al-Khwarizmi

c. 780-c. 850

Arab Mathematician and Astronomer

Although al-Khwarizmi was an early Arab proponent of the use of Hindu numerals—which were eventually adopted so widely throughout the Middle East that they came to be known as Arabic numerals—his advocacy in this area had its greatest impact when his books were translated for mathematicians in Western Europe. He used the term al-jabr, or restoration, for a method he applied in solving equations, and in the West this became algebra.

His name in full was Abu Ja'far Muhammad ibn Musa al-Khwarizmi, and he probably came from what is now Iraq. When Caliph al-Ma'mum (r. 813-833) established his Dar al-Hikma or House of Wisdom, a center of scholarship in Baghdad, al-Khwarizmi was among the scholars invited to join this early think tank.

Al-Khwarizmi's first important mathematical text was al-Kitab al-mukhtasar fihisab al-jab wa'lmuqa-bala, also written as Hisab al-jabr w'al muqabala (The compendious book on calculation by completing and balancing). Probably written in the period 825-830, the book addressed matters of practical mathematics, offering solutions to problems involving unknown quantities. It was here that he introduced his method of restoration or completion, or separating the variable from other figures: thus 2x - 4 = x would become x = 4.

In his second major mathematical work, whose title is translated as Treatise on Calculation with the Hindu Numerals, al-Khwarizmi provided a guide for the use of the numerals 0-9. Up to this time, the Arabs had generally used an alphabetic numbering system, which like the Roman numerals used by Europeans lacked the valuable concept of place value. With the Hindu system, as al-Khwarizmi showed, it was possible (for instance) to know at a glance that 238 represented two units of 100, three units of 10, and eight units of 1.

Though al-Khwarizmi's book gained only limited use among Arab mathematicians, it would have an enormous impact in Western Europe, where it was translated into Latin during the early part of the twelfth century. In the meantime, Hindu numerals had taken hold in the Arab world, and by then Europeans had come to believe the system had developed there rather than in India.

Al-Khwarizmi also wrote books on geography, in which he provided latitudinal and longitudinal calculations for a variety of locations around the Middle East. His astronomical works amplified concepts developed earlier by Indian scientists, and in two other books he described the uses of the astrolabe for making astronomical measurements. In addition to these, al-Khwarizmi produced a commentary on the Jewish calendar, a history of the Islamic world during the early ninth century, and other books.

JUDSON KNIGHT