The world's most artful and skillful stone architecture is found at Tiahuanaco at the southern end of Lake Titicaca in Bolivia. The precision of the stone masonry rivals that of the Incas to the point that writers from Spanish chroniclers of the sixteenth century to twentieth-century authors have claimed that Tiahuanaco not only served as a model for Inca architecture and stone masonry, but that the Incas even imported stonemasons from the Titicaca Basin to construct their buildings. Experiments aimed at replicating the astounding feats of the Tiahuanaco stonecutters--perfectly planar surfaces, perfect exterior and interior right angles, and precision to within 1 mm--throw light on the stonemasons' skill and knowledge, especially of geometry and mathematics. Detailed analyses of building stones yield insights into the architecture of Tiahuanaco, including its appearance, rules of composition, canons, and production, filling a significant gap in the understanding of Tiahuanaco's material culture.