Al-Khwarizmi

Muhammad ibn Musa al-Khwarizmi was a mathematician, astronomer and geographer at the court of the Abbasid caliphs in Baghdad in the first half of the ninth century. He wrote the first book on algebra in Arabic, and its title, al-jabr, became our word 'algebra'. He also wrote a short book on calculating with the nine Indian figures and a sign for nothing, the zero; in Latin it began 'Dixit Algorizmi', 'al-Khwarizmi said', and his name, turned into 'algorism', became our word 'algorithm'. Both books were translated into Latin in the twelfth century and taught medieval Europe to solve equations and to reckon on paper.

Very little is known about his life. Britannica gives his dates as about 780 to about 850. His name means 'the man from Khwarazm', the oasis on the lower Amu Darya south of the Aral Sea, around today's Khiva in Uzbekistan. But the historian al-Tabari also calls him al-Qutrubbulli, after Qutrubbul, a district just outside Baghdad, so perhaps only his family came from Khwarazm. Since the preface of his Algebra shows a believing Muslim, al-Tabari's further name for him, al-Majusi, 'the Zoroastrian', may only mean that his forebears followed the old Persian religion; the historian Roshdi Rashed thinks the words describe a second man. Under the caliph al-Ma'mun (813–833) he belonged to the House of Wisdom, the caliph's library and circle of scholars, together with the three Banu Musa brothers and al-Hajjaj, the translator of Euclid. How far it was a real academy is still debated.

His Algebra, 'The Compendious Book on Calculation by Completion and Balancing', is dedicated to al-Ma'mun and meant to be practical, for 'inheritance, legacies, partition, lawsuits, and trade', measuring land and digging canals. Every problem is brought to one of six standard equations of the first or second degree by two moves: al-jabr, 'restoring', which removes a quantity subtracted on one side, and al-muqabala, 'balancing', which cancels like terms on both sides. All is said in words, without symbols: the unknown is 'a thing', its square 'wealth'. He proves his rules with simple figures, the method we call completing the square. His astronomical tables, the Zij al-Sindhind, rest mostly on Indian astronomy brought to Baghdad around 770; they are the first Arabic astronomical work to survive almost whole, though only in Latin. His 'Book of the Image of the Earth' reworks Ptolemy's Geography as the latitudes and longitudes of 2,402 places, and improves on Ptolemy for the Islamic lands, shortening his far too long Mediterranean. He also wrote on the Jewish calendar, the astrolabe and the sundial, and a chronicle that is lost.

The last sure sign of him comes from al-Tabari: in 847 he was one of the astronomers called to the bed of the dying caliph al-Wathiq at Samarra, who read in his horoscope fifty more years of life; the caliph died ten days later. A story that al-Wathiq had sent him to the chief of the Khazars in 842 may confuse him with Muhammad ibn Musa ibn Shakir, one of the Banu Musa. Britannica says he helped to make al-Ma'mun's map of the world and to measure a degree of the meridian on the plain of Sinjar; other historians doubt his part in the measurement. He probably died around 850. No portrait of him was made in his lifetime; the statues raised to him in Uzbekistan and the Soviet stamp of 1983 are imagined.

His books lived on in other hands. Adelard of Bath put an Andalusian revision of the tables into Latin around 1126, Robert of Chester translated the Algebra at Segovia in 1145 and Gerard of Cremona made a second version, so that 'algebra' entered the languages of Europe; the Latin arithmetic spread the Indian numerals that Leonardo of Pisa would make popular. The Arabic Algebra survives in a copy of 1342 at Oxford, first printed with an English translation by Frederic Rosen in 1831. His geography stayed unknown in Europe until its single copy, made in 1036–37, was found in Cairo in the nineteenth century and came to Strasbourg; its four sketch maps, among them a map of the Nile, are the oldest surviving maps from the Islamic world. The historian G. J. Toomer called his achievements 'at best mediocre' but 'uncommonly influential'; others call him the father of algebra.