4 ms·

Mathematics isn't art. It doesn't gain its value in human affairs from being interesting to study. I fail to see why we should cater to that.

wrsh07 1mo ago
Importantly, which mathematicians will understand deep useful math? Who will actually care about the knowledge we can generate at will?
BeetleB 1mo ago
What is it, if not an art?
- daze42 1mo ago
  A science?
  - lanstin 1mo ago
    It isn’t even as constrained by material reality as mixing oil paints to get a certain effect is.
  - BeetleB 1mo ago
    Nope. Science demands empirical verification. Math doesn't. No theorem is violated based on experiments and observations.
- adastra22 1mo ago
  Truth.
  - BeetleB 1mo ago
    What is truth if we are free to pick our axioms? The universe is either Euclidean or not. If it were, how can theorems on non-Euclidean geometry be true?
    - gre 1mo ago
      You pick your axioms and you see what must be true. With math and logic, we can reason about any possible universe even though we live in only one of them.
wrsh07 1mo ago
Yes, open source isn't art either, yet my point is that the same principle applies to both There are many ways to stop progress and productivity
wrsh07 1mo ago
I think everyone is conflating a few things: * (1) Mathematics, the true things known by humans * Mathematics, the things that are true * (3) Mathematics, the institution which gets funding and manages resources to expand and maintain 1 AI agents can discover more true things, but that doesn't necessarily expand 1 and it might undermine 3 If someone is worried about 3 and you're talking about 2, then you are talking past each other
- formerlyknownas 1mo ago
  Yes, these things are definitely being conflated and there's a fourth conflated thing I think Tao is particular getting at: (4) Mathematics, the community which is a living system that decides what is interesting, constructs shared frameworks, transfers ideas between domains, develops taste, teaches new mathematicians, and continually emphasizes what counts as important mathematics, especially in it's overall value to humanity. This is the level in which theory building, simplification, integration and applications are built on. Contributing meaningfully here requires much more than generating solutions - it requires direction and restraint. Tao seems to be saying that this direction and restraint is the scarce resource that drives mathematical progress, not problem-solving ability. And AI is not only insufficient at it, but results generated by AI are destroying human ability to excercise this resource. This seems similar to another problem AI sucks at - drafting legal agreements. Despite being great at evaluating, interpreting, and comparing legal agreements it fails amazingly at drafting them. This is because what you don't say/do is vastly more important than what you do say/do. And AI is great saying and doing things, it's the selection based on implied values that it struggles with.

wrsh07 1mo ago

Importantly, which mathematicians will understand deep useful math? Who will actually care about the knowledge we can generate at will?

BeetleB 1mo ago

What is it, if not an art?

daze42 1mo ago
A science?
- lanstin 1mo ago
  It isn’t even as constrained by material reality as mixing oil paints to get a certain effect is.
- BeetleB 1mo ago
  Nope. Science demands empirical verification. Math doesn't. No theorem is violated based on experiments and observations.
adastra22 1mo ago
Truth.
- BeetleB 1mo ago
  What is truth if we are free to pick our axioms? The universe is either Euclidean or not. If it were, how can theorems on non-Euclidean geometry be true?
  - gre 1mo ago
    You pick your axioms and you see what must be true. With math and logic, we can reason about any possible universe even though we live in only one of them.

wrsh07 1mo ago

Yes, open source isn't art either, yet my point is that the same principle applies to both There are many ways to stop progress and productivity

wrsh07 1mo ago

I think everyone is conflating a few things: * (1) Mathematics, the true things known by humans * Mathematics, the things that are true * (3) Mathematics, the institution which gets funding and manages resources to expand and maintain 1 AI agents can discover more true things, but that doesn't necessarily expand 1 and it might undermine 3 If someone is worried about 3 and you're talking about 2, then you are talking past each other

formerlyknownas 1mo ago
Yes, these things are definitely being conflated and there's a fourth conflated thing I think Tao is particular getting at: (4) Mathematics, the community which is a living system that decides what is interesting, constructs shared frameworks, transfers ideas between domains, develops taste, teaches new mathematicians, and continually emphasizes what counts as important mathematics, especially in it's overall value to humanity. This is the level in which theory building, simplification, integration and applications are built on. Contributing meaningfully here requires much more than generating solutions - it requires direction and restraint. Tao seems to be saying that this direction and restraint is the scarce resource that drives mathematical progress, not problem-solving ability. And AI is not only insufficient at it, but results generated by AI are destroying human ability to excercise this resource. This seems similar to another problem AI sucks at - drafting legal agreements. Despite being great at evaluating, interpreting, and comparing legal agreements it fails amazingly at drafting them. This is because what you don't say/do is vastly more important than what you do say/do. And AI is great saying and doing things, it's the selection based on implied values that it struggles with.