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Yeah, the Jacobian conjecture counter-example was big news. In particular, it would have been news even if an AI hadn't done it. That's where the bar is now. Se

by moomin 2mo ago

Yeah, the Jacobian conjecture counter-example was big news. In particular, it would have been news even if an AI hadn't done it. That's where the bar is now. Settling Erdős conjecture 7529 or whatever no longer qualifies as AI news.

tsunamifury 2mo ago
Real talk. AI solving these makes me feel like mathematicians put far more importance on their work than was actually there. Many solutions seems to be tautological games, and games of logic where conjecture puzzles that few work on or care can be solved by AI which doesn’t care what it works on. It seems to always be some form of this: Mathematician: “Propose conjecture a and conjecture b can’t be true simultaneously” AI: “they can” Everyone: “ok…” I know this might be unfair or out of ignorance but it genuinely is how this field feels today. Games of games with self importance added in. Edit: the point I should have made is, should we be using AI to figure out what proofs MATTER now vs games of proofs?
- efficax 2mo ago
  "tautological games". All proofs are a form of tautology, you have to end up back at the point your theorem proposed. Math is games of logic. That's what it is.
- dwaltrip 2mo ago
  Look up how pure mathematics connects back to reality in countless unexpected and useful ways, time and time again.
- deeznuttynutz 2mo ago
  Don't do that...
- chermi 2mo ago
  Very useful games, self-importance or no. See pattern, conjecture generalization, test generalization. It's almost like empirical math. I like it and I also like mathematicians doing it the old way.
  - tsunamifury 2mo ago
    I feel like you should search through the thousands of papers that are generated nonsense math theory and laugh at how you cherry picked 3 things.
- jstanley 2mo ago
  We call a proof that is not tautological "wrong".
- wongarsu 2mo ago
  Academic math is a bit like basic research. You come up with funny ways to look at numbers or prove weird statements about this thing you came up with and call a "group", and a couple years or decades or centuries later it turns out that this solves real problems in electrical engineering or biology Or it ends up never becoming useful. But you can't know that in advance
  - tsunamifury 2mo ago
    Disagree, basic research, no matter how dull, is an observation of a measured reality. Math Theory are patterns of abstraction that may never be useful at all or representative of reality.
    - lyu07282 2mo ago
      “May never be useful“? You make it sound as if there aren't countless examples of those "abstractions" of theory/pure math turning out to be useful in all kinds of fields in the past. This feels like the more general anti-science argument of 90% of science is useless and never produces practical applications, the point people never understand is that nobody knows which 10% it's going to be so you have to do the 100% to get to the 10%.
    - fn-mote 2mo ago
      Parent seems to conflate “abstract” with “useless”. This comment addresses the “abstract” part only. > Math Theory are patterns of abstraction that may never be useful at all or representative of reality. This is a complete misunderstanding of (good) mathematical research. The results look abstract, but they are based on concepts that are real and have truth or falsehood. One example that comes to mind (sorry, technical): is it possible that all maps from a high dimensional sphere to a three dimensional sphere (S^2) might form a group that is not even finitely generated? This is not just “abstract nonsense”, but understanding any of this takes effort.
      - tsunamifury 2mo ago
        Abstraction is useless until its proves use in test against a base case of reality. its the defition of useless most of the time.
- throw-the-towel 2mo ago
  To borrow a common wisdom about marketing, half of all mathematics is a waste of time, but you can't know which half.
  - tsunamifury 2mo ago
    But the issues is you have the ratios wrong. 99% of math theory is useless and maybe 1% has value.
    - throw-the-towel 2mo ago
      Maybe so! My point was not about the exact percentages, just the fact that you can't predict which avenues of research will yield practical results.

by moomin 2mo ago

tsunamifury 2mo ago

Real talk. AI solving these makes me feel like mathematicians put far more importance on their work than was actually there. Many solutions seems to be tautological games, and games of logic where conjecture puzzles that few work on or care can be solved by AI which doesn’t care what it works on. It seems to always be some form of this: Mathematician: “Propose conjecture a and conjecture b can’t be true simultaneously” AI: “they can” Everyone: “ok…” I know this might be unfair or out of ignorance but it genuinely is how this field feels today. Games of games with self importance added in. Edit: the point I should have made is, should we be using AI to figure out what proofs MATTER now vs games of proofs?

efficax 2mo ago
"tautological games". All proofs are a form of tautology, you have to end up back at the point your theorem proposed. Math is games of logic. That's what it is.
dwaltrip 2mo ago
Look up how pure mathematics connects back to reality in countless unexpected and useful ways, time and time again.
deeznuttynutz 2mo ago
Don't do that...
chermi 2mo ago
Very useful games, self-importance or no. See pattern, conjecture generalization, test generalization. It's almost like empirical math. I like it and I also like mathematicians doing it the old way.
- tsunamifury 2mo ago
  I feel like you should search through the thousands of papers that are generated nonsense math theory and laugh at how you cherry picked 3 things.
jstanley 2mo ago
We call a proof that is not tautological "wrong".
wongarsu 2mo ago
Academic math is a bit like basic research. You come up with funny ways to look at numbers or prove weird statements about this thing you came up with and call a "group", and a couple years or decades or centuries later it turns out that this solves real problems in electrical engineering or biology Or it ends up never becoming useful. But you can't know that in advance
- tsunamifury 2mo ago
  Disagree, basic research, no matter how dull, is an observation of a measured reality. Math Theory are patterns of abstraction that may never be useful at all or representative of reality.
  - lyu07282 2mo ago
    “May never be useful“? You make it sound as if there aren't countless examples of those "abstractions" of theory/pure math turning out to be useful in all kinds of fields in the past. This feels like the more general anti-science argument of 90% of science is useless and never produces practical applications, the point people never understand is that nobody knows which 10% it's going to be so you have to do the 100% to get to the 10%.
  - fn-mote 2mo ago
    Parent seems to conflate “abstract” with “useless”. This comment addresses the “abstract” part only. > Math Theory are patterns of abstraction that may never be useful at all or representative of reality. This is a complete misunderstanding of (good) mathematical research. The results look abstract, but they are based on concepts that are real and have truth or falsehood. One example that comes to mind (sorry, technical): is it possible that all maps from a high dimensional sphere to a three dimensional sphere (S^2) might form a group that is not even finitely generated? This is not just “abstract nonsense”, but understanding any of this takes effort.
    - tsunamifury 2mo ago
      Abstraction is useless until its proves use in test against a base case of reality. its the defition of useless most of the time.
throw-the-towel 2mo ago
To borrow a common wisdom about marketing, half of all mathematics is a waste of time, but you can't know which half.
- tsunamifury 2mo ago
  But the issues is you have the ratios wrong. 99% of math theory is useless and maybe 1% has value.
  - throw-the-towel 2mo ago
    Maybe so! My point was not about the exact percentages, just the fact that you can't predict which avenues of research will yield practical results.