'm not clicking it
ctenb 55 minutes ago [-]
Same. There is such a thing as a title being too ridiculous or provoking to want to read the article
traes 39 minutes ago [-]
It's speculative fiction written by a professional mathematician about his idea of the worst case scenario of AI's effect on math.
mmoll 19 minutes ago [-]
And most of the discussion would immediately apply to almost any other facet of society…
carlob 15 minutes ago [-]
...on openai request to spin up some critihype
readthenotes1 52 minutes ago [-]
It may have been a little bit more interesting than the title would lead you to believe not but haruspicy is not a key affordance of mathematician so it still probably wasn't worth the read
If you have a system that gives you arbitrary on-demand math results, dedicating any resources, be they human labor or compute, to producing them for their own sake just seems like a waste. Why catalog the Library of Babel?
Edit: Perhaps I could have been terser here. Really the idea is that small jumps are easier to make than big jumps. Continually developing pure mathematics is a way to make small jumps in logic and intuition add up to big jumps in applications.
Assuming the ratio of answers per question remains the same (or drops because the answer quality raises) this is the sort of thing I would suspect.
It wouldn't even be theoretically surprising if the number of Qs & As on MathOverflow trend down purely because all the easy questions get answered. Wouldn't necessarily expect that, but because we can't really anticipate whether questions should trend up/down/sideways I don't think analysing MathOverflow is really all that interesting. Like the writer observes, kids these days are probably all over on Discord.