This paper is a short biography of one of the most famous Islamic mathematicians of the 9th century AD, Abu Jafar Muhammad ibn Musa Al-Khwarizmi also known as Al-Khwarizmi for short. The paper will include a short background of his life and times and concentrate on his major contributions to the field of mathematics.
Method and Literature Review
Al-Khwarizmi was a very famous mathematician of the 9th century and the internet is full of articles about his achievements. This paper will refer to some of the more reputable sources as it researches the life and times of this famous mathematician. The MacTutor History of mathematics archive has a well referenced biography of Al-Khwarizmi, and it will serve as the main source for this paper. Another respectable source is a paper by Overbay, Schorer and Conger, available on the University of Kentucky site. Finally Robert Nowlan has written chronicles of several of mathematicians which are available on his site. These too will be referred in this paper.
The Biography
Al-Khwarizmi was born around the year 780 AD possibly in Baghdad. His name gives rise to many speculations about his place of birth. Many historians, including Nowlan believe that his name indicates that he was born in Khwarizm, a town in present day Uzbekistan. However, others feel that he was probably born in Baghdad while his ancestors migrated from Khwarizm. Irrespective, Al-Khwarizmi grew up at a time and place when the Arabic world was going through a period of enlightenment. Al-Mamun, the sixth Caliph of the Abbasid dynasty was a great patron of learning and founded an academy called the House of Wisdom where Greek philosophical and scientific works were translated. Al-Khwarizmi was a scholar at this academy and worked under direct patronage of Al-Mamun, if dedicating some of his treatise to the Caliph.
Al-Khwarizmi wrote several treatise but his most important work was titled Hisab al-jabr wal Muqabala which means Calculation by Completion and Balancing. This book found its way to the west when the Moors conquered Spain and gave us the word algebra. The book was intended to help solve real life, every day problems like inheritance, legacies, partitions, trade etc. using mathematics. The book also hoped to help men with the measuring of land, digging canals and doing geometrical computations for other such usages. In fact, only the first part of the book discusses what we know today as algebra with the rest of the book devoted to highly practical ways to solve everyday problems. Unlike works of other mathematicians like Diophantus and Brahmagupta, the work is mostly simple elementary algebra with a much more practical approach to mathematics.
The book, which is written entirely in prose starts with introducing the readers to natural numbers. This is followed by six chapters which introduce the readers to six type of quadratic equations. These six types are
Squares equal of roots
Squares equal to numbers
Roots equal to numbers
Squares and roots equal to numbers
Squares and numbers equal to roots
Roots and numbers equal to squares.
To solve an equation he first removes the negative terms from the equation (al-jabr, meaning completion) and then reduces positive terms of the same power when they occur on both sides of an equation (al-muqabala, meaning balancing). He then solves these six types of equations by using both algebraic and geometric methods of solution. The book also extends the laws of arithmetic to algebraic objects. Once the reader is introduced to these basics of algebra, the book goes on to discuss practical applications of these equations. The book also delves into mensuration and shows how to find volumes of spheres, cones and pyramids.
Besides al-jabr, the other important work of Al- Khwarizmi is his treatise on Hindu-Arabic numerals. Although the original Arabic text is lost, it was translated into Latin as Algoritmi de numero Indorum or Al-Khwarizmi on the Hindu art of Reckoning. The title of this translation gave the word algorithm to the English language. Unfortunately, the original is not true to the original and omits and changes many things which are lost with the original. For example, it is believed that the original text gave a method to find square roots, which is missing from the Arabic version. Still, it manages to translate many of Al-Khwarizmis writings including the Hindu place-value system of numerals based on the number 1-9 and zero. Thus the first use of zero as a place holder in the positional base notation can probably be traced back to Al-Khwarizmi in this work.
Al-Khwarizmi also wrote a number of less important works such as Sindhind Zij, a book on astronomy. This book is based on Indian astronomical work unlike other which were based on the works of Ptolemy. Still, even his work was largely influenced by Ptolemy. Another book by Al-Khwarizmi was on geography which gave the latitudes and longitudes of 2402 localities to form the map of the world.
Al-Khwarizmi is also responsible for developing the trigonometric tables and formed calculus of two errors, leading to the concept of differentiation. He also did much work relating to time and some of his works were on clocks, astrolabes and sundials.
Discussion and Conclusion
There is very little information available about Al-Khwarizmis personal life. This has resulted in people making guesses about his life based on the little evidence which is available. Obviously, many of these guesses are way of the mark and have got mixed with the facts so that it has become almost impossible to separate facts from the guesses. This paper has drawn on only the reputable sources and it is hoped the material presented here is mostly facts. Also, since the paper has concentrated more on his contributions to the field of mathematics, about which there is little debate, hence the material presented here is mostly factual. There is no doubt that Al- Khwarizmi was one of the greatest mathematicians of all times and has often been referred as the Father of Algebra. As can be seen from this paper, no one perhaps deserves this title more than he does. After all, he is responsible for giving us the word algebra.
