Keeping in mind that your cult hero apparently picked 57 as an example of a prime number, it might not be inappropriate to commence my comment by observing that Kantor and I were invoking quite distinct modalities/narratives inherent in the mathematical experience. The narrative I was referencing, "Some Thoughts on Automation and Mathematical Research", I take both of us seriously pondered. If this is indeed the case, I trust you might agree that the ability of "AI system to work its way through all of the exercises in the Springer-Verlag Graduate Texts in Mathematics series" is not terribly removed from enabling it ("AI system") to, in due course, generate a competitive graduate dissertation, which, in turn, is (in effect) tantamount to a submission (in due course) to a competitive peer-reviewed journal, such as e.g. Inventiones Mathematicae.
Such a hypothetical capability, needless to say, is quite distinct from the context and narrative underlaying Poincare's transformational (once in a decade if not a century) insight referenced in Kantor's quest.
PS. "Some Thoughts on Automation and Mathematical Research" is based on the talk given in November 2021, preceding the pandemic advent of ChatGPT-4, and referencing AlphaGo accordingly. For what it is worth, personally, I find viewing mathematics as a “language” (as in "LLM") a somewhat less problematic “oversimplification” than viewing it as a “game” (as in "Go") — needless to say these are not mutually exclusive.
Keeping in mind that your cult hero apparently picked 57 as an example of a prime number, it might not be inappropriate to commence my comment by observing that Kantor and I were invoking quite distinct modalities/narratives inherent in the mathematical experience. The narrative I was referencing, "Some Thoughts on Automation and Mathematical Research", I take both of us seriously pondered. If this is indeed the case, I trust you might agree that the ability of "AI system to work its way through all of the exercises in the Springer-Verlag Graduate Texts in Mathematics series" is not terribly removed from enabling it ("AI system") to, in due course, generate a competitive graduate dissertation, which, in turn, is (in effect) tantamount to a submission (in due course) to a competitive peer-reviewed journal, such as e.g. Inventiones Mathematicae.
Such a hypothetical capability, needless to say, is quite distinct from the context and narrative underlaying Poincare's transformational (once in a decade if not a century) insight referenced in Kantor's quest.
PS. "Some Thoughts on Automation and Mathematical Research" is based on the talk given in November 2021, preceding the pandemic advent of ChatGPT-4, and referencing AlphaGo accordingly. For what it is worth, personally, I find viewing mathematics as a “language” (as in "LLM") a somewhat less problematic “oversimplification” than viewing it as a “game” (as in "Go") — needless to say these are not mutually exclusive.