Gottfried Wilhelm Leibniz designed a calculating machine he called the Stepped Reckoner, first demonstrated around 1673 and refined over the following decades. Where Pascal’s earlier machine handled addition and subtraction, Leibniz’s went further: using a cylindrical gear of his own invention - the stepped drum, or Leibniz wheel, with teeth of increasing length - the reckoner could also multiply and divide by repeated, shifted addition. The stepped-drum mechanism proved so sound that it remained the basis of mechanical calculators for roughly 275 years. Only one of Leibniz’s own machines survives, held at the Deutsches Museum in Munich.
Leibniz’s larger ambition went beyond arithmetic. He imagined a “characteristica universalis,” a universal symbolic language for concepts, paired with a “calculus ratiocinator,” a calculus of reasoning. His hope was that disputes could one day be resolved not by argument but by computation - two parties would simply say “let us calculate” and work out the answer. He was inspired in part by Ramon Llull’s combinatorial Art, and his vision anticipated the much later projects of Boole, Frege, and symbolic logic.
Leibniz thus sits at a hinge in the prehistory of computing: he built real hardware that mechanized multiplication, and he articulated, centuries early, the idea that thought itself might be reduced to calculation - a notion that became central to mathematical logic and artificial intelligence.