Liberty's Grid: A Founding Father, a Mathematical Dreamland, and the Shaping of America

by Evan Rothera
published on 11 March 2026

A bird’s eye view of the U.S. reveals perpendicular streets, rectangular fields, and uniformity in both urban and rural landscapes. "Liberty’s Grid" examines how this gridded landscape came to exist. It explores how the work of Isaac Newton and René Descartes shaped Thomas Jefferson’s ideas. It also shows how grids produced a backlash in favor of non-gridded landscapes. This book is well suited for both scholars and students and is highly recommended.

Amir Alexander begins Liberty’s Grid by considering the view of the San Fernando Valley from Castle Peak, a hill near his home. Although the Valley is peculiar in many respects, when viewed from the top of a 600-foot hill, it is easy to see the gridded landscape that matches other U.S. urban areas. “The street plan of the Valley, Alexander asserts, is “the street plan of America” (3). By this, he means that streets in cities across the U.S. offer rectilinear uniformity: “broad, arrow-straight avenues, regularly spaced and perfectly parallel to one another, are met at fixed intervals by equally straight and parallel streets that intersect them at precise right angles” (3). Rectilinear streets were not a U.S. invention, but they have become so prevalent that they “seem like components of a single, all-encompassing urban grid stretching from New York City to Chicago to Los Angeles” (3). Grids are not particularly practical or utilitarian, Alexander contends, and they generated significant resistance. However, Jefferson championed the grid, which embodied “an ideal of America as a land of unconstrained freedom and infinite opportunity” (8).

Alexander begins long before the Sage of Monticello was born and explores how René Descartes and Isaac Newton influenced Jefferson’s thinking. In November 1619, Descartes spent a consequential day and night in an inn near Ulm, where he transformed himself “from a restless young man into a systematic philosopher” (21). Descartes’s conclusions led to the idea that “space is mathematical, and everything within it—every location, every object, every shape, and every movement—can be precisely described through mathematics” (22). Descartes revised the Aristotelian cosmos, and his universe matched the one we know today, but with one difference: “its space was completely full, allowing no gaps of emptiness to exist between different bodies” (25). As Descartes revised Aristotle, Newton revised Descartes. Newton’s mathematics assumed that “geometrical objects exist in an absolute mathematical space—uniform, universal, and infinite” (43).

Jefferson embraced the concept of absolute space and applied it to the land. He frequently “insisted that America was a vast and empty virgin territory” (84) and that the American West was a “vast and all but limitless space” (85). Scholars have noted the problematic tendency among people throughout American history, including Jefferson, to see the land as empty space, a perspective that erases Indigenous people. Nevertheless, Jefferson saw America as a blank slate and the embodiment of the Newtonian absolute space. Jefferson also formulated a simple yet audacious rectilinear grid plan as he thought about how to survey, divide, and settle this allegedly empty land. The Confederation Congress accepted Jefferson’s vision when they passed the Land Ordinance of 1784 and imposed “a vast mathematical grid on western lands” (126). Jefferson seemingly won this debate because, as Alexander notes, “to a stunning degree, the western United States had become precisely what Jefferson had dreamed it would be: a vast uniform and undifferentiated space, marked by a vast uniform mathematical grid” (153).

Jefferson’s plan, although it triumphed in some ways, attracted scorn and criticism in others. Jefferson and Pierre Charles L’Enfant had very different visions for Washington, D.C. L’Enfant wanted a Euclidean landscape like Versailles. Jefferson, unsurprisingly, preferred a rectilinear grid. L’Enfant denounced Jefferson’s plans as “defective,” “tiresome and insipid,” and the product of “some cool imagination wanting a sense of the really grand and truly beautiful” (173). Jefferson lost that battle. He seemed to win in New York City, until, of course, one arrives at Central Park, the ultimate rebellion against the grid. Urban parks, suburbs, campuses, and national parks all, in their way, rebuke the grid.

This is a fascinating book about mathematics, space, and place, as well as how grids both order and disrupt the lives of many people in the modern U.S. It will work well in upper-level undergraduate courses and graduate seminars.

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