Conceptual Harmonies develops an original account of G. W. F. Hegel's perplexing Science of Logic from a simple insight: philosophical and mathematical thought have shaped each other since classical times. Situating Science of Logic within the rise of modern mathematics, Redding stresses Hegel's attention to Pythagorean ratios, Platonic reason, and Aristotle's geometrically inspired logic. He then explores how later traditions shaped Hegel's world, through both Leibniz and new forms of algebraic geometry. This enlightening reading recovers an overlooked stream in Hegel's philosophy that remains, Redding argues, important for contemporary conceptions of logic.