What I think Mathematicians should remind themselves is a lot of prestigious mathematicians, the likes of Cantor or Erdos, often only employed a handful of “tricks”/heuristics for their proofs over their career.
I know this claim is often made but it seems obvious that in this discussion, trick means something far wider and more subtle than any set computer program. In a lot of ways, "he just uses a few tricks" is akin to the way a mathematician will say "and the rest of the proof is elementary" (when it's still quite long and hard for anyone not versed in a given specialty). I mean, before category theory was formalized, the proofs that now are possible with it might classified as "all done with this trick" but grasping said trick was far from elementary matter.
I argue would not take a tremendous jump in performance for an AI to begin their own journey similar in kind to the greats, the only thing standing in their way (as with all contemporary mathematicians) is the extreme specialisation required to reach the boundary of unsolved problems.
Not that LLMs can't do some impressive things but your narrative seems to anthropomorphize them in a less than useful way.
I know this claim is often made but it seems obvious that in this discussion, trick means something far wider and more subtle than any set computer program. In a lot of ways, "he just uses a few tricks" is akin to the way a mathematician will say "and the rest of the proof is elementary" (when it's still quite long and hard for anyone not versed in a given specialty). I mean, before category theory was formalized, the proofs that now are possible with it might classified as "all done with this trick" but grasping said trick was far from elementary matter.
I argue would not take a tremendous jump in performance for an AI to begin their own journey similar in kind to the greats, the only thing standing in their way (as with all contemporary mathematicians) is the extreme specialisation required to reach the boundary of unsolved problems.
Not that LLMs can't do some impressive things but your narrative seems to anthropomorphize them in a less than useful way.