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.

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*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.