Between 1672 and 1694, the German mathematician Gottfried Wilhelm Leibniz (1646-1716) attempted to design a reckoning machine that would be able to perform the four basic arithmetic operations on multiple-digit numbers. Working closely with the French clockmaker Monsieur Ollivier, Leibniz eventually failed at producing a working prototype. This failure is usually attributed either to their time’s technology – supposedly not advanced enough to craft Leibniz’s wheel –, or to communication problems between the mathematician and the artisan. Yet, the rediscovery of Ollivier’s last model in 1879 showed that it needed a different mechanism to work than the one worded and depicted in Leibniz’s instructions. Indeed, along his correspondence, Leibniz left a bounteous collection of texts, drawings, and schematics dedicated to the technical specification of his envisioned machine. In his own words, this “arithmetic instrument” aimed at “transferring all the labour of the mind into wheels”, thus performing an operation of re-mediation. Following the distinction between the history of technology and the history of mathematics, it could be argued that Leibniz’s arithmetic is software while his machine would be hardware, that there could exist a lossless translation of information from one support to another – a possibility supported by Leibniz’s own metaphysics. Though, this leaves wide open a gap between technology and mathematics, as well as between media, that this paper aims at bridging. Can we account for Leibniz’s failure by arguing that his way of thinking was so inextricably entwined with paper that it could not be translated into another medium? From the spatial organisation of Leibniz’s working papers, to his schematics and drawings, and finally to Ollivier’s prototype, I will try and trace the very step-by-step process of re-mediating reckoning into a mechanical device.