In the Critique of Pure Reason, Kant advances the notion that there are certain kinds of judgment which are distinctly 'mathematical' in character. These 'mathematical judgments' are not confined solely to the realm of arithmetic and geometry, furthermore, but can in fact be discovered as part of every true judgment about the world: they are at the very core of the synthetic a priori judgments in which the world actually comes to be known to us, Kant believed, because the Transcendental Synthesis (the judgment considered as a whole) always takes 'mathematical judgments' as logically required in 'dynamical judgments.' The purpose of this essay is to show that Kant regarded the mathematical judgment as basic in the Transcendental Synthesis, because judgments making use of the 'dynamical' categories do in fact presuppose judgments employing 'mathematical' categories. Furthermore, I hold that these two types of 'judgements'-- which together comprise the Transcendental Synthesis-- are, according to Kant, synthetic in two different ways. The crucial distinction between mathematical and dynamical synthesis in the Kantian theory of judgment is treated at length, and mathematical synthesis is shown to be the more elementary of the two. The mathematical synthesis is a kind of simple composition from logically unrelated elements which, for Kant, represents the most fundamental sense of juxtaposition possible in the synthetic a priori judgment. The program of this essay is to examine Kant's theory of judgment as presented in the Transcendental Analytic and his discussion of the 'mathematical method' in the Discipline of Pure Reason, and thereby to make clear his notion of the mathematical synthesis as a synthesis which is 'fundamental,' both in its manner of combination and in terms of the manifold which it combines.