Al-Khwarizmi: The Father of Algebra | History Hit

Al-Khwarizmi: The Father of Algebra

Monument of Muhammad ibn Musa al-Khwarizmi in Uzbekistan. 24 May 2017
Image Credit: MehmetO /

Muḥammad ibn Mūsā al-Khwārizmī, often shortened to al-Khwarizmi (c. 780-850 AD), was a Muslim mathematician and astronomer whose major works introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics during the medieval era. Al-Khwarizmi is commonly nicknamed the ‘Father of Algebra’. The term algebra itself stems from the Arabic word ‘al-jabr’, which originates from al-Khwarizmi’s pivotal 9th-century manuscript on the subject.

In addition to his major works on mathematics and science, al-Khwarizmi contributed significant works on geography and languages. He rose in prominence throughout his life, enjoying privileges such as working at the House of Wisdom (a celebrated intellectual centre) and being involved in the first of two embassies to the Khazars, a semi-nomadic Turkic people. Today, his legacy lives on through the popular application of algorithms and algebra.

So, who was al-Khwarizmi, the famed ‘Father of Algebra’, and what contributions did he make to the world of mathematics?

He worked in the ‘House of Wisdom’

Little is known about al-Khwarizmi’s life. It is probable that he was Persian and from Khwarazm (which was then part of Greater Iran, and today belongs partly to Uzbekistan and partly to Turkmenistan). Indeed, his name means ‘the native of Khwarazm’.

Scholars in library of the ‘House of Wisdom’, Baghdad 1237 AD

Image Credit: Zereshk, Public domain, via Wikimedia Commons

After the Muslim conquest of Persia (also known as the Arab conquest of Iran) from 633 to 654 AD, Baghdad became a centre of trade and scientific study, a hub for merchants and scientists alike, from as far afield as China and India. Al-Khwarizmi was one such thinker who called Baghdad home.

He accomplished most of his work between 813 and 833 AD. He worked and studied in the House of Wisdom, also known as the Grand Library of Baghdad, which was a major public academy and intellectual centre, or possibly a large private library that belonged to the Abbasid Caliphs during the Islamic Golden Age. It was established by the seventh Abbasid caliph Al-Ma’mūn.

In the House of Wisdom, al-Khwarizmi studied algebra, geometry and astronomy, as well as the translation of Sanskrit and Greek scientific manuscripts. His colleagues included the Islamic scientist brothers, the Banu Musa.

He wrote the first book about algebra

Al-Khwarizmi wrote his two most foundational books, his treatise on algebra and his treatise on astronomy, while studying at the House of Wisdom. Both are dedicated to the Caliph. Written in around 820 AD, the algebra treatise ‘Hisab al-jabr w’al-muqabala’ (‘The Compendious Book on Calculation by Completion and Balancing’) was the most famous and important of all of al-Khwarizmi’s works.

Algorists vs. abacists, depicted in a sketch from 1508 CE

Image Credit: Gregor Reisch: Madame Arithmatica, 1508 via Wikimedia Commons / Public Domain

The treatise uses examples and real-life applications of mathematical functions, which distinguishes it from earlier works on the subject. The work, for example, contains sections on the use of algebra to settle inheritance, trade and surveying problems according to proportions prescribed by Islamic law. Elements within the treatise can be traced from mathematics from early 2nd century BC Babylonia right through to Hellenistic, Hebrew and Hindu works.

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The treatise’s title gives us the word ‘algebra’ (from ‘al-jabr’, meaning ‘restoration), while the word ‘algorithm’ also derives from the text. It is regarded to be the first book written on algebra. The book was later translated into Latin, a copy of which is kept in Cambridge. A unique Arabic copy was translated in 1831 and is housed in Oxford.

He also wrote other important works

Al-Khwarizmi also contributed to other scientific subjects via other works. His ‘Book of the Description of the Earth’, or ‘Geography’, was finished in 833 and is a significant reworking of Ptolemy’s ‘Geography’ from the second century. The work consists of a list of 2404 coordinates of cities and other significant geographical features. Al-Khwarizmi improved the values for the Mediterranean Sea and the location of cities in Africa and Asia.

He also assisted the Caliph Al-Ma’mun in a project to determine the circumference of the Earth by measuring the length of a degree of a meridian through the plain of Sinjār in Iraq.

The earliest extant map of the Nile by Muhammad ibn Musa al-Khwarizmi

Image Credit: Muḥammad ibn Mūsā al-Khwārizmī., Public domain, via Wikimedia Commons

He also penned a few minor works on topics such as the astrolabe (an early scientific instrument used for reckoning time and for observational purposes) and the Jewish calendar. Moreover, he wrote political histories that included the horoscopes of significant people.

Al-Khwarizmi also compiled a set of astronomical tables based upon a range of Greek and Hindu sources. These works were also translated into Latin.

Lucy Davidson