  The significance of the sort of connection that Descartes made between geometry and algebra was great indeed, for without it the mathematization of the physics and the development of the calculus might not have happened when they did—a generation later via Sir Isaac Newton (1642–1727) and Gottfried Leibniz (1646–1716). It should be noted, however, that as groundbreaking as this work may have been, contrary to the claims of many, nowhere in the Geometry is a “Cartesian Coordinate System” ever developed (that is, the x-y coordinate system taught to today’s students of algebra), nor is he the originator of other mathematical concepts that bear his name, for example, the “Cartesian Product”. Carl Boyer notes that various concepts that lead to analytic geometry are found for the first time in the Geometry, and that the Geometry’s mathematical notation is still used today. But, he argues, although Cartesian geometry is taken by many to be synonymous with analytic geometry, the fact is that the fundamental aim of Descartes’ system is quite different from that of contemporary analytic geometry (Boyer, pp. 370–1). And so, the claim that Descartes is the originator of analytic geometry, at least as we understand it today, overstates the case. As Boyer rightly points out, however, this does not diminish the importance of the work in the history of mathematics.