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Math that humans don't understand but nonetheless allows AI systems to develop breakthroughs in various fields of science, technology, physics, engineering, med

by nilkn 28d ago

Math that humans don't understand but nonetheless allows AI systems to develop breakthroughs in various fields of science, technology, physics, engineering, medicine, etc., would have great value to humanity even if it doesn't help humans understand abstract truth at all. Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it, it initially seemed useless, then another AI system found a predictive model of electromagnetism using it.

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Jensson 28d ago
But at that point you have full AGI and its not just today's models. Today's models still need humans to understand things since it builds upon human knowledge. When you have full AGI of course you no longer need humans to understand math. > Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it Developing multivariable calculus requires much more than just solving problems though, it requires defining an entirely new system and space. That is not the situation mathematicians face today, modern AI cannot do that. When talking about mathematicians and AI don't use fictive examples, we can look at what AI can do today and extrapolate that they can do more of that tomorrow, that is what we have to work with. In the case you posit where AGI exists there is no reason to even discuss what is left for humans to do, since AGI is defined as when humans are no longer needed for anything, the AGI can do every bit of thinking humans can.
- spacebanana7 28d ago
  It's reasonable to say that current or near future AI can find novel mathematical results and develop applications from those. The idea of AI stepping from a graph theory/combinatorics innovation to some new and useful algorithm isn't crazy.
  - a2ff6eeb0 28d ago
    Exactly. Soon, human brains are going to be obsolete.
- cman1444 28d ago
  So then it sounds like you agree that math has additional utility beyond just human comprehension. If I understand you correctly, you're just qualifying that that will only be the case when AGI exists. To be clear, I actually disagree with you here because I think it's very plausible to find a use case for human-incomprehensible math proofs before AGI exists. I'm just saying it sounds like you're agreeing with the parent comment that math is not purely about human comprehension.
- nilkn 28d ago
  I don't find AGI to be a useful technical term, as nobody can agree on what it means. For instance, you used it at least five times here, but you never defined it, and I could point to intellectually credible people who would say we've already reached AGI. Anyway, if we put the AGI framing aside, I think the main point you're making is that AI mathematics hasn't yet demonstrated the ability to theory-build in the way that the great human mathematicians have (Grothendieck, Scholze, etc.). And I'd agree with you on that. Where we disagree, I suppose, is I think that capability is coming -- I don't see anything that would prevent its development.

by nilkn 28d ago

deleted 28d ago

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Jensson 28d ago

But at that point you have full AGI and its not just today's models. Today's models still need humans to understand things since it builds upon human knowledge. When you have full AGI of course you no longer need humans to understand math. > Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it Developing multivariable calculus requires much more than just solving problems though, it requires defining an entirely new system and space. That is not the situation mathematicians face today, modern AI cannot do that. When talking about mathematicians and AI don't use fictive examples, we can look at what AI can do today and extrapolate that they can do more of that tomorrow, that is what we have to work with. In the case you posit where AGI exists there is no reason to even discuss what is left for humans to do, since AGI is defined as when humans are no longer needed for anything, the AGI can do every bit of thinking humans can.

spacebanana7 28d ago
It's reasonable to say that current or near future AI can find novel mathematical results and develop applications from those. The idea of AI stepping from a graph theory/combinatorics innovation to some new and useful algorithm isn't crazy.
- a2ff6eeb0 28d ago
  Exactly. Soon, human brains are going to be obsolete.
cman1444 28d ago
So then it sounds like you agree that math has additional utility beyond just human comprehension. If I understand you correctly, you're just qualifying that that will only be the case when AGI exists. To be clear, I actually disagree with you here because I think it's very plausible to find a use case for human-incomprehensible math proofs before AGI exists. I'm just saying it sounds like you're agreeing with the parent comment that math is not purely about human comprehension.
nilkn 28d ago
I don't find AGI to be a useful technical term, as nobody can agree on what it means. For instance, you used it at least five times here, but you never defined it, and I could point to intellectually credible people who would say we've already reached AGI. Anyway, if we put the AGI framing aside, I think the main point you're making is that AI mathematics hasn't yet demonstrated the ability to theory-build in the way that the great human mathematicians have (Grothendieck, Scholze, etc.). And I'd agree with you on that. Where we disagree, I suppose, is I think that capability is coming -- I don't see anything that would prevent its development.