The origins of algebra


The term “algebra” derives from the Arabic a!- jebr, which the mathematician Al-Khowarizmi adopted to explain his ideas for solving what we call equations. Later the term acquired a wider meaning and today it includes a broad range of mathematics.

Mohammed ibn Musa Al-Khowarizmi, an Arabian astronomer and mathematician (died ca.A.D. 850), was active in the ‘House of Wisdom” in Baghdad, a cultural center established about A.D. 825 by the Caliph Al-Mamun. Al- Khowarizmi wrote various books on arithmetic, geometry and astronomy and was later celebrated in the West. His arithmetic used the Indian system of notation. Although his original Arabic book on the system, probably based on an Indian text, is lost, a Latin translation survives as Algorithmi: De numero indorum (about Indian numbers). The author explains the Indian numerical system so clearly that when the system eventually spread through Europe, it was assumed the Arabs were its inventors. The Latin title gives us the modern term “algorithm”-a distortion of the name Al-Khowarizmi which became Algorithmiused today to denote any rule of procedure or operation in calculations.

Al-Khowarizmi’s most important book, AlIebr wa’1-muqabalah, literally “science of reducing and comparing,” gave us the word ”algebra.’ There are two versions of the text, one Arabic and the other the Latin Liber algebrae et almucabala which contains a treatment of linear and quadratic equations.
These works were of major importance in the history of mathematics. Indeed, al-ebr originally meant a few mathematical steps and transformations to simplify and hasten the resolution of problems.

Let us now turn to what we learned in school and begin with an equation of the first degree, 5x + 1 = 3(2x -1). An equation is generally an equality with one or several unknowns. It translates into numbers a problem whose solution consists of finding those values of x that make the equality true. In our example, we must find the value of x that makes the expressions on either side of the “equal” sign equal.

Al-Khowarizmi’s mathematical works contain all the solving procedures we learned mechanically in school, for example, reducing terms and transferring a term to the other side with a change of sign. Hence, in our case, adding 3 and subtracting 5x on both sides, and then changing sides, gives us x = 4, which solves the equation. Putting 4 for x in the first equation, 5x + 1 = 3(2x – 1), we find 21 = 21. Clearly, to solve an equation is to transform it into other, and simpler equations until we reach the solution.