Thursday, December 29, 2011

Algebra, algorithm and Uzbekistan

A page from al-Khwārizmī's Algebra (source)

The words "algebra" and "algorithm" were introduced to Latin Christendom through the 12th century Latin translation of the works of a Persian polymath, born in Khwarezm (in present day Uzbekistan), and working in the House of Wisdom in Baghdad during the Abbasid Caliphate.

He is al-Khwarizmi ("from Khwarezm", c.780-850) (Algoritmi in Latin, hence "algorithm"), a mathematician, geographer, and astronomer.

Algebra and Algorithm happen to be two subjects of which I have a modest degree of mastery. Their history illustrates the role of the Islamic civilization in bridging the Classical Greco-Roman world and the High Middle Ages and beyond.

As expected, there is an impressive Wikipedia article on al-Khwarizmi (here), where we learn the following:

In the twelfth century, Latin translations of al-Khwarizmi's work on the Indian numerals, introduced the decimal positional number system to the Western world.  His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although we now know that his work is based on older Indian or Greek sources.  He revised Ptolemy's Geography and wrote on astronomy and astrology.

Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name. His name is also the origin of (Spanish) guarismo and of (Portuguese) algarismo, both meaning digit.

His name may indicate that he came from Khwarezm (Khiva), then in Greater Khorasan, which occupied the eastern part of the Greater Iran, now Xorazm Province in Uzbekistan. Abu Rayhan Biruni calls the people of Khwarizm "a branch of the Persian tree"


Further interesting facts: Khwarezm, a region to the south of the Aral Sea, saw the rise of the Khwarazmian Empire (1077-1231, culturally Persianate, ethnically Turkic),  first as vassals of the Seljuqs, Kara-Khitan, and later as independent rulers,  until the Mongol invasions of the 13th century. Xorazm (or Khorezm, a variant spelling of Khwarezm) is the name of a present day province of Uzbekistan.

Interestingly, the Khwarezmians were briefly in control of Jerusalem, during 1244-1247. (See this for details)

Frederick II of the Holy Roman Empire gained control of Jerusalem by treaty with the Ayyubid (the dynasty founded by Saladin) sultan al-Kamil in 1229. Control of the city changed hands several times between the Ayyubids and the Christians  from 1239 to 1244. In 1244 Jerusalem was in Christian hands.

The Khawarezmi Turks, displaced by the advancing Mongols and allied with the Ayyubids, invaded Jerusalem (The siege of Jerusalem in 1244) on July 11, 1244, and the city's citadel, the Tower of David, surrendered on August 23. The Khwarezmians then ruthlessly decimated the city's population, leaving only 2,000 people, Christians and Muslims, still living in the city. This attack triggered the Europeans to respond with the Seventh Crusade, although the forces of King Louis IX of France never even achieved success in Egypt, let alone advancing as far as Palestine.

Egyptian Ayyubid Sultan al-Malik al-Salih then decided to use his new Mamluk army to eliminate the Khwarezmians, and Jerusalem soon returned to Egyptian Ayyubid rule in 1247.

The Khanate of Khiva existed in the historical region of Khwarezm from 1511 to 1920, except for a period of Persian occupation by Nadir Shah between 1740–1746.

Panoramic view of Khiva, Khorezm Province, Uzbekistan, a UNESCO World Heritage Site (for high resolution view: here)

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