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So what happens to this world view when AI not only clears the forest of problems we couldn't solve but also in the future discovers more forest with trees bigg

So what happens to this world view when AI not only clears the forest of problems we couldn't solve but also in the future discovers more forest with trees bigger than anything we've ever seen before? Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understand proofs if they are correct? If this is V0.5 of AGI/ASI then by V1 the only system that will be understanding any of this is the AI itself. If AI creates a new field of mathematics month 1, then solutions to new problems in month 2, then another field of mathematics on top of that at month 3 there's no human who will ever keep up with that. Or the alternative is a flattening of abilities, the AI cannot proceed further than the collective intelligence of humans and in that case this is correct. We'd be in a future where nobody wants to work in a field with an AI dominating it and when AI hits the limit of no useful training data input we'd have this giant gap of nobody know wtf it's done for years and nobody willing to figure it out and advance it. Ooo here's a dytopian story: - AI gets better at everything humans do - humans stop trying - AI cannot improve anymore than its input data + human support - AI slowly degrades itself (model collapse) for decades, it slowly hallucinates little by little until its hallucinating entire scientific fields losing quality over time - there's a mass population of people in the future who never learned to do anything and now have to relearn and figure out the equivalent of 100k years of AI work in order to prevent its slow degredation while all the systems they've come to rely on start failing around them. The AI has solved every problem but every real solution is saturated with 1000 false ones. - humanity starts from scratch? I love the idea of an archive of every solution to every problem existing but it's impossible to figure out the correct one. Infinite library like!

SpicyLemonZest 29d ago
> Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understand proofs if they are correct? Most modern mathematical problems are sufficiently abstract that their proofs or disproofs have no direct application. There's no problem you can fix or invention you can build based solely on OpenAI's construction, because analytic solutions to the Navier-Stokes equations are not used for practical purposes in fluid dynamics. The problems and their proofs are only interesting to the degree that they help us better understand how the math works. IIUC the Navier-Stokes proof is understandable by human beings, but if it weren't it would be no more useful than a proof that 3 dimensional florg-complete entry seams have no durdle-nodes.
- johnsmith1840 29d ago
  So...why can't an AI do the exact same thing? Make AI so it understands math better for future math to understand more math. Unless your argument is that mathematicians are effectively useless? I am assuming that's not your point though.
  - gpm 29d ago
    > Unless [...] mathematicians are effectively useless? It's always been a bit bizarre that this isn't the case. Mathematicians are almost always working on problems that there is no good reason to expect to have utility in the real world... problems they selected because of their elegance or whatever... yet there is a strong historical trend of their work having huge importance after the fact. Sometimes in fields that weren't even invented yet at the time of the work. There's something to be said for the idea that disrupting a system that is working well for no apparent reason is a bad idea.
    - johnsmith1840 29d ago
      So solving and discovering math is or is not the core value a mathematician provides? If AI can perfectly replicate their work but faster and better then what? SWE have nobody crying for them as they've been massively disrupted.
      - gpm 29d ago
        Mathematicians provide two complementary services bundled together. 1. Proving theorems - what AI can apparently replicate faster and better. 2. Creating definitions and new theorems from those definitions to prove, selecting which of the possible statements to work on. I.e. developing the "language" of mathematics. So far there is no evidence that LLM can do this at all well. And there's some reason to think that mathematicians won't be as good at this if they aren't also doing the first part. The value to society only comes when they do both "well", and it's 2 which is really the black magic where we don't understand why they've been so useful to us.
keithnz 29d ago
there's a book I read "The Practice Effect" such that technology becomes super advanced based on using something, it gets better and better, but the people regress and become more like a medieval society as they just care that using things improves them.
- johnsmith1840 29d ago
  Fun suggestion, thanks!
- kamaal 28d ago
  I think this is how Asgard worked. The tech got so advanced people kind of used the advanced tech, but looked pretty much like a how medieval society would. Even their politics.
qlte 29d ago
Pure mathematics (defined by anything without a known application) exists not to "solve problems" in the real world, but by whatever mathematicians find interesting or lacking in current knowledge. Based on the agreed set of rules formed over time that ensure rigor. It just so happens that even bizarrely esoteric math can later turn out to have some extremely useful and economically valuable applications. And even more useful to have mathematicians available who already understand that specific math.
- johnsmith1840 29d ago
  In that case isn't it actually more valuable to have an AI do this? It works faster and solves more math. The random engineer looking at a funny problem 10 years later now has the literal author of the math to talk to about it and implement it. I have never even spoken to a world class mathematician and now I can have them design with me? How is this not better in almost everyway?
  - pixl97 29d ago
    Guess it depends... If said human is kicked to the street with thousands of other homeless people that can't get jobs because AI then robots replaced them, then those fast math problems sound like a pretty bad trade off. Now, if there's some future where AI leads to abundance and we can all live off UBI, well, probably a worthwhile trade. The biggest issue I see is the more controversial people leading the AI race at the moment are not the kind of people I'd hand kids safety scissors much less the future of the human race.

