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ComplexSystems 10 minutes ago [-]
I can't relate to this at all. AI models will surely get better at writing "enjoyable proofs," but for now the situation is what it is. You're passionate about this problem, right? But you don't want to do the work to understand the result? Fine. There's a new generation of younger, hungry mathematicians that are highly interested in figuring out why the result is true and I am sure they'd be happy to wade through it and spoon-feed you the answer instead. Maybe they should be running things.
bamboozled 7 minutes ago [-]
So OpenAI should be able to flood the world with AI pollution and ask scientists and mathematicians to wade through it all and tell us if there is any sense in it, then sit back and wait for them to report in?
Nice idea.
ComplexSystems 4 minutes ago [-]
Yes, they should. They have invented a magic button that can tell you the long-awaited answers to the burning mathematical questions that you've spent your life researching. The caveat is that the explanations "are not fun to read" like set theory papers usually are (lol). If you don't think that's a worthwhile tradeoff, that's your call, but it sure as hell isn't everyone's.
poincareball 54 seconds ago [-]
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nullsanity 7 minutes ago [-]
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jdw64 2 minutes ago [-]
Is a proof that cannot be understood worthless? How would this be framed philosophically?
In fact, the academic system is a kind of worldview created by humans. And as it is shared and the community grows, the problem will gradually become more complex. Because when a discipline develops sufficiently, just as in a mine where rich veins are easy to extract early on but become very hard to extract once much has been dug out... in that sense, as things gradually become more complex, once a certain threshold is reached, won't scholarship surpass the limits of human understanding? Of course, scholarship is entirely for humans, but at some point the system itself may face its limits, and then wouldn't it again reduce the existing normalized minimum within that discipline and establish a new normalization of a new logical system?
In my view, perhaps for very complex work like today, AI will do it, and then there will be work that normalizes and further simplifies the results of that AI. Then, coming back to the human fold, if humans create the initial skeleton, the LLM will learn that again and it will become complex work again, and won't this create a continuing cycle?
I think verification and understanding can be separated. If the proof targets a correctly formalized proposition and passes a reliable proof checker, isn't it valuable? We have obtained knowledge justified as true, but there is simply no new theory that understands that knowledge.
As was the case with the Four Color Theorem...
I am always curious what shape the newly compressed new discipline will take. At that time, I hope even people like me, who are intellectually behind, will be able to learn that discipline.
transitivebs 9 minutes ago [-]
openai will take expert responses like this and improve the next set of papers
it won't be long before there's no more low hanging fruit like this to complain about, and the writing / explanations of the results are superhuman as well
separately, i really liked the author's denial-of-service analogy. super useful practical framing
bamboozled 8 minutes ago [-]
Look forward to seeing an LLM write something well, that will truly be a breakthrough in the field.
Nice idea.
In fact, the academic system is a kind of worldview created by humans. And as it is shared and the community grows, the problem will gradually become more complex. Because when a discipline develops sufficiently, just as in a mine where rich veins are easy to extract early on but become very hard to extract once much has been dug out... in that sense, as things gradually become more complex, once a certain threshold is reached, won't scholarship surpass the limits of human understanding? Of course, scholarship is entirely for humans, but at some point the system itself may face its limits, and then wouldn't it again reduce the existing normalized minimum within that discipline and establish a new normalization of a new logical system?
In my view, perhaps for very complex work like today, AI will do it, and then there will be work that normalizes and further simplifies the results of that AI. Then, coming back to the human fold, if humans create the initial skeleton, the LLM will learn that again and it will become complex work again, and won't this create a continuing cycle?
I think verification and understanding can be separated. If the proof targets a correctly formalized proposition and passes a reliable proof checker, isn't it valuable? We have obtained knowledge justified as true, but there is simply no new theory that understands that knowledge. As was the case with the Four Color Theorem...
I am always curious what shape the newly compressed new discipline will take. At that time, I hope even people like me, who are intellectually behind, will be able to learn that discipline.
it won't be long before there's no more low hanging fruit like this to complain about, and the writing / explanations of the results are superhuman as well
separately, i really liked the author's denial-of-service analogy. super useful practical framing