The Arabic Innovations
Common algebra is a theory of manipulating symbols representing constant and unknown numbers and geometrical magnitudes, and especially of expressing polynomial equations and finding roots by an algorithm that produces a formula. Its founders were the Arabs (that is, mathematicians usually writing in Arabic) from the ninth century, the main culture of the world outside the Far East. Some of the inspiration came from interpreting various Greek or Indian authors, including Euclid. The pioneer was Al-Khwarizmi (fl. c. 800–847) with his work Al-jabr wa'l-muqabala, known in English as the Algebra, and over the next five centuries followers elaborated his theory.
The problems often came from elsewhere, such as commerce or geometry; solutions usually involved the roots of polynomial equations. Algebra was seen as an extension of arithmetic, working with unknowns in the same way as arithmetic works with knowns. The Arabic manner of expression was verbal: the word shay denoted the unknown, mal its square, ka'b its cube, mal mal for the fourth power, and so on. Arabs also adopted and adapted the Indian place-value system of numerals, including 0 for zero, that is called Hindu-Arabic. They were suspicious of negative numbers, as not being pukka quantities.
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