Muḥammad ibn Mūsā al-Khwārizmī - Geographers, Facts and Personal Life

He was born as Abū ‘Abdallāh Muḥammad ibn Mūsā al-Khwārizmī in a Persian family in Chorasmia c. 780. Not much is known about his early life for lack of well-documented information.

It is often assumed from his name that he came from Khwarezm (Khiva), then in Greater Khorasan. However some other sources suggest that he might have come from Qutrubbul (Qatrabbul), a viticulture district near Baghdad.

Al-Khwarizmi lived during the Abbasid Caliphate, and he had a very meaningful career at the court of the Abbasid caliph al-Mamun. The caliph had a deep interest in science and philosophy and encouraged Al-Khwarizmi’s pursuits in scholarly investigations.

Since he lived several centuries ago, many facts regarding his professional life are also obscure. According to some sources, he may have been attached to al-Mamun's scientific academy in Baghdad, the House of Wisdom (Arabic, Bayt al-Hikma).

He is believed to have participated in the calculation of the length of a degree of latitude during this time. He was a part of a major project to determine the circumference of the Earth, following which he helped to make a world map for the caliph, overseeing 70 geographers.

He was a brilliant mathematician whose publication ‘On the Calculation with Hindu Numerals’, written around 825 CE played a major role in spreading the Indian system of numeration throughout the Middle East and Europe. The book was later also translated into Latin as ‘Algoritmi de numero Indorum’.

In 830 he completed his mathematical book ‘The Compendious Book on Calculation by Completion and Balancing’ (al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) in which he provided an exhaustive account of solving polynomial equations up to the second degree.

The book was translated into Latin twice in the 12th century. It was a seminal work in which solutions to several hundred simple quadratic equations by analysis as well as by geometrical methods were provided.

He revised Ptolemy's ‘Geography’ and corrected his data for Africa and the Middle East, publishing his work in his ‘Kitāb Ṣūrat al-Arḍ’ which he finished in 833. He gave a list of 2402 coordinates of cities and other geographical features based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa. Today, there is only one surviving copy of ‘Kitāb Ṣūrat al-Arḍ’, which is kept at the Strasbourg University Library.

He made invaluable contributions to the field of trigonometry as well. He is credited to have developed trigonometric tables containing sine functions which were later used to help form tangent functions.

His works in mathematics also led to the concept of differentiation which was derived from his development of the calculus of two errors.

In his book ‘Astronomical tables of Sind and Hind’, he provided tables for the movements of the sun, the moon and the five planets known at the time. The work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of sine values ushered in a new era in Islamic astronomy.

Al-Khwarizmi's mathematical works are so significant that scholars in the Renaissance Europe believed him to be the original inventor of algebra. He is credited to have introduced the Arabic numerals, based on the Hindu-Arabic numeral system developed in Indian mathematics, to the Western world.

The magnitude of his contribution to mathematics is apparent from the fact that both the terms "algorithm" and "algorism" are derived from the Latinized forms of Al-Khwarizmi's name, ‘Algoritmi’ and Algorismi’, respectively.

Al-Khwarizmi is best known for his comprehensive book on mathematics, ‘The Compendious Book on Calculation by Completion and Balancing’ in which an exhaustive account of solving the positive roots of polynomial equations up to the second degree was provided. The book also deals with computations involved in Islamic rules of inheritance.

He died in c. 850.