Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.

Introduction: René Descartes and Modern European Mathematics.- 1: The Formation of Descartes's Mathematical Thought.- 1 Descartes and Jesuit Mathematical Education.- 2 The Mathematical Thought of Christoph Clavius.- 3 The First Attempt at Reforming Mathematics.- 4 The Mathematical Background of the Regulae ad Directionem Ingenii.- 5 The Géométrie of 1637.- Interim Consideration: Descartes and the Beginnings of Mathematicism in Modern Thought.- II: The Concept of 'Mathesis Universalis' In Historical Perspective.- 6 'Universal Mathematics' in Aristotle.- 7 'Mathesis Universalis' in the Sixteenth Century.- 8 'Mathesis Universalis' in the Seventeenth Century.- Conclusion: Descartes and the Modern Scheme of Learning.- Indices.- Name Index.- Treatise Index.