Pioneering Mathematician And Jewel Of Islam's 'Golden Age' - Muhammad Ibn Musa al-Khwarizmi

The ‘Islamic Golden Age’ produced many remarkable scholars in science and literature. During the five-and-a-half centuries between circa 750 and 1300 AD, there was a proliferation of intellectual activities in the erstwhile Khorasan region as well as in Muslim Spain. The era not only preserved and furthered the knowledge inherited from Greek, Indian and Zoroastrian sources, it also pioneered a new understanding in philosophy, history, mathematics, optics, chemistry, medicine and astronomy. One of the brightest jewels of this period, among a galaxy of others, was al-Khwarizmi, whose name, as will be illustrated below, continues to be part of modern mathematics and computer sciences, twelve and a half centuries after his death.

Muhammad bin Musa al-Khwarizmi originated, as his last name indicates, from Khwarazm province that lies south of Aral Sea, now in Turkmenistan and Uzbekistan. He was born around 780 AD, either somewhere in Khwarazm, according to some traditions, or near Baghdad as per some other reports. Little is known about his early or personal life, family, education, teachers or training. His name appears in Tabari’s history as a source of some events in the reign of Caliph Mamun. Recently, according to the book The World of the Khazars, published in 1999 in Israel, he was part of an embassy to the Khazars inhabiting the steppes beyond the Caucasus and the Caspian. However, what is well known is that he spent his entire life, except for brief sojourns, in Baghdad and remained attached to Bait-ul-Hikmah, the famed House of Wisdom established by Caliph Harun and which flourished under his son Caliph Mamoon. Al-Khwarizmi laid the foundation for Islamic sciences. George Sarton, a science historian, has called the period 800-850 as ‘The Time of al-Khwarizmi.’

Al-Khwarizmi’s name has survived because of his mathematical works. He gave birth to two branches of mathematics. One, Algebra, which is the Latin corruption of a word, ‘al-Jabar’, in the title of one of his books. Two, Algorithm, which is the Latinised version of his name and refers to his methods of solving arithmetic problems employing Indo-Arabic numerals. The online version of Encyclopedia Britannica lists four of his Latinised mathematical works that made him a renowned scholar. These books are on algebra, Indian numerals, astronomy and geography.

Professor A.B. Arndt in his Al-Khwarizmi writes that in the early part of his career, the pioneering mathematician prepared an abridgement of the Indian astronomical tables that he called Zij al-Sindhind. The work made him known in literary circles and brought him to the notice of Caliph Mamun. The Zij contained accurate tables for sine and cosine, the first known tables for tangent and a treatise on spherical trigonometry. The book earned him a lifelong attachment to the House of Wisdom.

The work that made Al-Khwarizmi immortal and relevant forever is titled Al-kitab al-Mukhtasar fi Hisab Al-jabar wa’l muqabla. It was translated into Latin in 1145 AD and remained the principal book on mathematics in Europe till the 16th century. Many of the algebraic equations taught to school children round the world in our time first appeared in this book.

A large part of the book is devoted to the practical problem of calculating inheritance based on Islamic directives

The two words jabar and muqabla had not till then appeared in context of mathematics. They have variously been translated as ‘Completion and Cancellation’ or ‘Restoration and Balancing.’ These translations point to the algebraic processes of reducing one side to a single variable by cancellation of quantities, or forcing – jabar – numerals from one side of the equation to the other side while maintaining the balance of both sides.

The employment of notations currently in algebra came much after the era of al-Khwarizmi. He used descriptive method to describe hundreds of equations of the first and second order, and the process of their solution. For example, the equation (10-X)² = 81X has been described by al-Khwarizmi as “You divide ten into two parts: multiply one by itself; it will be equal to the other taken eighty-one times.” He then goes on to describe the solution in descriptive form till achieving the answer of 1 as the value of X. He has described six types of first- and second-degree equations, and their solution ascertained by analysis methods. He also employed geometric figures like squares and rectangles to solve equations, thereby linking arithmetic and geometry. The Al-jabar book includes calculation of areas and volumes of cubic figures. A large part of the book is devoted to the practical problem of calculating inheritance based on Islamic directives.

Al-Khwarizmi’s second most important book is Kitāb al-ḥisāb al-hindī translated to Latin as Algoritmi de numero Indorum. The book is lost in its original Arabic form and survives only in the translated version. It introduced the Indian numerals, invented centuries earlier, to the Arab world and then through Fibonacci to Europe, as described earlier by this author in this magazine. The book gives algorithmic methods for addition and subtraction and replaced the Abacus that was then used in Europe. The Latinised word Algoritm became Algorithm in English. Algorithmic methods acquired a new meaning and a new life with the introduction of computer age, making Al-Khwarzimi’s name alive in perpetuity.

The last known book of al-Khwarizmi is titled Suratul Ardh or Shape of Earth. An original copy of the book is placed in the University of Strasbourg, France, and one of the first Latin translations is in the National Library of Spain in Madrid. The book is a reworking of Ptolmey’s 2nd-century book ‘Geography’ and lists the coordinates for 2,402 cities and geographic features. Based on these coordinates, a map has been prepared that made many corrections to earlier depictions of the shape of the Earth. For instance, he improved the estimated size and shape of the Mediterranean Sea, and showed the Pacific and the Atlantic as open Oceans as against their earlier depiction of landlocked water bodies.

The book is lost in its original Arabic form and survives only in the translated version. It introduced the Indian numerals, invented centuries earlier, to the Arab world and then through Fibonacci to Europe

Al-Khwarizmi died in Baghdad in 850 AD. He is one of the most respected medieval scientists in the world. He is honoured by the Al-Khwarzimi crater, discovered in 1973, on the far side of the moon, the Al-Chwarizmi asteroid discovered in 1986 and the Al-Khwarismi asteroid discovered in 1997. There are several educational institutions, research facilities, streets and buildings in the Islamic world named after him. His statutes stand at Khiva in Uzbekistan and Tehran in Iran.

Al-Khwarizmi is a guiding star for Muslim youths to emulate in the field of scientific and technological research. While advocating Muslim role models of the past, our schools and colleges would do well to project scholars; and not warriors, as is the unfortunate norm. Early Muslims may have extended their empire through sword but their greatness as a civilization is due to the innumerable scholars who thrived during the Islamic golden Age.

 

Parvez Mahmood retired as a Group Captain from the Pakistan Air Force (PAF) and is now a software engineer. He lives in Islamabad and writes on social and historical issues. He can be reached at parvezmahmood53@gmail.coms