6 ms·

That's true of the entirety of mathematics. Its validity is a social construct. That is not to relativize it entirely, but much of what was considered good and

That's true of the entirety of mathematics. Its validity is a social construct. That is not to relativize it entirely, but much of what was considered good and sound mathematics in the ancient Agean for example would now fall way short of what mathematicians consider valid proofs. Mathematics is a human endeavor funded on communicating and sharing mental constructs. Some are useful but most of it is not about producing useful things, quite the opposite in fact. Gödel showed you need to agree on definitions to even do any valid mathematical construct. Truth is also ill defined. That's what I don't get about generating math with LLMs. Who cares if you make hundreds of pages and lean code and it gets a thumbs up for logical validity? Mathematics is so much more then concatenating valid logical statements.

zamadatix 6d ago
There's a large difference between "wrong for the given definitions" and "right in that context, but wrong for other definitions" though.
- huurtehoog 6d ago
  I think I am make a much more basic point than what you're talking about but then again I am not sure what you're tying to say here...
  - zamadatix 6d ago
    The problem with the acceptance of the given proof of the abc conjecture is rooted in beliefs the proof had at least one erroneous step in its logic which leaves gaps not able to be filled back in without significant new work in the proof. It's not rooted in a difference of starting axioms, what Gödel wrote about, or what kind of truth there can be (though the foreignness has certainly never sped its review up). Your comment may have separate points to make about those things in general but it does not make the problem with the proposed proof the same as the issues which apply to all of mathematics.
    - huurtehoog 5d ago
      Yeah I'm not talking about that one proof, I'm talking about the whole of mathematics. It's not manufacturing theorems, it's an ongoing conversation. It's poetry in the etymological sense, poesis, it's creative. Why would anyone think that manufacturing mathematics is a good idea? “Good, he did not have enough imagination to become a mathematician. [Upon hearing that one of his students had dropped out to study poetry]” ― David Hilbert
      - cindyllm 5d ago
        [dead]

zamadatix 6d ago

There's a large difference between "wrong for the given definitions" and "right in that context, but wrong for other definitions" though.

huurtehoog 6d ago
I think I am make a much more basic point than what you're talking about but then again I am not sure what you're tying to say here...
- zamadatix 6d ago
  The problem with the acceptance of the given proof of the abc conjecture is rooted in beliefs the proof had at least one erroneous step in its logic which leaves gaps not able to be filled back in without significant new work in the proof. It's not rooted in a difference of starting axioms, what Gödel wrote about, or what kind of truth there can be (though the foreignness has certainly never sped its review up). Your comment may have separate points to make about those things in general but it does not make the problem with the proposed proof the same as the issues which apply to all of mathematics.
  - huurtehoog 5d ago
    Yeah I'm not talking about that one proof, I'm talking about the whole of mathematics. It's not manufacturing theorems, it's an ongoing conversation. It's poetry in the etymological sense, poesis, it's creative. Why would anyone think that manufacturing mathematics is a good idea? “Good, he did not have enough imagination to become a mathematician. [Upon hearing that one of his students had dropped out to study poetry]” ― David Hilbert
    - cindyllm 5d ago
      [dead]