Muhammad ibn Musa al-Khwarizmi, also known as al-Khwarizmi (around 780 to around 850), was a mathematician who lived during the Islamic Golden Age. He wrote important books in Arabic about mathematics, astronomy, and geography. Around 820, he worked at the House of Wisdom in Baghdad, which was the capital of the Abbasid Caliphate at that time. He was one of the most important scholars of his era, and his writings greatly influenced later writers in both the Islamic world and Europe.

Al-Khwarizmi wrote a famous book on algebra called Al-Jabr (which means "completion" or "rejoining"). This book, written between 813 and 833, explained how to solve linear and quadratic equations for the first time in a clear and organized way. He showed how to solve quadratic equations by completing the square and used geometry to explain his methods. Because he was the first person to treat algebra as its own subject and introduced techniques like "reduction" and "balancing," he is often called the father of algebra. The word "algebra" comes from the title of his book. His name also led to the creation of words like "algorithm" and "algorism," which are used in many languages to describe the study of numbers and calculations.

In the 12th century, Latin translations of al-Khwarizmi’s book on Indian arithmetic, Algorithmo de Numero Indorum, helped introduce the decimal-based number system to Europe. This system uses digits and place value to represent numbers. His book Al-Jabr, translated into Latin by Robert of Chester in 1145, was a major math textbook in European universities until the 16th century.

Al-Khwarizmi also updated Ptolemy’s 2nd-century geography book by listing the longitudes and latitudes of cities and places. He created astronomical tables, wrote about calendars, and explained how to use tools like the astrolabe and sundial. He made important progress in trigonometry by creating accurate tables for sine and cosine.

Life

Few details about al-Khwārizmī's life are known for sure. Ibn al-Nadim mentions that al-Khwārizmī was born in Khwarazm, and most people believe he came from this region. He was of Persian heritage, and his name means "from Khwarazm," which was part of Greater Iran and is now in Turkmenistan and Uzbekistan. Even though he was Persian, he wrote all his scientific works in Arabic.

Al-Tabari lists his full name as Muḥammad ibn Musá al-Khwārizmī al- Majūsī al-Quṭrubbullī. The title al-Qutrubbulli might suggest he was from Qutrubbul, a place near Baghdad. However, Roshdi Rashed disagrees with this idea. On the other hand, David A. King supports the connection to Qutrubbul, explaining that al-Khwārizmī was called al-Qutrubbulli because he was born near Baghdad.

Regarding al-Khwārizmī's religion, Toomer writes about it in his work. Ibn al-Nadīm's book, Al-Fihrist, includes a short biography of al-Khwārizmī and a list of his writings. Most of his work was completed between 813 and 833. After the Muslim conquest of Persia, Baghdad became a center for science and trade. Around 820 CE, he was chosen to be the astronomer and head of the library at the House of Wisdom. The House of Wisdom was created by the Abbasid Caliph al-Ma'mūn. Al-Khwārizmī studied subjects like science and mathematics, including translating Greek and Sanskrit texts. He was also a historian, and his work is referenced by scholars such as al-Tabari and Ibn Abi Tahir.

During the time of al-Wathiq, al-Khwārizmī is said to have taken part in the first of two missions to the Khazars. Douglas Morton Dunlop suggests that Muḥammad ibn Mūsā al-Khwārizmī might have been the same person as Muḥammad ibn Mūsā ibn Shākir, the eldest of the three Banū Mūsā brothers.

Contributions

Al-Khwārizmī made important contributions to mathematics, geography, astronomy, and mapmaking. His work laid the foundation for later developments in algebra and trigonometry. He developed a clear method for solving linear and quadratic equations, which led to the creation of algebra. The word "algebra" comes from the title of his famous book, Al-Jabr.

In the year 820, Al-Khwārizmī wrote a book called On the Calculation with Hindu Numerals. This work helped spread the Hindu–Arabic numeral system across the Middle East and Europe. When the book was translated into Latin in the 12th century, it became known as Algoritmi de numero Indorum. This is where the word "algorithm" first appeared in the Western world.

Some of his ideas were based on earlier work from Persian, Babylonian, and Indian mathematicians, as well as Greek mathematics. He improved the accuracy of Ptolemy’s maps for Africa and the Middle East. Another important book he wrote was Kitab surat al-ard (The Image of the Earth), which included updated coordinates for places in the Mediterranean Sea, Asia, and Africa.

Al-Khwārizmī also wrote about tools like the astrolabe and sundial. He helped measure the Earth’s circumference and created a world map for the caliph al-Ma'mun, working with 70 geographers. His works reached Europe in the 12th century through Latin translations, which greatly influenced the development of mathematics there.

Al-Jabr (The Compendious Book on Calculation by Completion and Balancing) is a mathematical book written around 820 CE. It was written with the support of Caliph al-Ma'mun and included many examples of solving problems related to trade, land measurement, and inheritance. The word "algebra" comes from the Arabic term al-jabr, which means "restoration" and refers to a method of solving equations. The book was translated into Latin as Liber algebrae et almucabala by Robert of Chester and Gerard of Cremona. A copy of the original Arabic text is kept at Oxford University.

The book explained how to solve equations up to the second degree. It described two key methods: "reduction" and "balancing." These methods involved moving terms from one side of an equation to the other and simplifying the equation. Al-Khwārizmī’s approach involved reducing equations to six standard forms by dividing out coefficients and using al-jabr and al-muqābala. For example, al-jabr meant adding the same value to both sides of an equation to eliminate negative numbers, while al-muqābala involved combining like terms on the same side.

Although modern math uses symbols to describe these problems, Al-Khwārizmī used written text instead, as symbols were not yet developed. For example, he might write a problem in full sentences rather than using numbers and symbols.

Al-Khwārizmī’s second major work focused on arithmetic. His writings, such as Kitāb al-ḥisāb al-hindī (Book of Indian Computation), described methods for using Hindu–Arabic numerals on a dust board. These methods were used for nearly three centuries before being replaced by techniques that used paper and pen.

In the 12th century, translations of his works reached Europe and changed how people performed calculations. His name became the basis for the word "algorithm," which describes a step-by-step method for solving problems. His work helped replace older methods, like the abacus, in Europe.

Several Latin translations of his works survive today, even though none are exact copies of the original Arabic texts. These include Dixit Algorizmi, Liber Alchoarismi de Practica Arismetice, Liber Ysagogarum Alchorismi, and Liber Pulveris.

Al-Khwārizmī’s work on arithmetic introduced Hindu–Arabic numerals to the Western world. The term "algorithm" comes from the Latin version of his name, Algoritmi, and refers to the methods he developed for using these numerals.

Al-Khwārizmī also wrote Zīj as-Sindhind, a book with 37 chapters on astronomy and 116 tables containing data for calendars, stars, and other astronomical calculations. This was one of the first Arabic works based on Indian astronomical methods, which were later called Sindhind. The word Sindhind is derived from the Sanskrit word Siddhānta, which means a complete or established system.

Honours

• Al-Khwarizmi (Crater) — A crater located on the far side of the Moon, which is the side that does not face Earth.
• 13498 Al Chwarizmi — A main-belt asteroid discovered on August 6, 1986, by E. W. Elst and V. G. Ivanova at Smolyan.
• 11156 Al-Khwarismi — A main-belt asteroid discovered on December 31, 1997, by P. G. Comba at Prescott.