From Algorism to Algorithm: A Brief History of Calculation from the Middle Ages to the Present Day

Abstract. This very brief essay proposes that the algorithm and the number have a joint history. It will show how these two notions have always been implicitly connected and how algorithmic practices are probably even older than mathematics itself. Specifically, the evolution of the idea of the algorithm will be reconstructed in relation to numeral systems from the medieval period to the present day, beginning with a linguistic coincidence that indicates deeper historical processes. Just as the medieval term algorismus signalled the passage from an additive (Roman) numeral system to a positional (Indo-Arabic) system, the contemporary term algorithm signalled the passage from a decimal system to a binary one. This happened not only for cultural and technological reasons, but also for fundamentally economic reasons, marking two transitions: in the first, from medieval society to commercial capitalism, and in the second, from industrial capitalism to the information society.