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His view is the "capability gap" one, and you can just read the the statement and Tao's other writings for far more eloquent explanations of the difference betw

His view is the "capability gap" one, and you can just read the the statement and Tao's other writings for far more eloquent explanations of the difference between a raw LLM proof dump and real mathematical insight, and what it takes to get from the former to the latter, than I can provide. Again, nobody is accusing anyone of deliberately trying to harm mathematics. It's about misaligned objectives. Eg. Tao wrote the following before the Navier-Stokes announcement (referring to exactly the project OpenAI was undertaking): > At this point, I would not be surprised if one could batter out such an extension by pouring an enormous amount of compute and AI assistance at such a task. But such an exercise does not particularly hold my interest; I am far more interested in digesting the proof methods and extracting out the key new insights uncovered by this approach. And then went further to say that such activity could be actively harmful to the field. (All this can be read on Mathstodon: https://mathstodon.xyz/@tao https://mathstodon.xyz/@tao). The misalignment is that this activity that he and 24 other Fields medalists think is actively harmful to their field is deemed by OpenAI and others to be worth ploughing vast financial, human and compute resources into.

zozbot234 21d ago
> 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 21d 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 21d 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 21d 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?”

zozbot234 21d ago

> 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 21d 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 21d 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 21d 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?”