In Formulations: Architecture, Mathematics, Culture (MIT Press, 2022), Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects.

Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design.

Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.

Bryan Toepfer, AIA, NCARB, CAPM is the Principal Architect for TOEPFER Architecture, PLLC, an Architecture firm specializing in Residential Architecture and Virtual Reality. He has authored two books, “Contractors CANNOT Build Your House,” and “Six Months Now, ARCHITECT for Life.” He is an Assistant Professor at Alfred State College and has served as the Director of Government Affairs and as the Director of Education for the AIA Rochester Board of Directors. Always eager to help anyone understand the world of Architecture, he hosts the New Books Network – Architecture podcast, is an NCARB Licensing Advisor and helps coach candidates taking the Architectural Registration Exam. btoepfer@toepferarchitecture