 As powerful as Viète’s program was, questions remained for practicing mathematicians. Should we, as Viète urged, accept the neusis postulate as “not difficult” and thus as a foundational construction principle for geometry? And should we follow Viète in claiming that other curves that had significant problem-solving power in geometry—such as the spiral and quadratrix—were not legitimately geometrical because they could not be constructed by neusis? Moreover, there were questions about the connection Viète forged between algebra and geometry. For Descartes in particular, there were questions of whether there was a deeper, more fundamental connection that could be forged between the solutions of algebraic problems that were expressed in terms of equations and the solutions of geometrical problems that required the construction of curves. However, these questions did not come into full relief for Descartes until the early 1630s, after more than a decade of studying problems in both geometry and algebra.