Mapping the Mathematical Mind: Lines of Thought in Islamic Art and Architecture

During the past one hundred and fifty years of Western scholarship on the architecture of Iran, the interpretation of ornament has undergone profound reassessment. Relying upon both textual and visual sources, recent research on geometric patterns constructed of cut brick on Seljuk and post-Seljuk buildings allows for a reinterpretation of these patterns as visual expressions of contemporary mathematical thinking. A substantive change seems to have taken place in the use of geometric patterns around the year 1000 CE. The new style demonstrates a fascination with points, lines, angles, planes, intersecting planes, and three-dimensional muqarnas. This interest in geometry is evident in brick tomb towers at Ghazna, Kharraqan, and Maragha, and in mosques, minarets and madrasas built in Iran, Afghanistan, and elsewhere, and in the stone monuments of Syria and Anatolia. This paper proposes a cultural milieu of mathematics, poetry, architecture, philosophy, and theology, within which the historian Jūzjānī’s expression, “geometry made manifest,” takes on new meaning, offering insight into intersections of the histories of architecture and mathematics.