# Muslim scientists and thinkers: Muhammad ibn Musa Al-Khwarizmi

March 27, 2008 by TMO

**By Syed Aslam**

Muhammad ibn Musa al-Khwarizmi was born in 780 CE at a place called Khwarizm which is a part of present day Khiva, Uzbekistan. Like many other thinkers and scientists of his time he also moved to Baghdad which was center of learning of science and philosophy in the middle ages. He studied the sciences and mathematics at House of Wisdom established by Khalifa Ma’mun, which included the translation of Greek and Sanskrit scientific manuscripts. He worked and lived in Baghdad where died in the year 850 CE.

Al-Khwarizmi developed the concept of the algorithm in mathematics and for this reason he called the grandfather of computer science by some people. The words “algorithm” came from Latin corruptions of his name from al-Khwarizmi to Algorisms. He also made major contributions to the fields of algebra, trigonometry, astronomy, geography and cartography. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his book on this subject; Hisab al-jabr wa al-muqabala ( Calculation by Completion and Balancing). It will be interesting to see what al-Khwarizmi wanted to say about the purpose of his book in his own word. He says: 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.

This does not sound like the contents of an algebra text, and indeed only the first part of the book has a discussion of what we would today recognize as algebra. However it is important to realize that the book was intended to be highly practical, and that algebra was introduced to solve real life problems that were part of everyday life in the Islamic world at that time.

Al-Khwarizmi continues his study of algebra by examining how the laws of arithmetic extend to his algebraic objects. For example he showed how to multiply out expressions such as (a + bx) (c + dx). Though it looks elementary, now, yet one can see a remarkable depth and novelty in these calculations done more than eleven centuries ago. The next part of al-Khwarizmi’s Algebra consists of applications and worked examples. He then goes on to look at rules for finding the area of figures such as the circle, and also finding the volume of solids such as the sphere, cone, and pyramid.

While major contributions of al-Khwarizmi were the result of original research, he also did a lot to synthesize the existing knowledge in these fields from Greek, Indian, and other sources. He was also responsible for the use of Arabic numerals in mathematics which originated in India but introduced to Arab world finally to Europe. His treatise on Hindu-Arabic numerals Ketab al-Jam wal tafriq hisab al Hind was translated in Latin as Algoritmi de numero Indorum and in English as Al-Khwarizmi on the Hindu Art of Reckoning. Unfortunately the Arabic version is lost. The work describes the Indian system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. The first use of zero as a place holder in positional base notation was explained by al-Khwarizmi in his work. When translation of his book came into the hands Europeans, they wrote a song for it and it reads like this: Here begins the Algorismus, The new art is called Algorismus, in which out of this twice five figures (1 to 9 & 0) we derive such benefit. This numeral system did not became very poplar in Europe till the fifteenth century mainly because of Church’s resistance to this new idea. Methods for arithmetical calculation and a method to find square roots is also described in this book. The decimal system was a fairly recent arrival from India, but it was al-Khwarizmi who expounded on it systematically and introduced it to Middle East and to the world at large.

Al-Khwarizmi did important work in astronomy, his book Zij al-Sindhind contains many important astronomical calculations, covering calendars, calculating true positions of the sun, moon and planets, tables of sine and tangents, spherical astronomy, parallax and eclipse calculations, and visibility of the moon. Although his astronomical work is based on that of the Indian astronomers, he must have been influenced by Ptolemy’s work also.

Al-Khwarizmi systematized and corrected Ptolemy’s research in geography, using his own original findings. He supervised the work of 70 geographers to create a map of the then known world. In his book Kitab surat al ard (The image of earth) he presented the latitudes and longitudes for 2400 localities including the big cities of Asia and Africa and located them on the map he created. He also wrote a book on mechanical devices like the clock, sundial, Jewish calendar, construction of astrolabes and a book of history.

There is no doubt that al-Khwarizmi was one of the brilliant Muslim scientist of his time and according to G. Sarton author of History of Science: one of the greatest mathematicians of all time. When his work became known in Europe through Latin and English translations, it made an indelible mark on the development of science and mathematics in Europe. His algebra book introduced that discipline to Europe and became the standard mathematical text at their universities until the 16th century. A crater on the far side of the moon is named after him.

Aslamsyed1@yahoo.com

10-14

Al-Khwarizmi did important work in astronomy, his book Zij al-Sindhind contains many important astronomical calculations, covering calendars, calculating true positions of the sun, moon and planets, tables of sine and tangents, spherical astronomy, parallax and eclipse calculations, and visibility of the moon. Although his astronomical work is based on that of the Indian astronomers, he must have been influenced by Ptolemy’s work also.

Al-Khwarizmi systematized and corrected Ptolemy’s research in geography, using his own original findings. He supervised the work of 70 geographers to create a map of the then known world. In his book Kitab surat al ard (The image of earth) he presented the latitudes and longitudes for 2400 localities including the big cities of Asia and Africa and located them on the map he created. He also wrote a book on mechanical devices like the clock, sundial, Jewish calendar, construction of astrolabes and a book of history.