Kant's transcendental philosophy is used to answer the questions about the nature of mathematics, how mathematics relates to the physical world, why we are self-aware and perceive ourselves in the world described by mathematics. Kant's architectonic system of reason is used to derive the invariant framework of the mind within which our thoughts originate - the original synthetic unity of apperception. It is the logical framework underlying all our possible knowledge - the framework of the cognitive faculty of understanding. This framework lies at the foundation of our thinking, logic, mathematics, natural language and organization of sense-data (experience). Phenomenal world in space and time is an output of this framework after the synthesis of the productive imagination. The nature of mathematics is discussed as based on this framework from intuitionist and logicist perspectives. Logic defines the structure of space and time.