5 ms·

> His view is the "capability gap" one That's the far more sensible reading, so thanks for confirming I guess. But then the misalignment talk is pretty clearl

> His view is the "capability gap" one That's the far more sensible reading, so thanks for confirming I guess. But then the misalignment talk is pretty clearly a distraction. > ...And then went further to say that such activity could be actively harmful to the field. If true (and there is as of yet insufficient evidence of this), that's merely a contingent fact about very real institutional misalignment within the human mathematical community, not about AI itself or even AI frontier labs. There's simply zero inherent reason why providing a bare truth value or a completely inscrutable proof about the status of some open conjecture should make that entire subfield of math "contaminated" for the foreseeable future when it comes to extracting further human-relevant insight. That's the misalignment we should be caring about.

SpicyLemonZest 4d ago
The declaration is about that institutional misalignment. They want to change the norms of the mathematical community, so that producing inscrutable proofs is a low-value activity nobody cares much about rather than a high-value activity that AI frontier labs can make headlines by performing. Their ask of the frontier labs is to please be aware of the problems with the old norms and not exploit them during the transition period; they agree this doesn't have much to do with AI itself, which they acknowledge is a powerful technology that will improve and accelerate mathematical research.
- zozbot234 4d ago
  Broadly agreed, with a key proviso: producing inscrutable proofs has negligible value as a mathematician's finished output but that doesn't make it a "low-value activity" in and of itself. Ultimately, the status of these proof-like objects as a raw input into mathematical practice will probably be comparable to any other sort of computationally-driven https://en.wikipedia.org/wiki/Experimental_mathematics https://en.wikipedia.org/wiki/Experimental_mathematics . These are not new problems: "computer" used to be a job description for humans before it was the name of a machine, but we now view raw computations as a trivial matter that's not worthy of any human credit.
  - SpicyLemonZest 4d ago
    Agreed. I’m sure there was a time in the early history of computational mathematics where someone with access to more computer time than others went around telling people how easy it is to generate books of trigonometric tables, and other people got annoyed at him, until soon computation was so thoroughly automated that the very idea of computing sines by hand became obsolete. I expect that’s about how math students in the 2040s will learn about this: “what do you mean, they had prizes for writing proofs, why would an educated mathematician spend their time writing proofs?”

SpicyLemonZest 4d ago

The declaration is about that institutional misalignment. They want to change the norms of the mathematical community, so that producing inscrutable proofs is a low-value activity nobody cares much about rather than a high-value activity that AI frontier labs can make headlines by performing. Their ask of the frontier labs is to please be aware of the problems with the old norms and not exploit them during the transition period; they agree this doesn't have much to do with AI itself, which they acknowledge is a powerful technology that will improve and accelerate mathematical research.

zozbot234 4d ago
Broadly agreed, with a key proviso: producing inscrutable proofs has negligible value as a mathematician's finished output but that doesn't make it a "low-value activity" in and of itself. Ultimately, the status of these proof-like objects as a raw input into mathematical practice will probably be comparable to any other sort of computationally-driven https://en.wikipedia.org/wiki/Experimental_mathematics https://en.wikipedia.org/wiki/Experimental_mathematics . These are not new problems: "computer" used to be a job description for humans before it was the name of a machine, but we now view raw computations as a trivial matter that's not worthy of any human credit.
- SpicyLemonZest 4d ago
  Agreed. I’m sure there was a time in the early history of computational mathematics where someone with access to more computer time than others went around telling people how easy it is to generate books of trigonometric tables, and other people got annoyed at him, until soon computation was so thoroughly automated that the very idea of computing sines by hand became obsolete. I expect that’s about how math students in the 2040s will learn about this: “what do you mean, they had prizes for writing proofs, why would an educated mathematician spend their time writing proofs?”