Al-Khwārizmi Invents the Algorithm; Introduction of the Decimal Positional Number System to the West

Circa 825 CE
Detail map of Baghdad, Al Saadoon Park, Baghdad Governorate, Iraq Overview map of Baghdad, Al Saadoon Park, Baghdad Governorate, Iraq

A: Baghdad, Al Saadoon Park, Baghdad Governorate, Iraq

Statue of al-Khwarizmi in front of the Faculty of Mathematics of Amirkabir University of Technology in Tehran.

Statue of al-Khwarizmi holding an astrolable toward the sky in front of the Faculty of Mathematics of Amirkabir University of Technology in Tehran.

About 825 Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī, a Persian mathematician, astronomer, and geographer at the House of Wisdom (Arabic: بيت الحكمة‎; Bait al-Hikma) in Baghdad, developed the concept of a written process to be followed to achieve some goal. Al-Khwarizmi wrote a book on Hindu-Arabic numerals, giving the name algorithm to this process through the Latinization of his last name:

"The Arabic text is lost but a Latin translation, Algoritmi de numero Indorum (in English Al-Khwarizmi on the Hindu Art of Reckoning) gave rise to the word algorithm deriving from his name in the title. Unfortunately the Latin translation . . . .  is known to be much changed from al-Khwarizmi's original text (of which even the title is unknown). The work describes the Hindu place-value system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. The first use of zero as a place holder in positional base notation was probably due to al-Khwarizmi in this work. Methods for arithmetical calculation are given, and a method to find square roots is known to have been in the Arabic original although it is missing from the Latin version" (http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Al-Khwarizmi.html, accessed 01-23-2010).

Information in Al-Khwarizmi's work eventually reached Europe in books on Algorithmus by other authors that were distributed by manuscript copying, and eventually by print . . . .  Allard, "La diffusion en occident des premières oeuvres latines issues de l'arithmétique perdue d'al-Khwarizmi," J. Hist. Arabic Sci. 9 (1-2) (1991), 101-105, discusses seven twelfth century Latin treatises based on this lost Arabic treatise by al-Khwarizmi on arithmetic.

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