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The father of Algebra - The great mathematician Al-Khwarizmi

Muhammad ibn Musa Khwarizmi (780-850 CE), from Khwarezm (based around north western Uzbekistan) was the greatest scientist of his time, working in mathematics, geography, and astronomy. From a variant of his name "Al-Khwarizimi", has come the words "algorism/algorithm," and "logarithm". The word 'algorithm' signifying arithmetic, or at any rate any process involving repeated calculation.  He wrote a treatise in Arabic language in the 9th century, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latin for Al-Khwarizmi's name. The book introduced the concept of the Algorithm, which is used in our everyday lives. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through his other book, Compendious Book of Calculation by Completion and Balancing, known in the west simply as the "Algebra" This work became 'the prototype' for all works on Algebra and is undoubtedly the beginning of algebraic calculus and decimal arithmetic.

In CE 825 Al-Khwarizmi wrote his famous treatise on Algebra entitled 'Kitab al Mukhtassar fi'l hisab al jabr wa'l muqabalah' (Compendious Book of Calculation by Completion and Balancing). The book introduced the fundamental concept of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation (termed the completing part) , that is, the cancellation of like terms on opposite sides of the equation. This is the operation which Al-Khwarizmi originally described as al-jabr. In it he gave numerous detailed examples including an exhaustive account of solving polynomials up to the second degree.^]

Kitab al-mukhtasar was also instrumental in introducing the numerical system and the use of the zero, which derives from the Arabic sifr, 'void.The book was the first to introduce squares, roots, and numbers to describe equations. It also introduced a method similar to long division to extract the square root (jithr) of a number and was the first to introduce the concept of mal (power) for the squared unknown variable. In he gave geometrical solutions of quadratic equations. And set out geometric representations of quadratic equations having two variables, e.g. the circle, ellipse, parabola and hyperbola (conic sections) etc. He also dealt with measuring areas and volumes. It was also the first work in which that word Algebra appears in the mathematical sense, 'Algebra' meaning in Arabic 'restoration', that is the transposing of negative terms of an equation and set algebra as a subject independent of geometry" This is perhaps one of the most significant advances ever made in mathematics and was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of mathematics in later times.

The Origins of Algebra - al khorezmi

Al khorezmi

The first treatise on algebra was written by Diophantus of Alexandria in the third century AD. The term derives from the Arabic al-jabr or literally "the reunion of broken parts.'' As well as its mathematical meaning, the word also means the surgical treatment of fractures. 'the setting of broken bones'.  Algebra gained widespread use through the title of a book " ilm al-jabr wa'l-mukabala - the science of restoring what is missing and equating like with like".

Written by the mathematician Abu Ja'far Muhammad (active c.800-847), who subsequently has become know as al-Khwarazmi, the man of Khwārazm. The words Algorism (the Arabic or decimal system of writing numbers) and algorithm also both derive from his name.

Abu Jofar Mohammed ben Musa al Khorezmiy al Majusi al-Katrabbuli (Muhammad ibn Musa al-Khwarizmi) was born in 783 in Kath located on the outskirts of Beruni in Southern Karakalpakstan.

In 809, he left for Merv to become a scholar at the court of Al-Mamun, the ruler of the Eastern province of the Caliphate and a famous patron of the arts and sciences. On Al-Mamum assuption of the Caliphate in 819 he followed his patron to Bagdad where he was nominated him head of the House of Wisdom, the first and largest scientific center of the Middle Ages, later called the "Academy of Al-Mamun".

Here from 829 Mohammed Al-Khorezmi wrote more than twenty research works, the most famous of which is the "Concise Book of Calculus in Algebra and Almukabula". It was translated into Latin in the twelfth century; its Arabic and Latin variants have been preserved. Al-Khorezmiy wrote "A Book of Indian Calculus", a work known in the Latin version translated by Adelard Bat in the 12th century; he also wrote the Zij - renowned astronomical tables. The tables were translated into Latin, and those Latin manuscripts remain preserved. Al-Khorezmiy also wrote "The Book of Survey of the Orient" represented by the one and only Arabic manuscript in Strasbourg, France. The manuscript was re-copied in 1037. Fragments of his "Book of history" in Arabic still exist.
 

Al Khawarizmi was the founder of several basic principles of mathematics. In his "Book of Indian Calculus" he for the first time in science, describes the arithmetical operations of decimal positioning, based on nine digits and zero. His publication spread the concept of zero across the world. He was also the first to describe the concept, written in Latin language of the "algorithm" which signifies "a constant calculating process". Algorithm is one of the basic concepts not only of mathematics, but also cybernetics.

In another book Al-Jabr wa-al-Muqabilah (Book of Calculations, restoration and reduction) is where the word algebra (Al Jabr in Arabic) was first used. Al-Khorezmi was also the first scientist to define and represent algebra as a science. In his work he submitted six canonical types of linear and square equations and basic methods of solving them, methods which are still used.

The word "algebra" was latinised from the Arabic word "al-jabr", which is evident from the Arabic title of the treatise. The word stands for "filling in" - one of the fundamental operations in algebra at that time.

These works tremendously influenced the development of Science in both the Muslim World and in Europe making him one of the most important mathematician, astronomer and geographer of his age.

Source: Wikipedia http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB and  www.orexca.com/p_khorezmiy.shtml