Al-Khwarizmi
780 – 850 · Persia
Known for: Persian mathematician who established algebra as a discipline and whose name became the word algorithm
“From his book came the word algebra, and from his name the word algorithm.”
Biography
Muhammad ibn Musa al-Khwarizmi was born in the late eighth century, most probably in Khwarazm, the region south of the Aral Sea whose name he carried and which now lies across Uzbekistan and Turkmenistan. He was of Persian descent, and although Arabic was not his mother tongue he wrote all of his scientific work in it. Almost nothing certain is known of his family or schooling; the earliest bibliographers preserved little more than a list of his titles. By about 820 he was in Baghdad, capital of the Abbasid Caliphate, serving as astronomer and head of the library at the House of Wisdom established by the caliph al-Ma'mun.
His treatise on algebra, compiled between 813 and 833 and known by the short title Al-Jabr, set out the first systematic solution of linear and quadratic equations, including the method of completing the square, which he justified geometrically. Two operations, reduction and balancing, allowed an equation to be brought to a standard form, and by treating such procedures as a subject in their own right rather than as isolated puzzles he made algebra an independent discipline. A second book, written about 825, explained the Indian decimal numerals and the positional arithmetic that goes with them. He also revised Ptolemy's Geography with corrected coordinates for the Mediterranean, Africa and Asia, compiled astronomical and trigonometric tables, wrote on the astrolabe and the sundial, and oversaw the geographers who prepared a world map for al-Ma'mun.
He is said to have taken part in an embassy to the Khazars during the reign of the caliph al-Wathiq, and he died around the middle of the ninth century; the year is not securely recorded. Three centuries later his work reached Latin Europe: Robert of Chester translated Al-Jabr in 1145, and the book served as a principal mathematical text in European universities into the sixteenth century, while the Latin version of his arithmetic carried the Hindu-Arabic numerals westward. His short title gave European languages the word algebra, and his own name, Latinized as Algoritmi, produced algorism and algorithm, along with the Spanish guarismo and Portuguese algarismo for digit. The step by step procedures he set down are now carried out by machines that still bear his name.