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In opening the proceedings of “Basic Questions of Design Theory”, an NSF-funded symposium held at Columbia University in 1974, academic engineer William Spillers cast mathematical abstraction as foundation of a “common ground” between engineering and architecture — disciplines traditionally separated by professional circumstance. In invoking abstraction, Spillers’ alluded to methodological and theoretical operations of concretizing, in mathematical models, abstract and immaterial concepts of organization and connectivity that he saw as underpinning all design. Far from launching a new intellectual agenda, Spillers was documenting the ongoing dovetailing between ecumenist design theories and the mathematics of network and graph theory. During the 1960s design theory and methodology manuscripts were marked by an unprecedented proliferation of skeletal abstractions of “problem structures” and forms, seemingly denuding design of its visual, material, and embodied traditions. Complicating design’s turn to mathematical abstraction —a move that has been historicized as iconoclastic and dematerializing— this paper illuminates the role that the graph’s perceived visual and material concreteness played in rendering it the technique of choice in 1960s movements towards mathematization. Following famed mathematician and 1974 symposium keynote Frank Harary’s aesthetic reading of “Graphs as Designs”, the paper examines perpetual transpositions of concreteness between design and mathematics as they unfolded in the seminal design theories of Christopher Alexander (Harvard), the LUBFS Centre (Cambridge, UK), and Yona Friedman (France). Ultimately, this paper unveils the role of a mathematical object seductively oscillating between the visually concrete and the mathematically abstract in fusing epistemic cultures and introducing a new visuality in design.