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Sometime at the beginning of the 9th century AD, in an area on the lower Amu Darya (formally in the USSR), Muhammad ibn Musa Al-Khowarizmi was born. Today, his name would be translated as Mohammed the son of Moses from Khorezm. Not much is known about Al-Khowarizmi; however, he was a member of the academy called "the House of Wisdom" of the Baghdad Caliph Al-Ma'mum (813-833 AD). He had been invited by the Caliph to take observations at Bagdad and Damascus, to revise the tables of Ptolemy, and to measure a degree of the earth's meridian.

In approximately 825 AD, Al-Khowarizmi wrote a treatise on equations. The title of this Arabic work was Hisãb al-jabr w'al-muqãbala, meaning "The calculation of reduction and restoration." This meant the transposing of negative terms to the other side of the equation (restoration) and uniting similar terms (reduction). The "al-jabr" was translated into Latin by Robert of Chester in 1140 AD. This Latin translation, Liber algebrae et almucabala, popularized the name algebra for the theory of equations. It is interesting to note that in Arabic, jabr means the setting of a bone and is related to the word reduction. In fact, during the Middle Ages, the Moors carried the word to Spain where an algebrista became the name for a bone-setter.

The algebra of Al-Khowarizmi did not use the algebraic notation with which we are familiar. This came in the sixteenth century with Francois Viète. Al-Khowarizmi wrote every problem out in words, which is referred to as rhetorical algebra. His solutions were accompanied by geometric demonstrations. He used the value of 3 1/7 for Pi. Al-Khowarizmi was not the first to solve "algebraic" problems. As early as 1550 BC, Ahmes, the Egyptian scribe and mathematician, had certain problems on his papyri with linear equations and series. In addition, Diophantus (c.250 AD) is considered by many to be the "Father of algebra."

Another arithmetic of Al-Khowarizmi was translated into Liber Algorismi de numero Indorum (the book of Al-Khowarizmi) giving rise to the word algorithm.

The following is an English translation of a popular verse in Arab schools over six hundred years ago:

Cancel minus terms and then
Restore to make your algebra;
Combine your homogeneous terms
And this is called muqabalah. (Smith)

For more information about the mathematics of Al-Khowarizmi read:

Smith, D.E. (1959). History of Mathematics. Dover Publications.

Struik, D.J. ed. (1967). A Source Book in Mathematics. 1200-1800. Princeton University Press.

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From http://www.aug.edu/dvskel/MichSP93.htm by permission with minor edits.