Al-Khwarizmi Writes on Algebra
Around 820 AD, the Baghdad scholar Muhammad ibn Musa al-Khwarizmi composed a short treatise usually known as The Compendious Book on Calculation by Completion and Balancing (Kitab al-jabr wa'l-muqabala). The title's word al-jabr, meaning "completion" or "restoration," gave algebra its name. The book presented a systematic method for solving equations, and it became one of the most influential mathematical texts in history. The date is approximate; scholars generally place the work in the reign of the Abbasid caliph al-Ma'mun, roughly the 810s to 830s.
Al-Khwarizmi worked in the House of Wisdom, a center of learning supported by the Abbasid court, where scholars gathered, translated, and extended knowledge from Greek, Persian, and Indian sources. Mathematical problems of inheritance, trade, land measurement, and legal disputes were pressing practical concerns in the growing Islamic empire. Earlier traditions, including Babylonian methods, Greek geometry, and Indian arithmetic, had dealt with problems of this kind, but they lacked a single, general framework. Al-Khwarizmi's aim, as he explains in his introduction, was a practical work useful in everyday affairs.
The book's central idea was to reduce a wide range of problems to a small number of standard forms. Al-Khwarizmi classified linear and quadratic equations into six types, involving "roots," "squares," and plain numbers. He then gave rules for solving each. Al-jabr referred to moving a subtracted term to the other side of an equation to eliminate it, while al-muqabala meant balancing by cancelling like terms on both sides. Notably, he wrote everything in words rather than symbols, and he justified his solutions to quadratics with geometric diagrams. He also included chapters on measurement and on inheritance problems.
The work's influence spread widely. In the twelfth century it was translated into Latin, notably by Robert of Chester, and helped introduce systematic algebra to European scholars. Al-Khwarizmi's name also lives on in another way: another of his works, on Hindu-Arabic numerals, was translated into Latin, and his Latinized name gave us the word "algorithm." Later mathematicians, including Abu Kamil and Omar Khayyam, built on his foundations in the Islamic world.
Historians sometimes caution against calling al-Khwarizmi the sole "father of algebra." He drew on earlier knowledge, and the symbolic algebra we use today developed much later, in Europe, over many centuries. Even so, his book was the first known work to treat the solving of equations as a distinct discipline with its own methods and vocabulary, and that achievement earned it a lasting place in the history of mathematics.