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I don't know why anyone should care about understanding the results if the AI is better at math than us. It'd be like demanding that human mathematicians are ba

I don't know why anyone should care about understanding the results if the AI is better at math than us. It'd be like demanding that human mathematicians are banned from publishing until their cats understand the theorems. If Amazon uses AI math to come up with better routing, the cats can benefit from cheaper delivery fees just as much as humans can. No understanding needed. The human brain is being obsoleted, soon thinking is going to be a recreational activity like weightlifting. If you want to think as a hobby, that's fine, but most people will be free of that toil of unwanted brain labor.

hintymad 2mo ago
> I don't know why anyone should care about understanding the results if the AI is better at math than us This is a big if, right? AI can still generate subtle or even silly mistakes that any normal human, let alone a mathematician, wouldn't make. Besides, math is more than just getting a conclusion but to understand and to generalize new ways of solving problems. After all, mathematicians are a curious bunch. To quote Hilbert's epitaph: We must know. We shall know.
- bayesnet 2mo ago
  It’s a bit of an ominous quote given that Hilbert’s program was dismantled shortly thereafter by Gödel…
  - pfdietz 2mo ago
    I'm reminded of the joke about the two friends who come across a bear in the woods. When one puts on running shoes, his friend chides him that he can't outrun the bear. He responds, "I don't need to outrun the bear, I just need to outrun you." AI doesn't have to implement Hilbert's vision and be able to prove everything. I just has to out-prove human mathematicians.
- a2ff6eeb0 2mo ago
  Well, that's why we have automated proof checking. And again, I don't think humans will be able to solve problems at a commercial scale in the future. Maybe we'll have some hobbyist dabblers, but any real progress will be done by machines that skip the human.
mohamedkoubaa 2mo ago
What if the better routing leads to an outage that the AI can't explain or fix and all the humans who might have understood it were laid off or otherwise unavailable?
TSiege 2mo ago
I’m not anti AI but thinking the human brain is obsolete and using it will become a hobby is a dystopian view of the future where no one has any agency anymore. By your logic since our brains provide no value why not just shoot ourselves in the head while we’re at?
- a2ff6eeb0 2mo ago
  What's wrong with sitting on the beach with a bottle of wine for eternity, with no need to do anything, knowing that all your needs and desires will be automatically taken care of? I don't think you can be coherently pro-AI without thinking that the human brain will be obsolete, unless you believe in some inherent magic that the brain is imbued with. The only other option is that you haven't thought through the long term consequences of the innovation.
  - Jblx2 2mo ago
    Are dolphins obsolete?
    - a2ff6eeb0 2mo ago
      They're certainly endangered.
  - copemaxxxing 2mo ago
    That's not gonna happen. What's gonna happen is you'll be in forever slavery. You think those in power will let you enjoy your life?
    - a2ff6eeb0 2mo ago
      Why do you think any humans would stay in power? The AI will know what's good for you better than other people would.
- Calazon 2mo ago
  I think they meant obsolete relative to economic, scientific, and engineering objectives. That doesn't mean they don't provide any value of any kind to anyone.
FuckButtons 2mo ago
If you are free from physical and mental labor, you are in fact, not supplying labor, and are therefore surplus to requirements.
- auggierose 2mo ago
  Whose requirements?
  - esafak 2mo ago
    The employer's, whose salary affords your subsistence.
    - visarga 2mo ago
      If AI is so great it can do your job it is good enough to provide for your needs directly by automation. Just buy a robot and a plot of land and you don't have to worry about jobs.
      - esafak 2mo ago
        Robots can't do that yet, and even then you still need to pay for food, healthcare, land (taxes), transportation, etc.
    - auggierose 2mo ago
      I don't think anyone wants to be employed. They want the money that comes with employment. If you can make get money without employment, like rich kids, for example, I think most people would prefer that.
      - deleted 2mo ago
        [deleted]
      - feoren 2mo ago
        And you think that once the poor are no longer needed by the rich, the rich will decide to just give them money anyway? We already have dedicated campaigns to make sure people die sick and homeless on the streets when they become obsolete. You think that is not going to get much, much worse?
BeetleB 2mo ago
The essay On Proof and Progress in Mathematics by a Field's medalist is worth reading: https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236 He wrote it in 1994. He writes about how he almost "destroyed" a subdiscipline in mathematics by becoming so good at it that he outclassed everyone. PhD students were advised to stay away from the whole field. When he discovered this, he realized his error was that he was focusing on producing results, and not focusing on explaining his thought process. It's that thought process that is valuable in advancing the frontier - results alone won't do it. It didn't matter how many theorems he proved, if he was the only one who had the mental framework in mind on how to think about the whole field. I'm sure we've come across abstruse books where every theorem has a rabbit being pulled out of a hat, whereas other readers find it intuitive. It's because the latter has developed a mental model for the discipline, and you haven't. So he set about slowing down, and focusing on holding lots of seminars where he worked with other mathematicians to explain the thought process. Eventually others started publishing proofs of key theorems. When people publish in a journal, they are not merely doing it to show the result. They are having a conversation with other mathematicians. If they cannot explain their own proof, they're not having a conversation. This is why even decades after the Four Color Theorem was proved, plenty of mathematicians don't consider it "mathematics".
- a2ff6eeb0 2mo ago
  I don't understand why people are so fixated on the minds doing the mathematics being made out of meat. It seems obvious that soon, minds made of meat aren't going to be able to keep up. Useful thought, rather than hobbyist thought, seems destined to be the exclusive domain of silicon.
  - BeetleB 2mo ago
    > I don't understand why people are so fixated on the minds doing the mathematics being made out of meat. I don't follow - are you surprised that mathematicians have social rules on how they interact with others? You're definitely welcome to set up a journal that takes whatever types of papers you deem acceptable. It's not like they're preventing the dissemination of information by taking this stance. Personally, I wouldn't hire a SW engineer who only showcases output from LLMs, and can't explain the code it wrote.
cubefox 2mo ago
> If Amazon uses AI math to come up with better routin Most research mathematics is pure mathematics which is completely useless. No routing algorithms. It's only relevant because we (or at least mathematicians) are interested in it. So an AI producing incomprehensible proofs would be completely pointless. That's why Tao insists on the importance of human understanding.
- a2ff6eeb0 2mo ago
  If it's just a hobby, why would you use an LLM at all?
  - black_knight 2mo ago
    It is not a hobby when you are paid to do it! But I take it you mean “Done for the art of it”. Which I guess is a concept foreign to many. A few different reasons why use an LLM when mathematics is done for its own sake: Formally verifying my proofs catches any mistakes I make, but verifying is also hard work. LLMs shaves off a lot of time when formally verifying a proof. I can still read through an LLM generated proof and understand it. This is a way for me to understand the result I am working on (usually in order to know what to prove next, results are not proven in a vacuum). My experience thus far is that, while correct, an LLM generated proof is often unnecessarily complicated or inelegant. I take pleasure in elegant proofs and will spend time iterating on the first proof until I find it conveys the idea in the most elegant way. Having the initial LLM proof to start with is really useful, but is thus far rarely the final product.
applecoffeecake 2mo ago
If a result has a real-world application, then it can easily be published in an engineering or applied scientific journal in which it is already the norm to present methods that work empirically with little to no understanding of how.
fooker 2mo ago
Your analogy is great. What happens when it's the cats who get to decide what's published? Not an ideal scenario, but that's exactly the situation here. Mathematicians decide what gets reviewed and published in a a top journal. In the long run, this can and should make journals obsolete.
- a2ff6eeb0 2mo ago
  Exactly, the cats aren't going to be part of any real decision making soon enough.
gn_200826 2mo ago
Most of mathematics is more akin to philosophy than physics or engineering. Sure, if AI can prove a result that leads to practical applications, who cares if humans can't understand it. If AI performs a series of convoluted arguments demonstrating the existence of souls (feel free to replace souls with abstract nonsense), but nobody understands why, then what's the point?

