Building upon the arguments of Jacob Klein and Edmund Husserl that we can only understand the meaning of modern science by investigating its historical development, this dissertation aims to uncover the nature and conceptual presuppositions of Descartes’s concept of space. In analyzing this concept, the dissertation extends Klein’s analysis of Descartes’s contribution to the development of modern symbolic mathematics to Descartes’s equally important role in developing the conceptual underpinnings of modern mathematical physics by showing that Descartes’s concept of space, which spans and unites the mathematical and physical domains, is an expansion of the symbolic concept of number. The analysis of Descartes’s concept of space depends upon connecting the following aspects of Descartes’s writings: the account of mind and mathematical cognition in the Rules for the Direction of the Mind, the conceptual structure of the mathematical objects and the mathematical understanding of space in the Geometry, and the physical understanding of space in the Principles of Philosophy. The dissertation ultimately concludes that Descartes’s concept of space allows the distinctive conceptual structure of modern mathematics to be applied to the physical world, whereby that concept provides a conceptual framework within which mathematical physics can exist.