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## Al-Khwarizmi and Algebra

Abu Ja’far Muhammad ibn Musa Al-Khwarizmi was an Arab mathematician who lived and worked in Baghdad during the 8th and 9th centuries.  Not much is known of his life.  He is primarily recognized as the author of two books, one on arithmetical computation and one on algebra.  The word algebra comes from the title of his most famous book Hisab al-jabr w’al-muqabala or The Compendious Book on Calculation by Completion and Balancing.  In this book Al-Khwarizmi discussed methods of solving linear and quadratic equations, although he used prose writing to do this.  The notation that we use today in algebra class was developed by European mathematicians between 1400-1800.

Al-Khwarizmi’s other notable book was about the Hindu-Arabic place-value number system that we learn about in elementary school.  The Hindu used 10 symbols to represent the numbers 0-9 with positional or place values to represent larger numbers.  The other important subject of this book were the methods of calculation that we learn in elementary school.  These “algorithms” for calculation in the number system allow us to add, subtract, multiply and divide any collection of numbers.  The Arab title of the book is not known.  It was translated into Latin as Algoritmi de numero Indorum or, in English, Al-Khwarizmi on the Hindu Art of Reckoning.  The word “algorithm” comes from the Latin representation of Al-Khwarizmi’s name.

The usefulness of Al-Khwarizmi’s work is explained by the author himself

… what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, and other objects of various sorts and kinds are concerned.

Here is a link to a biography of Al-Khwarizmi

Here is a link to a Wikipedia article on his book

Next week I’ll write about the importance of Al-Khwarizmi’s work to European mathematicians.