Proof!

July 15, 2019
A lively explanation of how geometry structures aspects of the natural and human worlds. In this bracingly enthusiastic account of geometry's role in shaping a variety of institutions, Alexander (History/UCLA; Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, 2014, etc.) turns to Euclid's Elements and its complete world of mathematical proofs, founded on indisputable postulates and proven through impeccable logic. (The book isn't overrun with mathematics, but when it is unavoidable, the author is clear in his language.) Geometry revealed truths stripped of anything erroneous, unessential, and transitory, truths that were deployed by such luminaries as Copernicus, Galileo, and Leon Battista Alberti, setting the scientific agenda. Geometry is everywhere, underlying the natural and human-made worlds, infusing even our social arrangements. Guided by the art and architectural works of Alberti, which demonstrated "that the seemingly limitless variety one encounters in nature was in fact governed by the fixed eternal laws of geometry," Alexander applies that thought to the royal gardens of, in particular, France. Gardens were central to the monarchy's public presentation, ideology, identity, power, and legitimacy, especially so at Versailles, where Louis XIV's hierarchical state was reflected in the layout of the vast but tightly ordered gardens. "At the apex of this universe was, inevitably, the king in his palace, whose rule was as inescapable and unchallengeable as geometry itself," writes the author. This modernizing state was governed by a rational and efficient central bureaucracy, which is how the story moves forward beyond the monarchy into city planning. "The geometrical ideal of an efficient rational state found expression...on the bustling streets of capital cities--the homes of state bureaucracies." This is the case in Rome, Paris, St. Petersburg, and Berlin, where harmony and order reflect the organs of state. The stamp of Versailles can also be found in New Delhi and Washington, D.C., the latter being a fine example of geometry accommodating several nodes of power. A deep immersion into geometric determinism at its most entertaining.

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May 27, 2019
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.