hintymad 2mo ago

> I don't know why anyone should care about understanding the results if the AI is better at math than us This is a big if, right? AI can still generate subtle or even silly mistakes that any normal human, let alone a mathematician, wouldn't make. Besides, math is more than just getting a conclusion but to understand and to generalize new ways of solving problems. After all, mathematicians are a curious bunch. To quote Hilbert's epitaph: We must know. We shall know.

bayesnet 2mo ago
It’s a bit of an ominous quote given that Hilbert’s program was dismantled shortly thereafter by Gödel…
- pfdietz 2mo ago
  I'm reminded of the joke about the two friends who come across a bear in the woods. When one puts on running shoes, his friend chides him that he can't outrun the bear. He responds, "I don't need to outrun the bear, I just need to outrun you." AI doesn't have to implement Hilbert's vision and be able to prove everything. I just has to out-prove human mathematicians.
a2ff6eeb0 2mo ago
Well, that's why we have automated proof checking. And again, I don't think humans will be able to solve problems at a commercial scale in the future. Maybe we'll have some hobbyist dabblers, but any real progress will be done by machines that skip the human.

mohamedkoubaa 2mo ago

What if the better routing leads to an outage that the AI can't explain or fix and all the humans who might have understood it were laid off or otherwise unavailable?

TSiege 2mo ago

I’m not anti AI but thinking the human brain is obsolete and using it will become a hobby is a dystopian view of the future where no one has any agency anymore. By your logic since our brains provide no value why not just shoot ourselves in the head while we’re at?

a2ff6eeb0 2mo ago
What's wrong with sitting on the beach with a bottle of wine for eternity, with no need to do anything, knowing that all your needs and desires will be automatically taken care of? I don't think you can be coherently pro-AI without thinking that the human brain will be obsolete, unless you believe in some inherent magic that the brain is imbued with. The only other option is that you haven't thought through the long term consequences of the innovation.
- Jblx2 2mo ago
  Are dolphins obsolete?
  - a2ff6eeb0 2mo ago
    They're certainly endangered.
- copemaxxxing 2mo ago
  That's not gonna happen. What's gonna happen is you'll be in forever slavery. You think those in power will let you enjoy your life?
  - a2ff6eeb0 2mo ago
    Why do you think any humans would stay in power? The AI will know what's good for you better than other people would.
Calazon 2mo ago
I think they meant obsolete relative to economic, scientific, and engineering objectives. That doesn't mean they don't provide any value of any kind to anyone.

