 Attention to this interpretive issue in Kant’s philosophy of mathematics is vital for the light it sheds on the more general question of what makes synthetic a priori cognition possible, the central question of Kant’s Critique of Pure Reason. With respect to this more general question, it is important to differentiate Kant’s use of the terms “analytic” and “synthetic” to mark a logico-semantic distinction between types of judgments—which Kant uses to defend the distinctive thesis that mathematical cognition is synthetic a priori—from his use of the same terms to mark a traditional mathematical distinction, between analytic and synthetic methods. He deploys the latter distinction in order to identify two distinct argumentative strategies for answering the question of the “possibility of pure mathematics.” The analytic method is characterized by reasoning that traces a given body of cognition, such as mathematics, to its origin or sources in the mind. By contrast, the synthetic method aims to derive real cognition directly from such original cognitive sources, which sources or powers are first explicated independently of any particular body of cognition (including mathematics) that the powers might ultimately produce. Kant adopts the former method in his Prolegomena, arguing from the synthetic and a priori nature of mathematical judgment to the claim that space and time are the forms of human sensibility; he adopts the latter method in the Critique of Pure Reason, arguing that the forms of human sensibility, space and time, provide the basis from which to derive synthetic and a priori mathematical judgments (Shabel 2004). These arguments, together with the details of his account of the synthetic and a priori nature of all mathematical judgment, provide an answer to the question of the possibility of mathematics: the practices that yield the paradigmatically synthetic and a priori judgments of the science of mathematics are grounded in and explained by the very nature of human sensibility, and, in particular, by the spatio-temporal form of all (and only) the objects of human experience (Van Cleve 1999). But, this answer raises further questions, in particular about how to distinguish between metaphysical and geometric representations of space (Carson 1997; Friedman 2000, 2015, 2020; Onof and Schulting 2014; Tolley 2016).