Al-Khwarizmi was also known as Abu Ja’far Muhammad ibn Musa al-Khwarizmi. He was known for writing major works on astronomy and mathematics that introduced Hindu-Arabic numerals and the idea of algebra to European scholars. The Latinized version of his name gave us the term “algorithm,” and the title of his most famous and important work gave us the word “algebra.”
Muhammad ibn Musa al-Khwarizmi was born in Baghdad in the 780s, around the time Harun al-Rashid became the fifth Abbasid caliph. Harun’s son and successor, al-Mamun, founded an academy of science known as the “House of Wisdom” (Dar al-Hikma). Here, research was conducted and scientific and philosophic treatises were translated, particularly Greek works from the Eastern Roman Empire. Al-Khwarizmi became a scholar at the House of Wisdom.
At this important center of learning, al-Khwarizmi studied algebra, geometry, and astronomy. He wrote influential texts on the subjects. He appears to have received the specific patronage of al-Mamun, to whom he dedicated two of his books: his treatise on algebra and his treatise on astronomy. Al-Khwarizmi’s treatise on algebra, al-Kitab al-mukhtasar fi hisab al-jabr waʾl-muqabala (“The Compendious Book on Calculation by Completion and Balancing”), was his most important and well-known work. Elements of Greek, Hebrew, and Hindu works that were derived from Babylonian mathematics of more than 2,000 years earlier were incorporated into al-Khwarizmi’s treatise. The term “al-jabr” in its title brought the word “algebra” into western use when it was translated into Latin several centuries later.
Although it sets forth the basic rules of algebra, Hisab al-jabr w’al-muqabala had a practical objective: to teach. As al-Khwarizmi put it:
…what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, and other objects of various sorts and kinds are concerned.
Hisab al-jabr w’al-muqabala included examples as well as algebraic rules in order to help the reader with these practical applications.
Al-Khwarizmi also produced a work on Hindu numerals. These symbols, which we recognize as the “Arabic” numerals used in the west today, originated in India and had only recently been introduced into Arabic mathematics. Al-Khwarizmi’s treatise describes the place-value system of numerals from 0 to 9 and may be the first known use of a symbol for zero as a place-holder (a blank space had been used in some methods of calculation). The treatise provides methods for arithmetical calculation, and it is believed that a procedure for finding square roots was included. Unfortunately, the original Arabic text is lost. A Latin translation exists, and though it is thought to be considerably changed from the original, it did make an important addition to western mathematical knowledge. From the word “Algoritmi” in its title, Algoritmi de numero Indorum (in English, “Al-Khwarizmi on the Hindu Art of Reckoning”), the term “algorithm” came into western usage.
In addition to his works in mathematics, al-Khwarizmi made important strides in geography. He helped create a world map for al-Mamun and took part in a project to find the Earth’s circumference, in which he measured the length of a degree of a meridian in the plain of Sinjar. His book Kitab surat al-arḍ (literally “The Image of the Earth,” translated as Geography), was based on the geography of Ptolemy and provided the coordinates of approximately 2,400 sites in the known world, including cities, islands, rivers, seas, mountains, and general geographical regions. Al-Khwarizmi improved on Ptolemy with more accurate values for sites in Africa and Asia, and for the length of the Mediterranean Sea.
Al-Khwarizmi wrote yet another work that made it into the western canon of mathematical studies: a compilation of astronomical tables. This included a table of sines, and either its original or an Andalusian revision was translated into Latin. He also produced two treatises on the astrolabe, one on the sundial and one on the Jewish calendar, and wrote a political history that included the horoscopes of prominent people.
The precise date of al-Khwarizmi’s death is unknown.