FuckButtons 2mo ago

If you are free from physical and mental labor, you are in fact, not supplying labor, and are therefore surplus to requirements.

auggierose 2mo ago
Whose requirements?
- esafak 2mo ago
  The employer's, whose salary affords your subsistence.
  - visarga 2mo ago
    If AI is so great it can do your job it is good enough to provide for your needs directly by automation. Just buy a robot and a plot of land and you don't have to worry about jobs.
    - esafak 2mo ago
      Robots can't do that yet, and even then you still need to pay for food, healthcare, land (taxes), transportation, etc.
  - auggierose 2mo ago
    I don't think anyone wants to be employed. They want the money that comes with employment. If you can make get money without employment, like rich kids, for example, I think most people would prefer that.
    - deleted 2mo ago
      [deleted]
    - feoren 2mo ago
      And you think that once the poor are no longer needed by the rich, the rich will decide to just give them money anyway? We already have dedicated campaigns to make sure people die sick and homeless on the streets when they become obsolete. You think that is not going to get much, much worse?

BeetleB 2mo ago

The essay On Proof and Progress in Mathematics by a Field's medalist is worth reading: https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236 He wrote it in 1994. He writes about how he almost "destroyed" a subdiscipline in mathematics by becoming so good at it that he outclassed everyone. PhD students were advised to stay away from the whole field. When he discovered this, he realized his error was that he was focusing on producing results, and not focusing on explaining his thought process. It's that thought process that is valuable in advancing the frontier - results alone won't do it. It didn't matter how many theorems he proved, if he was the only one who had the mental framework in mind on how to think about the whole field. I'm sure we've come across abstruse books where every theorem has a rabbit being pulled out of a hat, whereas other readers find it intuitive. It's because the latter has developed a mental model for the discipline, and you haven't. So he set about slowing down, and focusing on holding lots of seminars where he worked with other mathematicians to explain the thought process. Eventually others started publishing proofs of key theorems. When people publish in a journal, they are not merely doing it to show the result. They are having a conversation with other mathematicians. If they cannot explain their own proof, they're not having a conversation. This is why even decades after the Four Color Theorem was proved, plenty of mathematicians don't consider it "mathematics".

a2ff6eeb0 2mo ago
I don't understand why people are so fixated on the minds doing the mathematics being made out of meat. It seems obvious that soon, minds made of meat aren't going to be able to keep up. Useful thought, rather than hobbyist thought, seems destined to be the exclusive domain of silicon.
- BeetleB 2mo ago
  > I don't understand why people are so fixated on the minds doing the mathematics being made out of meat. I don't follow - are you surprised that mathematicians have social rules on how they interact with others? You're definitely welcome to set up a journal that takes whatever types of papers you deem acceptable. It's not like they're preventing the dissemination of information by taking this stance. Personally, I wouldn't hire a SW engineer who only showcases output from LLMs, and can't explain the code it wrote.

cubefox 2mo ago

> If Amazon uses AI math to come up with better routin Most research mathematics is pure mathematics which is completely useless. No routing algorithms. It's only relevant because we (or at least mathematicians) are interested in it. So an AI producing incomprehensible proofs would be completely pointless. That's why Tao insists on the importance of human understanding.

a2ff6eeb0 2mo ago
If it's just a hobby, why would you use an LLM at all?
- black_knight 2mo ago
  It is not a hobby when you are paid to do it! But I take it you mean “Done for the art of it”. Which I guess is a concept foreign to many. A few different reasons why use an LLM when mathematics is done for its own sake: Formally verifying my proofs catches any mistakes I make, but verifying is also hard work. LLMs shaves off a lot of time when formally verifying a proof. I can still read through an LLM generated proof and understand it. This is a way for me to understand the result I am working on (usually in order to know what to prove next, results are not proven in a vacuum). My experience thus far is that, while correct, an LLM generated proof is often unnecessarily complicated or inelegant. I take pleasure in elegant proofs and will spend time iterating on the first proof until I find it conveys the idea in the most elegant way. Having the initial LLM proof to start with is really useful, but is thus far rarely the final product.

applecoffeecake 2mo ago

If a result has a real-world application, then it can easily be published in an engineering or applied scientific journal in which it is already the norm to present methods that work empirically with little to no understanding of how.

fooker 2mo ago

Your analogy is great. What happens when it's the cats who get to decide what's published? Not an ideal scenario, but that's exactly the situation here. Mathematicians decide what gets reviewed and published in a a top journal. In the long run, this can and should make journals obsolete.

a2ff6eeb0 2mo ago
Exactly, the cats aren't going to be part of any real decision making soon enough.

gn_200826 2mo ago

Most of mathematics is more akin to philosophy than physics or engineering. Sure, if AI can prove a result that leads to practical applications, who cares if humans can't understand it. If AI performs a series of convoluted arguments demonstrating the existence of souls (feel free to replace souls with abstract nonsense), but nobody understands why, then what's the point?