Often called the "father of algebra," al‐Khwarizmi composed the first algebra text to be written in Arabic. This Arab scholar is also responsible for the Arab adoption of Hindu numerals. He is an essential link in their eventual acceptance by the West. Because of both his writings and his own name, two words--"algebra" and "algorithm"--were introduced into the language of mathematics.

### Origins

Few details of the early life and education of al‐Khwarizmi (pronounced al‐KWAR‐iz‐mee) are known. Historians usually focus on any meanings contained in his full name, which is Abu Ja'Far Muhammad Ibn Musa al‐Khwarizmi, as well as examining other names he was called. "Al‐Khwarizmi" means that he came "from Khwarizm," which is now the city of Khiva (pronounced KEE‐va) in the central Asian country of Uzbekistan (pronounced uhz‐BEK‐i‐stan). However, because al‐Khwarizmi was also called *Qutrubbulli,* he may have been from the region between the Tigris and the Euphrates rivers, which corresponds to present‐day Baghdad in Iraq. (Perhaps only his ancestors came from Khwarizm.) A further claim that he was of Persian ancestry because he was sometimes called *al‐Majusi* may mean only that he or his forebears were members of an old Persian religion. However, regardless of which region he is from, al‐Khwarizmi was always an orthodox Muslim, so most scholars consider him to be an Arab.

### Scholarly career

As an adult, al‐Khwarizmi was a scholar in astronomy and mathematics at Dar al‐Hikma, or the "House of Wisdom." This was an Arab institution similar to the ancient Museum at Alexandria (set up in that city by Ptolemy after the death of Alexander the Great). Created in Baghdad by the caliph (spiritual leader), al‐Ma'mun (786-833), who was its patron, Dar al‐Hikma drew scholars from all parts of the Arab world. The city of Baghdad became for a time the new Alexandria.

Al‐Khwarizmi was one of the first to join Dar al‐Hikma, which was dedicated to the promotion of science. He became a faculty member, specializing in both mathematics and astronomy. As an astronomer, he was often required to work with astrology as well. In the year 847, when al‐Khwarizmi was called upon to cast the horoscope (to tell the future using a person's birth date and the positions of the stars and planets) of a dying caliph, he predicted that the caliph would live another 50 years. Although the caliph died ten days later, al‐Khwarizmi was able to survive his mistake.

### Mathematical contributions: algebra

Although he wrote many books in different fields (such as geography), two books were to play an especially important role in the history of mathematics. The first of these was his work on algebra. In this first book, part of whose title contained the Arab words *al‐jabr,* he dealt with the development of solutions to mathematical problems in which there was an unknown quantity. His purpose in writing such a book was for it to have a real, practical usefulness, "such as men constantly require ... in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations ... are concerned," he wrote.

Ancient algebra was very different from today's algebra. It used no symbols at all but instead used actual words for functions and even for numbers (which were also written out). Although his work is the first Arab book on algebra, al‐Khwarizmi should not be considered the "inventor" of algebra but rather one who best represented and summarized the teachings of his time.

There is no doubt, however, that algebra got its European name through the title of al‐Khwarizmi's book. His long title contained the Arabic word *al‐jabr,* meaning "transposing," "restoring," or "completion." The Western monks who were translating his book into Latin often would simply shorten the long Arabic title to the words *al‐jabir.* Because mathematicians in the West first learned about the new techniques of algebra through his book, it is not surprising that they came to describe any aspect of the mathematics of solving for unknown quantities--or even any other Arabic book on the same subject--after the well‐known shortened version of his Arabic title. Thus, when *al‐jabir* was transliterated (spelled using the characters of the Latin alphabet), it became "algebra."

### Mathematical contributions: Hindu numbering system

Al‐Khwarizmi's second book on mathematics contained an equally significant if not greater contribution--the description and explanation of the Hindu system of number symbols. Number symbols that are similar to those used today were a very ancient accomplishment in India. The related ideas of positional value and the use of zero were introduced into India not too long before al‐Khwarizmi lived. In fact, al‐Khwarizmi wrote what is considered the earliest text that deals with the new Hindu symbols for numbers; he is therefore responsible for their eventual adoption by Arab mathematicians. Because Europeans learned them from the Arabs about 400 years later, they came to be called Arabic numerals instead of Hindu numerals. Today they are correctly described as Hindu‐Arabic numerals.

Al‐Khwarizmi's book introduced the nine characters (the number symbols for 1 through 9) as well as the use of a circle for zero. The use of a zero was most important, since it functioned mainly as a place‐holder. The number 307, therefore, means that there are 3 hundreds, 0 tens, and 7 ones. Although the value would be written as three hundred seven, the number could not be written in symbols without a zero. A key part of this example is also the concept called "positional notation," or place value. In the previous example, the 3 in 307 is in the third place from the right, meaning it signifies groups, or units, of a hundred. The second place is for groups of ten, and the first is for groups of ones. The Hindu system was based on the value ten, and each change (to the left) in the position of a number meant an increase by ten. Thus, the fourth position was for thousands, the fifth for ten thousands, and so on.

With the support of this system by al‐Khwarizmi and its eventual acceptance in the Arab world, the benefits of this system, especially to the world of business and commerce, inevitably became obvious to those in the West. Nonetheless, this took a very long time to be introduced into Europe and then to be really accepted.

As the Western word "algebra" was derived from al‐Khwarizmi's work, so too was the word "algorithm." Once Europe fully understood the Hindu‐Arabic system and began to use it regularly, Europeans also attributed the algorithm completely to al‐Khwarizmi. Soon, today's "algorithm" was called *al‐khwarizmi,* or more carelessly, *algorismi.* Eventually, "algorithm" began to be used to name any step‐by‐step procedure for solving a mathematical problem.

Al‐Khwarizmi's algebra and his introduction of the Hindu numeral system to the Arab world make him a highly significant link between time and cultures. Because of his study and writings, the West was eventually able to benefit, via the Arabs, from the mathematical learning and experience of the East.

### For More Information

*Biographical Dictionary of Mathematicians.*New York: Charles Scribner's Sons, 1991.- Boyer, Carl B., and Uta C. Merzbach.
*A History of Mathematics.*New York: John Wiley & Sons, 1989. - Katz, Victor J.
*A History of Mathematics: An Introduction.*New York: HarperCollins College Publishers, 1993. *MacTutor History of Mathematics Archive.*"Abu Abd‐Allah ibn Musa al‐Khwarizmi." http://www‐groups.dcs.st‐and.ac.uk/~history/Mathematicians/Al'Khwarizmi.html (accessed on April 23, 1999).- Young, Robyn V., ed.
*Notable Mathematicians: From Ancient Times to the Present.*Detroit: Gale Research, 1998.