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Al-Khawarazmi; Algebra

This is the second article of a series that will be focused on influential Muslim scientists. To see if any other articles have been uploaded, search the tag or keywords ‘Muslim scientists’ 

Muhammad ibn Musa al-Khawarazmi, who is justly regarded “the father of Algebra,” was a great Muslim mathematician who left a tremendous affect on the science of Algebra. His works comprise of development of Algebra, geometric solutions, degree measurements, and trigonometric tables. The term algorithm is derived from this great mathematician’s name. His works on Algebra provided strong roots to this subject. His fundamental  work entitled “The Book of Summary in the Process of Calculation for Compulsion and Equation” (Al-Kitab al-Mukhtasar fi Hisab al-Jabr wa’l-Muqabala) paved the way for establishment of mathematical branch of Algebra. In this book of Al-Khawarazmi, for the first time the Arabic term of al-jabr meaning compulsion and also restoration was used. This Arabic term al-jabr used by al-Khawarazmi  gave origin to the English/Latin word Algebra.

The Algebra worked out by al-Khawarizmi is a science of equations and algebraic calculations on related binomials and trinomials. He established the unity of Algebra. Al-Khawarazmi’s book provides a manual for usage of arithmetical problems, for commercial transactions, in cases of inheritance, and for the measurement of lands. His book is divided into several sections. The first section is concerned with hisab and al muqabala (algebraic equations). In the second, he determines the bases of normal procedures which allow practical calculations to be reduced to fundamental algebraic types. The last sections deal with practical applications which are concerned with the applications of the methods to commercial transactions, to land surveys, to geometric measurements, and lastly to the testaments. His books extends the scope of algebra from being mere theoretical to practical applications in the fields of numbers and metric geometry. He believed that Algebra was an applied science. The principal concepts used by al-Khawarazmi are the first and second degree equation, the related binomials and trinomials, normal form, the arithmetic solution, and the demonstrability of solution formulae.

His works spread in Europe through Latin transactions in around 12th century and up until the 17th century, his mathematical works were used in European universities. Al-Khawarazmi’s contributions in mathematics are well acknowledged in Europe: “Mathematical science in Europe was more vitally influenced by Mohammed ibn Musa than by any other writer from the time of the Greeks to Regiomontanus (1436-1476). Through his arithmetic, presenting the Hindu art of reckoning, he revolutionized the common processes of calculation and through his Algebra, he laid the foundation for modern analysis. Evidence of the influence of the great Arab is presented by the relatively large number of translations and adaptations of his various mathematical works which appeared before the invention of printing. Undoubtedly the earliest translation of the Arabic algebra.” [1]

George Sarton, the author of “An Introduction to the History of Science,” regards al-Khawarizmi as “one of the founders of analysis or Algebra as distinct from Geometry.” According to George Sarton: “During the thirteenth century, trigonometrical progress was entirely due to Muslim efforts.” [2] Al-Khawarizmi
 extended the Indian number system and placed the zero as a placeholder in positional base notation.

Apart from mathematics, al-Khwarizmi also contributed in the sciences of Geography, History, and Astronomy. “His book on geography entitled Kitâb Sûrat al-Ard (Book of the Image of the Earth) consists almost entirely of lists of longitudes as well as latitudes of localities and gives in a tabulated form the coordinates of the places such as cities, mountains, seas, rivers and islands. The book is arranged according to the Greek system of the seven climes (aqalim) giving contemporary data but the knowledge acquired by other Muslims is also incorporated into it. The first section lists cities, the second, mountains (giving the coordinates of their extreme points and their orientation); the third, seas (giving the coordinates of salient point on their coastlines and a rough description of their outlines); the fourth, islands (giving the coordinates of their centers, and their length and breadth); the fifth, the central points of various geographical regions; the sixth, rivers (giving their salient points and towns on them).” [3]
“The Islamic sciences developed owing to the civilization’s open-ness to the achievements of other civilizations, especially the sciences in Persia, India, and ancient Greece. The translation movement
encouraged by Muslim rulers played a significant role, and the Islamic sciences went on to influence the Renaissance.”[4], and this openness is very much evident in the writings of al-Khwarizmi. As a great lover of knowledge, he acknowledges the contributions of other nations. Al-Khwarizmi himself says:

“The learned in times which have passed away, and among nations which have ceased to exist, were constantly employed in writing books on the several departments of science and on the various branches of knowledge, bearing in mind those that were to come after them, and hoping for a reward proportionate to their ability, and trusting that their endeavors would meet with acknowledgement, attention, and remembrance — content as they were even with a small degree of praise; small, if compared with the pains which they had undergone, and the difficulties which they had encountered in revealing the secrets and obscurities of science.”

1. Ccontributions to the History of Science, Part I. Robert of Chester’s Latin translation of the Algebra of Al-Khowarizmi (Eng. Version)
2. Muslim Contribution to Civilization Conceptual Foundation and Historical Manifestations by Jamala Badawi
3. Contribution of Al-Khwarizmi to Mathematics and Geography by N. Akmal Ayyubi
4. Studies in Islamic Civilization the Muslim Contribution to the Renaissance by Ahmad Essa with Osman Ali

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