The Hometown of Algorithms

Panoramic view of Khiva, August 2015.

Once there lived a man named Muḥammad ibn Musa al-Khwarizmi, (محمد بن موسى الخوارزمی). He was born into a Persian family in Khwarezm (hence the last name “al-Khwarizmi,” meaning “of Khwarezm”)), also variously spelled Chorasmia, Khwarezmia, Khwarizm, Khwarazm, Khorezm, Khoresm, Khorasam, Kharazm, Harezm, Horezm, and Chorezm. It was Χορασίμα (Chorasíma) to Herodotus and 花剌子模 (Hualazimo) to the Chinese. According to local tradition, Shem, son of Noah, founded the city of Khiva, a center of Khorezm life, soon after the flood. 

Once an independent Khanate and slave-trading entrepot, Khorezm was incorporated into the Russian empire in the 19th century before becoming part of the Soviet Union, and now of Uzbekistan. When I visited Khiva in the summer of last year, I found a dreamy medieval town ringed by crenellated mud fortifications, with a cityscape punctuated by magnificent minarets.

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A 1983 Soviet stamp commemorating al-Khwarizmi. Public domain.

But Muhammad lived long before that, under the Abbasid Caliphate in the 8th and 9th centuries. Young Muhammad relocated to Baghdad, capital of the Abbasids and at the time the center of learning in the Islamic world. Caliph Harun al-Rashid (of Salman Rushdie’s “Haroun and the Sea of Stories”) had established the so-called House of Wisdom there, and Muhammad joined the ranks of its scholars.
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Here in 825 A.D., Muhammad published “On the Calculation with Hindu Numerals,” in which he adopted the numeral system invented in ancient India. When Europeans learned the same system from him, they mistakenly called it “Arabic numerals,” a misnomer we still perpetuate today.

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A page from al-Khwarizmi's book on Algebra. Public domain.

In Baghdad Muhammad also began working on something he called “al-jabr,” Arabic for “restoration.” This new area of mathematics involved adding or subtracting the same terms to or from both sides of an equal sign in order to manipulate and ultimately to solve an equation. Muhammad’s 830 book, “The Compendious Book on Calculation by Completion and Balancing,” explained how to solve polynomial equations up to the second degree. When the book was translated into Latin in 1145, “al-jabr” was transliterated as “algebra.”

As for the author’s name, “al-Khwarizmi,” man of Khorezm, it was transliterated into Latin as “Algorizmi” or “Algoritmi.” Hence the word “algorithm.”

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