Grothendieck Topoi: Architectural and Plastic Imagination beyond Material Number and Space

Abstract

Fernando Zalamea begins with an emphatic argument that from mathematics to its plastic influence, Grothendieck topoi are used to understand the human and the nonhuman creativity in three variously relevant and yet different disciplines; that of cinema through the work of Andrei Tarkovsky, architecture through the work of Frank Gehry and art through the work of Anselm Hiefer. The chapter starts by introducing the work of Alexandre Grothendieck from a conceptual standpoint, focusing on his topos theory (1962), a general setting which encompasses both arithmetic (number) and geometry (space) under a common abstract perspective (sheaves: a far-reaching tool which helps to glue the local and the global). Grothendieck's revolution, wider than Einstein's interlacing of space and time, has radically changed mathematics, but its plastic influence beyond the specialty has yet to be developed.