SpicyLemonZest 29d ago

> Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understand proofs if they are correct? Most modern mathematical problems are sufficiently abstract that their proofs or disproofs have no direct application. There's no problem you can fix or invention you can build based solely on OpenAI's construction, because analytic solutions to the Navier-Stokes equations are not used for practical purposes in fluid dynamics. The problems and their proofs are only interesting to the degree that they help us better understand how the math works. IIUC the Navier-Stokes proof is understandable by human beings, but if it weren't it would be no more useful than a proof that 3 dimensional florg-complete entry seams have no durdle-nodes.

johnsmith1840 29d ago
So...why can't an AI do the exact same thing? Make AI so it understands math better for future math to understand more math. Unless your argument is that mathematicians are effectively useless? I am assuming that's not your point though.
- gpm 29d ago
  > Unless [...] mathematicians are effectively useless? It's always been a bit bizarre that this isn't the case. Mathematicians are almost always working on problems that there is no good reason to expect to have utility in the real world... problems they selected because of their elegance or whatever... yet there is a strong historical trend of their work having huge importance after the fact. Sometimes in fields that weren't even invented yet at the time of the work. There's something to be said for the idea that disrupting a system that is working well for no apparent reason is a bad idea.
  - johnsmith1840 29d ago
    So solving and discovering math is or is not the core value a mathematician provides? If AI can perfectly replicate their work but faster and better then what? SWE have nobody crying for them as they've been massively disrupted.
    - gpm 29d ago
      Mathematicians provide two complementary services bundled together. 1. Proving theorems - what AI can apparently replicate faster and better. 2. Creating definitions and new theorems from those definitions to prove, selecting which of the possible statements to work on. I.e. developing the "language" of mathematics. So far there is no evidence that LLM can do this at all well. And there's some reason to think that mathematicians won't be as good at this if they aren't also doing the first part. The value to society only comes when they do both "well", and it's 2 which is really the black magic where we don't understand why they've been so useful to us.

keithnz 29d ago

there's a book I read "The Practice Effect" such that technology becomes super advanced based on using something, it gets better and better, but the people regress and become more like a medieval society as they just care that using things improves them.

johnsmith1840 29d ago
Fun suggestion, thanks!
kamaal 28d ago
I think this is how Asgard worked. The tech got so advanced people kind of used the advanced tech, but looked pretty much like a how medieval society would. Even their politics.

qlte 29d ago

Pure mathematics (defined by anything without a known application) exists not to "solve problems" in the real world, but by whatever mathematicians find interesting or lacking in current knowledge. Based on the agreed set of rules formed over time that ensure rigor. It just so happens that even bizarrely esoteric math can later turn out to have some extremely useful and economically valuable applications. And even more useful to have mathematicians available who already understand that specific math.

johnsmith1840 29d ago
In that case isn't it actually more valuable to have an AI do this? It works faster and solves more math. The random engineer looking at a funny problem 10 years later now has the literal author of the math to talk to about it and implement it. I have never even spoken to a world class mathematician and now I can have them design with me? How is this not better in almost everyway?
- pixl97 29d ago
  Guess it depends... If said human is kicked to the street with thousands of other homeless people that can't get jobs because AI then robots replaced them, then those fast math problems sound like a pretty bad trade off. Now, if there's some future where AI leads to abundance and we can all live off UBI, well, probably a worthwhile trade. The biggest issue I see is the more controversial people leading the AI race at the moment are not the kind of people I'd hand kids safety scissors much less the future of the human race.