algorism

Algorism is a term that refers to the system of arithmetic based on the Hindu–Arabic numeral system that uses the digits zero through nine. The word originates from the Latinized form of the name of the 9th‑century Persian mathematician al‑Khwarizmi, whose work on arithmetic introduced algorithmic methods to the wider world. In medieval Europe, “algorismus” distinguished the new positional decimal system from the Roman numerals and other non‑positional systems that had previously dominated arithmetic practice.

During the 12th and 13th centuries the adoption of algorism spread through the European continent, largely through translations of Arabic mathematical texts. Monastic and scholarly communities used algorism to perform calculations for commerce, astronomy, and engineering. The system’s key innovation—place value and the inclusion of zero—enabled more efficient computation, allowing practitioners to carry out addition, subtraction, multiplication, and division with methods such as the long multiplication algorithm that are still taught today.

Algorism also influenced the development of algebra. Its rules provided a foundation for symbolic manipulation and the eventual formalization of algebraic notation. The Computation System of the Rhind Mathematical Papyrus and the works of later European scholars such as Johannes Widmann and Regiomontanus illustrate the practical applications of algoristic methods.

By the early modern period, algorism had largely supplanted older numerals in scientific and commercial contexts. Its legacy persists in the universal numeral system and in the algorithms that underpin contemporary computing. The term “algorism” remains a historical reference to the early stages of modern arithmetic and algorithmic thinking.