Kant’s account of the sublime in the Critique of Judgment has been extremely influential, prompting extensive discussion of the psychology, affect, moral significance, and relevance to artistic representation of the sublime on his provocative view. I focus instead on Kant’s account of the mathematical sublime in connection to his theoretical critical project, namely his attempt to characterize human cognitive powers and to limit human pretensions to knowledge of the supersensible. I argue, first, that his account of the psychology of the sublime is designed to explain not just its affective character (its displeasure-pleasure), but also to address challenges concerning the coherence of an experience of something as transcending one’s cognitive abilities. Thereby, I argue moreover, Kant provides an alternative, demystifying account of mystical experiences, in which humans might take themselves to intuit that which is beyond human understanding or reason, and thus to claim that they have special cognitive access to the supersensible, transcending the limits Kant claims to establish for human cognition. Kant’s account of the mathematical sublime is not merely so reductive of mystical experience, however; it also, I suggest, describes the aesthetic of Kantian critique itself.