Method and Literature Review
Al-Khwarizmi was a very famous mathematician of the 9th century and the internet is full of articles about his achievements. This paper will refer to some of the more reputable sources as it researches the life and times of this famous mathematician. The MacTutor History of mathematics archive has a well referenced biography of Al-Khwarizmi, and it will serve as the main source for this paper. Another respectable source is a paper by Overbay, Schorer and Conger, available on the University of Kentucky site. Finally Robert Nowlan has written chronicles of several of mathematicians which are available on his site. These too will be referred in this paper.
The Biography
Al-Khwarizmi was born around the year 780 AD possibly in Baghdad. His name gives rise to many speculations about his place of birth. Many historians, including Nowlan believe that his name indicates that he was born in Khwarizm, a town in present day Uzbekistan. However, others feel that he was probably born in Baghdad while his ancestors migrated from Khwarizm. Irrespective, Al-Khwarizmi grew up at a time and place when the Arabic world was going through a period of enlightenment. Al-Mamun, the sixth Caliph of the Abbasid dynasty was a great patron of learning and founded an academy called the House of Wisdom where Greek philosophical and scientific works were translated. Al-Khwarizmi was a scholar at this academy and worked under direct patronage of Al-Mamun, if dedicating some of his treatise to the Caliph.
Al-Khwarizmi wrote several treatise but his most important work was titled Hisab al-jabr wal Muqabala which means Calculation by Completion and Balancing. This book found its way to the west when the Moors conquered Spain and gave us the word algebra. The book was intended to help solve real life, every day problems like inheritance, legacies, partitions, trade etc. using mathematics. The book also hoped to help men with the measuring of land, digging canals and doing geometrical computations for other such usages. In fact, only the first part of the book discusses what we know today as algebra with the rest of the book devoted to highly practical ways to solve everyday problems. Unlike works of other mathematicians like Diophantus and Brahmagupta, the work is mostly simple elementary algebra with a much more practical approach to mathematics.
The book, which is written entirely in prose starts with introducing the readers to natural numbers. This is followed by six chapters which introduce the readers to six type of quadratic equations. These six types are
Squares equal of roots
Squares equal to numbers
Roots equal to numbers
Squares and roots equal to numbers
Squares and numbers equal to roots
Roots and numbers equal to squares.
To solve an equation he first removes the negative terms from the equation (al-jabr, meaning completion) and then reduces positive terms of the same power when they occur on both sides of an equation (al-muqabala, meaning balancing). He then solves these six types of equations by using both algebraic and geometric methods of solution. The book also extends the laws of arithmetic to algebraic objects. Once the reader is introduced to these basics of algebra, the book goes on to discuss practical applications of these equations. The book also delves into mensuration and shows how to find volumes of spheres, cones and pyramids.
Besides al-jabr, the other important work of Al- Khwarizmi is his treatise on Hindu-Arabic numerals. Although the original Arabic text is lost, it was translated into Latin as Algoritmi de numero Indorum or Al-Khwarizmi on the Hindu art of Reckoning. The title of this translation gave the word algorithm to the English language. Unfortunately, the original is not true to the original and omits and changes many things which are lost with the original. For example, it is believed that the original text gave a method to find square roots, which is missing from the Arabic version. Still, it manages to translate many of Al-Khwarizmis writings including the Hindu place-value system of numerals based on the number 1-9 and zero. Thus the first use of zero as a place holder in the positional base notation can probably be traced back to Al-Khwarizmi in this work.
Al-Khwarizmi also wrote a number of less important works such as Sindhind Zij, a book on astronomy. This book is based on Indian astronomical work unlike other which were based on the works of Ptolemy. Still, even his work was largely influenced by Ptolemy. Another book by Al-Khwarizmi was on geography which gave the latitudes and longitudes of 2402 localities to form the map of the world.
Al-Khwarizmi is also responsible for developing the trigonometric tables and formed calculus of two errors, leading to the concept of differentiation. He also did much work relating to time and some of his works were on clocks, astrolabes and sundials.
Discussion and Conclusion
There is very little information available about Al-Khwarizmis personal life. This has resulted in people making guesses about his life based on the little evidence which is available. Obviously, many of these guesses are way of the mark and have got mixed with the facts so that it has become almost impossible to separate facts from the guesses. This paper has drawn on only the reputable sources and it is hoped the material presented here is mostly facts. Also, since the paper has concentrated more on his contributions to the field of mathematics, about which there is little debate, hence the material presented here is mostly factual. There is no doubt that Al- Khwarizmi was one of the greatest mathematicians of all times and has often been referred as the Father of Algebra. As can be seen from this paper, no one perhaps deserves this title more than he does. After all, he is responsible for giving us the word algebra.
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