Al-Khwarizmi

Al-Khwarizmi

Al-Khwarizmi (Persian: خوارزمی), or by his full name Abū Jaʿfar Muḥammad ibn Mūsā al-Khwārizmī (b. 780, Khwarezm – d. 850, Baghdad), was a Persian scholar who worked in the fields of mathematics, astronomy, geography and algorithms. Al-Khwarizmi was born in 780 in the city of Khiva in the Khwarezm region. He died in 850 in Baghdad.

The Latin translations of his work on Hindu numerals introduced the decimal positional number system to the Western world in the 12th century. Al-Khwarizmi's Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations. Because he was the first to teach algebra as an independent discipline and to introduce the methods of "reduction" and "balancing" (simplifying an equation by moving like terms on different sides to the same side), al-Khwarizmi has been described as the father or founder of algebra. His work in the field of algebra was used as the basic mathematics textbook in European universities until the 16th century.

He revised and edited Ptolemy's work titled "Geography" and carried out studies in the fields of astronomy and astrology.

Some words reflect the importance of al-Khwarizmi's contributions to mathematics. The word "algebra" derives from al-jabr, one of the two operations he used to solve quadratic equations. The word "algorithm" comes from Algoritmi, the Latin form of his name. His name also forms the origin of the words (Spanish) "guarismo" and (Portuguese) "algarismo," both meaning digit.

His life

The details known with certainty about al-Khwarizmi's life are few in number. He was born into an Iranian family in the city of Khwarezm in Greater Khorasan (modern Khiva, Khwarezm region, Uzbekistan). He was born in 780.

On the other hand, the epithet "al-Qutrubbulli" in his name suggests that he may have come from Qutrubbul, a vine-growing district in Baghdad. However, Rashed advances another view:

"One need not be a philologist specializing in this period to read Tabari's second citation, 'Muhammad ibn Mūsā al-Khwārizmī and al-Majūsī al-Qutrubbullī.' Between 'al-Khwārizmī' and 'al-Majūsī al-Qutrubbullī,' the letter 'wa' (Arabic 'و', used for conjunction) meaning 'and,' which was omitted in the first copies, shows us that they are two separate persons. Had a series of errors not been made regarding al-Khwarizmi's identity, this would not be worth mentioning."

Toomer writes the following about al-Khwarizmi's religious view:

"The epithet 'al-Majūsī,' another given to him by al-Tabari, indicates that he was an adherent of the old Zoroastrian religion. Contrary to this view, which is quite likely to have been true for an Iranian person at that time, the pious preface al-Khwarizmi wrote in his work titled Algebra shows that he was in fact a Sunni Muslim. For this reason it is probable that he was a Zoroastrian only in his youth."

Ibn al-Nadīm's work Kitāb al-Fihrist contains, together with a short biography of al-Khwarizmi, a list of his works. Al-Khwarizmi carried out most of his work between the years 813 and 833. After the Muslim conquest of Iran, Baghdad became the center of scientific work and trade, and many merchants and scholars traveled to Baghdad, as al-Khwarizmi did. At the House of Wisdom built in Baghdad by the caliph al-Ma'mun, al-Khwarizmi worked as a scholar in the fields of science and mathematics, including the translation of Greek and Sanskrit scientific manuscripts. Douglas Morton Dunlop holds the view that al-Khwarizmi may in fact be the same person as Muhammad ibn Mūsā ibn Shākir, the eldest of the three Banū Mūsā.

His works

Al-Khwarizmi's contribution to mathematics, geography, astronomy and cartography formed the foundation of innovation in algebra, logarithms and trigonometry. The title of his book, which gave rise to algebra with its systematic approach to solving linear and quadratic equations, is as follows: "The Compendious Book on Calculation by Completion and Balancing."

The book titled "On Calculation with Hindu Numerals," written by al-Khwarizmi around 820, is the main reason for the spread of the Hindu-Arabic numeral system to the Middle East and Europe. It was translated into Latin as "Algoritmi de numero Indorum."

Some of his works are based on the astronomy of the Persians and Babylonians, Hindu numbers and Greek mathematics.

Al-Khwarizmi systematized and corrected Ptolemy's data concerning Africa and the Middle East.

Another important book, Kitāb ṣūrat al-arḍ (The Appearance of the Earth; translated as Geography), while based on the coordinates of places in Ptolemy's Geography, presented improved values for the existing figures for the Mediterranean, Asia and Africa.

He accompanied and assisted in the project of some 70 geographers commissioned by the caliph al-Ma'mun to determine the circumference of the Earth and to prepare a world map.

With the spread of his works to Europe through their Latin translations in the 12th century, he had a profound influence on the development of mathematics in Europe.

His work in the field of algebra

The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) is a mathematics book written around the year 820. This book was written at the encouragement of the caliph al-Ma'mun as a popular work of calculation filled with examples and applications for solving a very wide range of problems in the fields of trade, measurement and legal inheritance. The term "algebra" comes from al-jabr, one of the fundamental operations defined in this book (the meaning of al-jabr is "restoration," referring to adding a number to both sides of an equation to combine or simplify terms). This work also has the distinction of being the first independent algebra book of both East and West. This book was translated into Latin by Robert of Chester (Segovia, 1145) and later by Gerard of Cremona. An original Arabic copy is in Oxford and was translated by F. Rosen in 1831. A Latin translation is preserved in Cambridge.

His work in the field of mathematics formed the foundation of algebra. During a period he spent in India, he determined that a positional number system was used to express numbers instead of letters or syllables. As a result of the translation into Latin of the book al-Khwarizmi wrote on this subject under the title Algoritmi de numero Indorum, this system consisting of symbols, together with zero, was presented to the Western world in the 12th century. His book titled Ḥisāb al-Jabr wa al-Muqābala is, in the history of mathematics, the first work to contain the systematic solutions of first- and second-degree equations. For this reason al-Khwarizmi is also known (together with Diophantus) as the "father of algebra." The English word "algebra" and its Turkish equivalent "cebir" come from "al-jabr," one of the methods for solving quadratic equations in al-Khwarizmi's book.

Arithmetic

Al-Khwarizmi's second fundamental work was on the subject of arithmetic, whose Arabic original has been lost but whose Latin translation has survived. This translation was most likely made in the 12th century by Adelard of Bath, who also translated astronomical tables in 1126.

Sources

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