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Notation in medieval Arabic algebra

Abstract

Arabic algebra had been practiced for over three centuries before a notation specific to the art emerged in the twelfth century in the Maghreb. To properly understand how the notation functioned it is necessary to situate it in its cultural and mathematical context. From the perspective of culture this includes the relationship between books, memorization, and recitation, as well as the ways people performed calculations in medieval Arabic societies. Mathematically one must take into account that premodern algebraists conceived of polynomials differently than we do today. Where our 3x2 + 4 entails the operations of addition, multiplication, and exponentiation, the medieval equivalent 鈥渢hree m膩ls and four dirhams鈥�, whether rhetorical or in notation, was conceived as an aggregation of seven objects of two different kinds with no operations present. The Arabic algebraic notation was created with this 鈥渁ggregations鈥� interpretation in mind, and was practiced according to their relationship with books and writing.聽