Baylee Brits's Literary Infinities is original, insightful, and intelligent, but falls victim to its ambitions, introducing a vast matrix of concepts, many of which overlap to the point of indistinguishability. Her primary argument is that the work of Jorge Luis Borges, Samuel Beckett, and J.M. Coetzee all demonstrates a kind of allegory corresponding to Georg Cantor's concept of transfinites, or "actual infinities." The argument is successful with respect to Borges, but only convincingly demonstrates a general concern with mathematics in the other two writers, not specific "transfinite allegories." Though it does not fulfill its introductory promise, Literary Infinities is full of sharp readings, both of fiction and criticism. Moreover, it strikes an excellent interdisciplinary balance, drawing upon complex mathematics concretely to introduce exciting new interpretations of twentieth-century classics.