A Scholar at the House of Wisdom
Muhammad ibn Musa al-Khwarizmi lived roughly between 780 and 850, and very little of his personal life is recorded. His name means from Khwarazm, a region once part of Greater Iran and now split between Turkmenistan and Uzbekistan. He was of Persian descent, yet wrote all his scientific work in Arabic.
He did most of that work between 813 and 833. Around 820 he was appointed astronomer and head of the library at the House of Wisdom in Baghdad, then the capital of the Abbasid Caliphate and the centre of scientific study and trade. The institution had been established by the Caliph al-Ma'mun, who also encouraged the book that would make al-Khwarizmi's name.
There he studied mathematics and the sciences and worked on translations of Greek and Sanskrit manuscripts. He was a historian as well, cited by later writers such as al-Tabari.
The Book That Named Algebra
His treatise on algebra, compiled between 813 and 833, is usually called Al-Jabr, short for The Compendious Book on Calculation by Completion and Balancing. It laid out the first systematic method for solving linear and quadratic equations, including solving by completing the square, with geometric arguments to justify each step.
The title gave us the word. Algebra comes from al-jabr, meaning restoration, the operation of adding the same quantity to both sides to clear negative terms. Its partner operation, al-muqabala or balancing, brings like quantities to the same side.
He was the first to treat algebra as a subject in its own right rather than a set of tricks, which is why he is often called its founder. Notation did not exist yet, so every problem and solution had to be written out in ordinary sentences. The book was aimed at practical readers, full of examples from trade, surveying and the division of inheritance.
How His Name Became a Word
His second great work was on arithmetic, and it survives only in Latin translation. In it he set out step by step procedures for calculating with Hindu-Arabic numerals, the decimal system developed in India.
The calculations were done on a takht, a board covered with a thin layer of dust or sand, where figures could be written with a stylus and wiped away as the work progressed. His procedures stayed in use for nearly three centuries before methods designed for pen and paper replaced them.
When these texts reached Europe in the 12th century, they brought the decimal positional system with them and gradually displaced the abacus. His Latinised name, Algorismus, became the name of the method itself, and that word wore down over the centuries into algorithm. His book on algebra, translated by Robert of Chester in 1145, remained the main mathematics textbook in European universities until the 16th century.
Mapping the Sky and the Earth
Mathematics was only part of his output. His astronomical tables, known as a zij, ran to about 37 chapters and 116 tables covering the movements of the Sun, the Moon and the five planets known at the time, along with a table of sine values. It drew on Indian astronomical methods and marked a turning point, moving Muslim astronomers from translating other people's work toward producing their own.
The original Arabic is lost. What survives is a later Spanish version carried into Latin, in four manuscripts now held in Chartres, Paris, Madrid and Oxford.
His third major work, finished in 833, was a description of the Earth listing 2,402 coordinates of cities and landmarks. It was a thorough reworking of Ptolemy's Geography, and it corrected a serious error: Ptolemy had stretched the Mediterranean to 63 degrees of longitude, while al-Khwarizmi put it at close to 50, which is nearly right. A crater on the far side of the Moon now carries his name.
