(Fun tangent, not directly addressing this argument thread.)
There’s a trio of great posts from 2015 by @JonahS : The Truth About Mathematical Ability ; Innate Mathematical Ability ; Is Scott Alexander bad at math? which (among other things) argues that you can be “good at math” along the dimension(s) of noticing patterns very quickly, AND/OR you can be “good at math” along the dimension(s) of an “aesthetic” sense for concepts being right and sensible. (My summary, not his.)
The “aesthetics” is sorta a loss function that provides a guidestar for developing good deep novel understanding—but that process may take a very long time. He offers Scott Alexander, and himself, and Alexander Grothendieck as examples of people with lopsided profiles—stronger on “aesthetics” than they are on “fast pattern-recognition”.
I found it a thought-provoking hypothesis. I wish JonahS had written more.
(Fun tangent, not directly addressing this argument thread.)
There’s a trio of great posts from 2015 by @JonahS : The Truth About Mathematical Ability ; Innate Mathematical Ability ; Is Scott Alexander bad at math? which (among other things) argues that you can be “good at math” along the dimension(s) of noticing patterns very quickly, AND/OR you can be “good at math” along the dimension(s) of an “aesthetic” sense for concepts being right and sensible. (My summary, not his.)
The “aesthetics” is sorta a loss function that provides a guidestar for developing good deep novel understanding—but that process may take a very long time. He offers Scott Alexander, and himself, and Alexander Grothendieck as examples of people with lopsided profiles—stronger on “aesthetics” than they are on “fast pattern-recognition”.
I found it a thought-provoking hypothesis. I wish JonahS had written more.