His full name was Muhammad ibn Musa al-Khwarizmi. He was born in Khwarizm (North western part of Khorasan in what is now the countries of Turkmenstan and Uzbekistan) in the year 780 A. D. and died in Baghdad in 850 A. D. The name Khwarizmi literally means "from Khawrizm" and is as a designation that refers to his place of origin, Khwarizm. Khwarizmi lived most of his life in Baghdad during the reign of al-Mamun and al Mutasim.

Khwarizmi is regarded as one of the outstanding scientific figures and his contribution in the fields of Mathematics, astronomy and geography are inarguable. He wrote many important mathematical books. His works on algebra, arithmetic and astronomical tables greatly advanced mathematical thought. Early Arab scholars like ibn Khaldun and Katib Celebi credited him with being the first mathematician who wrote about algebra. One of the best known works of Khwarizmi is the book of Kitab al-jabar wa al-muquabalah which literally mean "the book of integration and equation." The word "algebra" originated from the second word of the title of this book. It discussed rules for arithmetical solutions of linear and quadratic equations for elementary geometry and for inheritance problems concerning the distribution of wealth according to proportions. Khwarizmi believed in an ordered universe which is evident from his opening of his book. It was translated to English from a Latin version by Louis Charles Karpinski in 1915:

The Book of Algebra and Almucabola, concerning arithmetical and geometrical problems.

"In the name of God, tender and compassionate, begins the book of Restoration and opposition of number put forth by Mohammed Khwarizmi, the son of Moses. Mohammed said, Praise God the creator who has bestowed upon man the power to discover the significance of numbers. Indeed, reflecting that all things which men need require computation, I discovered that all things involve number and I discovered that number is nothing other than that which is composed of units. Unity therefore is implied in every number. Moreover I discovered all numbers to be so arranged that they proceed from unity up to ten."

Khwarizmi, in the same book and introduction, categorized the numbers into three types, "roots, squares, and numbers" and describes the relationship between them as the following:

Squares equals to roots, Squares equal to numbers, and Roots equal to numbers.

Louis Charles Karpinski, the translator the his works, explains that these three types: "corresponds in modern algebraic notation to the following: ax²=bx, ax²=n, bx=n"The first six chapters of Khwarizmi's algebra (Kitab al-jabr wa al-muquabalah) deals with the following mathematical relationships:

"Concerning squares equal to roots"

"Concerning squares equal to numbers"

"Concerning roots equal to numbers"

"Concerning squares and roots equal to numbers"

"Concerning squares and numbers equal to roots"

"Concerning roots and numbers equal to a square"

Each chapters were followed by geometrical demonstration and then many problems are worked out. Some of his problems are formal while others were in practical context. An example of his formal problem follows:

"If from a square I subtract four of its roots and then take one-third of the remainder, finding this equal to four of the roots, the square will be 256. "

He explained it as following:

"Since one-third of the remainder is equal to four roots, one knows that the remainder itself will equal 12 roots. Therefore, add this to the four, giving 16 roots. This (16) is the root of the square. The above can also be stated in terms of modern notation as 1/3 (x² - 4x ) = 4x."

Khwarizmi in a chapter on commercial transactions states that "mercantile transactions and all things pertaining thereto involve two ideas and four numbers." Karpinski in his translation of the book explains:

The two ideas appear to be the notions of quantity and cost; the four numbers represent unit of measure and price per unit, quantity desired and cost of the same.

An example of Khwarizmi's mercantile problem:

"A man is hired to work in a vineyard 30 days for 10 pence. He works six days. How much of the agreed price should he receive?"

Explanation: "It is evident that sic days are one-fifth of the whole time; and it is also evident that the man should receive pay having the same relation to the agreed price that the time he works bears to the whole time, 30 days. What we have proposed, is explained as follows. The month, i.e., 30 days, represents the measure, and ten represents the price. Six days represents the quantity, and in asking what part of the agreed price is due to the worker you ask the cost. Therefore multiply the price 10 by the quantity 6, which is inversely proportional to it. Divide the product 60 by the measure 30, giving 2 pence. This will be the cost, and will represent the amount due to the worker."

Khwarizmi developed a detailed trigonometric tables containing the sine functions which later included tangent functions. Khwarizmi's book on arithmetic was translated into Latin and published in Rome in 1857 by Prince Baldassare Boncompagni and appears as part 1 of a volume entitled Tratti d' aritmetica. The book is titled as Algorithmi de numero indorum which means "Khwarizmi concerning the Hindu art of reckoning." Many of his books were translated into Latin and used as a principle mathematical text book in European universities until sixteenth century. Among them these two books had important place: Kitab al-Jama wal-Tafreeq bil Hisab al-Hindi and Kitab al-Jabr wa al-muquabalah.

In geography, he wrote the book called Kitab surat al- ard (book of the form of the earth). His works differed from Ptolemy's and he corrected Ptolemy's views in detail. It is a description of a world (known world at that time) map and contains a list of the coordinates of the important places on it. He corrected the distortion that Ptolemy's map had with regard to the length of the Mediterranean. It was much more accurate. However, it failed to replace the Ptolemaic geography used in Europe. He wrote many other books on topics such as clocks, sundials and astrolabes.

Khwarizmis contribution and influence are tremendous. Two important books on arithmetic, Carmen de Algorismo and Algorismus vulgaris which were written in twelfth and thirteenth century respectively owe a lot to the Khwarizmi's book and were used for several hundred years in Europe. Abu Kamil whose work on mathematics were based on Khwarizmi's works kept the influence of Khwarizmi on Leonardo of Pisa, a thirteenth century scholar and up to Middle Ages and during the Renaissance.

Bibliography

Bell, Eric T. The Development of Mathematics. New York: McGraw-Hill Book Co., 1945.

Cajori, Florian. A History o Mathematics. New York: Macmillan, 1931.

Karpinski, Louis Charles. Robert of Chester's Latin Translation of the Algebra of Al-Khwarizmi. London: Macmillan, 1915.

Kennedy, E. S., ed. Studies in the Islamic Exact Sciences. Beirut, Lebanon: American University of Beirut Press, 1983.

King, D. A. Al-Khwarizmi and New Trends in Mathematical Astronomy in the Ninth Century. New York: Hagop Kevorkian Center for Near Eastern Studies, New York University, 1983.

Nasr, Seyyed Hossein. Islamic Science: An Illustrated Survey. London: World of Islam Festival,

1976.

Science and Civilization in Islam. Cambridge, Mass.: Harvard University Press, 1968.