In effect, the term applies to a greatly diverse collection of practices and ‘cognitive constructions’ spanning various practical, historical and philosophical contexts. In Bernard Cache’s account of the work of French mathematician Girard Desargues (pp 90-9), projective geometry represents a practical expedient to determine metric relationships, as well as an embodiment of Gottfried Leibniz’s mystical monad. For Amy Dahan-Dalmedico, geometry can be understood either as a realistic practice rooted in human perception and the world itself, or as a Platonist realist collection of concepts totally independent of the human mind. For Dennis Shelden and Andrew Witt, recent developments in digital computation posit the emergence of a higher geometry at once continuous and discrete – until the very distinction is itself abolished (see pp 36-43). Wading through this collection of theoretical and applied reflections on mathematics in space, we are indeed struck by the many themes our subject can simultaneously embody, by the many dualities it is apt to represent. Mathematics, as Amy Dahan-Dalmedico reminds us in the historical account that opens this issue (see pp 18-27), is hardly a ‘stable and well-defined’ object.