AlephZero and Mathematical Experience

Abstract: This essay explores the impact of automated proof construction on three key areas of mathematical cognition: on how we judge the role one piece of mathematics plays in another, on how we make mistakes in reasoning about mathematical objects, and on how we understand what our theorems are truly about. It concludes by speculating on a new form of mathematical experience that these methods could make possible: ``glitching'', a game-like search for uncanny consequences of our definitions.