In Proof!, Amir Alexander argues that Euclidean geometry has been uniquely responsible for how modern societies are structured. Geometry has shaped how our cities are built and has even been used as a rationale to explain political structures, because the proofs in Euclid’s Elements are not just true but are provable by reason alone.

Alexander tracks the rediscovery of Euclidean geometry in 15th century Italy and recounts the French royals' centuries-long love affair with geometrical gardening. One night in 1661, Nicolas Fouquet, a superintendent under Louis XIV, was even arrested for the peculiar crime of having dared construct a grand geometrical garden for himself. In doing so, he had violated an irrefutable hierarchy: that geometry, in its perfection, was a testament to the divine right of kings. Elegant, symmetrical garden designs were more than just ornaments; they were proofs of incontestable certainty, and thus the authority to rule. Royal geometrical gardens proved to be a visual symbol of the French king’s consolidation of power during a time of violence and upheaval, with geometrical garden design reaching its apogee in Versailles. 

Proof! tells the monumental story of how geometry was carved into our world, the beliefs geometry supported and the ways geometry continues to shape our lives to this day.