Al-Khwarizmi — Founder of Algebra and the Algorithm

Muhammad ibn Musa al-Khwarizmi was born around 780 into a Persian family in the Khwarazm region south of the Aral Sea, as recorded by the bibliographer Ibn al-Nadim. Few details of his life survive with certainty; almost everything known about him comes from his works and from later scholars' references to them.

Location: Khwarazm, Abbasid Caliphate (present-day Uzbekistan)

Around 820 al-Khwarizmi took up scholarly work at the House of Wisdom in Baghdad, the translation and research institution patronized by Caliph al-Ma'mun. The institution gathered Greek, Persian, and Indian scientific texts and the astronomers and mathematicians who worked on them, giving al-Khwarizmi access to the full range of inherited mathematical knowledge.

Location: Baghdad, Abbasid Caliphate

Drawing on Indian astronomical texts transmitted through the work of Brahmagupta, al-Khwarizmi compiled the Zij al-Sindhind, a set of astronomical tables with accompanying rules for calculating the positions of the sun, moon, and planets. The zij became a standard reference for Islamic astronomers and was later translated into Latin, carrying Indian computational methods into Europe.

Location: Baghdad, Abbasid Caliphate

Between 813 and 833, commonly dated to around 825, al-Khwarizmi compiled Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala, "The Compendious Book on Calculation by Completion and Balancing." The book gave the first systematic treatment of linear and quadratic equations, solving them by the operations of al-jabr (completion) and al-muqabala (balancing) with geometric proofs; the word "algebra" derives from al-jabr in its title.

Location: Baghdad, Abbasid Caliphate

Al-Khwarizmi wrote a separate treatise explaining the decimal place-value numeral system used in Indian mathematics, including the use of zero. A Latin translation of the book, titled Algoritmi de numero Indorum, circulated in medieval Europe under his name and gave the word "algorithm" its European form, linking his name permanently to computation.

Location: Baghdad, Abbasid Caliphate

Caliph al-Ma'mun sponsored a geodesic project to measure the circumference of the Earth, and al-Khwarizmi is recorded among the scholars who participated. Teams measured the length of a degree of the meridian on the plain of Sinjar, producing a value for the Earth's circumference that was used in his later geographical work.

Location: Sinjar plain, Abbasid Caliphate (present-day Iraq)

In the Kitab Surat al-Ard, "The Image of the Earth," al-Khwarizmi revised Ptolemy's second-century Geography, correcting longitudes and latitudes and listing coordinates for thousands of cities and localities. The work replaced several of Ptolemy's values, including his overestimate of the length of the Mediterranean, and remained a reference for Islamic cartographers.

Location: Baghdad, Abbasid Caliphate

Al-Khwarizmi died around 850, probably in Baghdad. By then his textbooks on algebra, arithmetic, and astronomy were established works of the Islamic scientific curriculum, and later mathematicians such as Abu Kamil of Egypt built directly on his methods.

Location: Baghdad, Abbasid Caliphate

In 1145 the English scholar Robert of Chester translated the algebra treatise into Latin while working in Spain, and earlier translators including Adelard of Bath had carried the astronomical tables and the book on Indian reckoning to Latin readers. The translations introduced the decimal positional number system to the Western world, and al-Khwarizmi's algebra textbook remained in use at European universities until the sixteenth century.

Location: Segovia, Kingdom of Castile