Since much of this sequence has focused on case studies (Grothendiek, Scott Alexander), I'd be curious as to what you think of Douglas Hofstadter. How does he fit into this whole picture? He's obviously a man of incredible talent in something - I don't know whether to call it math or philosophy (or both). Either way it's clear that he has the aesthetic sense you're talking about here in spades. But I distinctly remember him writing something along the lines of how, upon reaching graduate mathematics he hit a "wall of abstraction" and couldn't progress any further. Does your picture of mathematical ability leave room for something like that to happen? I mean, this is Douglas freakin' Hofstadter we're talking about - it's hard to picture someone being more of a mathematical aesthete than he is. And even he ran into a wall!