Hollis Frampton’s much-discussed film Zorns Lemma is a complex and fascinating film that has a labyrinthine structure, alluding to a mathematical reading of the film as a visual metaphor for Max Zorn’s famous axiom Zorn’s Lemma. In the extensive literature about Zorns Lemma, there have been many different interpretations offered; however, none of these readings has provided a satisfactory mathematical interpretation of the film. After first providing an overview of Zermelo’s Axiom of Choice and some of its equivalent statements, this article provides a mathematical interpretation of Zorns Lemma that shows the film as a cinematic/poetic demonstration of the Axiom of Choice, a statement that is mathematically equivalent to Zorn’s Lemma. In addition, this paper explores some of the consequences of such an interpretation, including one that connects the film to the ideas Frampton was exploring in Magellan.