This year marks the fiftieth anniversary of Terry Riley's seminal composition In C, a groundbreaking piece that led to the minimalism movement in music. Strikingly, In C also presents a tangible embodiment of several abstract mathematical structures. This essay explores three mathematical perspectives on In C. The first is that of diffeomorphisms and differential geometry; the second is functional integration; and the third is a strange hybrid of finite state automata, Markov chains, and Conway's Game of Life. Through Riley's composition, listeners can directly experience abstract mathematical ideas in these three arenas. In addition, the piece suggests new ways to look at finite state automata.