Muhammad ibn Musa al-Khwarizmi
Native spelling: محمد بن موسى الخوارزمي
780–850, Khwarazm (traditional attribution; exact birthplace debated), Baghdad, Abbasid Caliphate
Persian mathematician and astronomer at the House of Wisdom in Baghdad whose treatise on restoring and balancing equations gave algebra its name and its first systematic treatment, and whose book on Indian numerals helped transmit the Hindu-Arabic decimal system to the western mathematical tradition.
Muhammad ibn Musa al-Khwarizmi was born around 780 CE, probably in or near Khwarazm, a region in Central Asia corresponding to parts of present-day Uzbekistan and Turkmenistan, though the exact birthplace is debated. He worked in Baghdad, then the capital of the Abbasid Caliphate and the leading center of learning in the world, where he was attached to the House of Wisdom (Bayt al-Hikma) under the patronage of Caliph al-Ma'mun, and where he is believed to have died around 850 CE — the modern territory of both regions is reflected in his listed countries.
Around 820 CE al-Khwarizmi wrote al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala (The Compendious Book on Calculation by Completion and Balancing), a practical manual for solving problems of inheritance, trade, land division and other everyday matters. The book is written entirely in prose, without symbolic notation, negative numbers or an equals sign, yet it systematically reduces every linear and quadratic equation to one of six standard forms and gives a method — al-jabr, 'restoration', moving a subtracted term to the other side of an equation, and al-muqabala, 'balancing', cancelling like terms on both sides — for solving each form, together with geometric justifications using areas of squares and rectangles for why completing the square works. This treatise gave the discipline of algebra both its name, from al-jabr, and its first systematic, general treatment, decisively distinguishing it as a subject from the specific numerical problems addressed by earlier Greek and Indian mathematicians.
Al-Khwarizmi also wrote a treatise on arithmetic, known in its Latin translation as Algoritmi de numero Indorum, that explained the Indian decimal place-value system and the use of zero; the medieval Latinization of his name, Algoritmi, is the direct source of the modern word 'algorithm'. He additionally compiled astronomical tables (Zij al-Sindhind) and, as part of a project commissioned by al-Ma'mun, supervised geographers correcting and extending Ptolemy's world map in his Kitab Surat al-Ard (The Face of the Earth). Through 12th-century Latin translations of his algebra and arithmetic, al-Khwarizmi's work became one of the principal channels by which Indian numerals and Islamic algebra reached medieval Europe.
Workplaces: House of Wisdom, Baghdad
Iraq, Uzbekistan, Turkmenistan