Proof!: How the World Became Geometrical

The tenets of Euclidean geometry and artistry of formal garden design become keystones shaping modernity in the latest exploration by historian Alexander (Infinitesimal) of math’s influence on history. For the ancient Greeks, Alexander writes, geometry showed that “truth could be discovered by reason alone.” It described a rational universe, unlike the world the Catholic Church later regarded as merely a “pale shadow” of heaven. Alexander describes how 15th-century Florentine artist Filippo Brunelleschi drew on classical, geometry-driven style to bring grandeur to his architecture, thereby discovering principles of linear perspective that added realism to his paintings. Italian garden designers embraced geometrical ideas, too, impressing King Charles VIII of France while he was on campaign near Naples in 1495, so much that he eagerly brought them home. There, they eventually informed Louis XIV’s ambitious overhaul, begun in 1688, of the Versailles gardens into a grand and precisely arranged showcase for his reign, symbolizing his God-given power over the natural order of things. Crossing Europe and carried around the globe, Alexander writes, geometrical theory even influenced the design of the American capital (and defeated Jefferson’s proposal for a Philadelphia-style grid.) Alexander’s lucid and convincingly argued book fully demonstrates how ideas ancient in origin continue to shape the contemporary world. Agent: Lisa Adams, Garamond Agency. (Sept.)