Al Khawarizmi ” Algebra’s Father”

The terms Algebra and Algorithm are familiar to all of us but how many have heard of their founder Mohammed Al-Khawarizmi. In Geography he revised and corrected Ptolemy’s view and produced the first map of the known world in 830 CE.

His Life

Abu Abdallah Muhammad ibn Musa Al-Khawarizmi. The last-mentioned name (his nisba) refers to his birthplace, Khwarizm, modern Khiva, south of the Aral Sea. He was born around 780 in the town of Kath part of Khwarism. He died around 850. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, ” Al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala”.

In the twelfth century Gerard of Cremona and Roberts of Chester translated the algebra of Al-Khawarizmi into Latin. Mathematicians used it all over the world until the sixteenth century.

He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma’mun, the caliph, overseeing 70 geographers.

When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

Work:

Al-Khawarizmi was a mathematician, astronomer and geographer. He was perhaps one of the greatest mathematicians who ever lived, as, in fact, he was the founder of several branches and basic concepts of mathematics. In the words of Phillip Hitti:

“He influenced mathematical thought to a greater extent than any other mediaeval writer.”

His work on algebra was outstanding, as he not only initiated the subject in a systematic form but he also developed it to the extent of giving analytical solutions of linear and quadratic equations, which established him as the founder of Algebra.

Hisab Al-jabr wAl-muqabala, contains analytical solutions of linear and quadratic equations and its author may be called one of the founders of analysis or algebra as distinct from geometry. He also gives geometrical solutions (with figures) of quadratic equations, for example x2 + 1Ox = 39, an equation often repeated by later writers. The ‘Liber ysagogarum Alchorismi in artem astronomicam a magistro A. [Adelard of Bath] compositus!’ deals with arithmetic, geometry, music, and astronomy; it is possibly a summary of Al-Khawarzmi’s teachings rather than an original work.

His astronomical and trigonometric tables, revised by Maslama Al-Majrti (Second half of tenth century), were translated into Latin as early as l126 by Adelard of Bath. They were the first Muslim tables and contained not simply the sine function but also the tangent (Maslama’s interpolation).

His arithmetic synthesised Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. Thus, he explained the use of zero, a numeral of fundamental importance developed by the Arabs. Similarly, he developed the decimal system so that the overall system of numerals, ‘algorithm’ or ‘algorizm’ is named after him. In addition to introducing the Indian system of numerals (now generally known as Arabic numerals), he developed at length several arithmetical procedures, including operations on fractions. It was through his work that the system of numerals was first introduced to Arabs and later to Europe, through its translations in European languages.

He developed in detail trigonometric tables containing the sine functions, which were probably extrapolated to tangent functions by Maslamati.

He also perfected the geometric representation of conic sections and developed the calculus of two errors, which practically led him to the concept of differentiation. He is also reported to have collaborated in the degree measurements ordered by Al-Mamun which were aimed at measuring of volume and circumference of the earth.

Al-Khwārizmī corrected Ptolemy’s gross overestimate for the length of the Mediterranean Sea from the Canary Islands to the eastern shores of the Mediterranean; Ptolemy overestimated it at 63 degrees of longitude, while al-Khwarizmi almost correctly estimated it at nearly 50 degrees of longitude. He “also depicted the Atlantic and Indian Oceans as open bodies of water, not land-locked seas as Ptolemy had done.”

His Books

Several of his books were translated into Latin in the early 12th century. In fact, his book on arithmetic, Kitab Al-Jam’a wal- Tafreeq bil Hisab Al-Hindi, was lost in Arabic but survived in a Latin translation. His astronomical tables were also translated into European languages and,later,into Chinese. His geography captioned Kitab Surat-Al-Ard,(The Face of the Earth) together with its maps, was also translated. In addition, he wrote a book on the Jewish calendar Istikhraj Tarikh Al-Yahud, and two books on the astrolabe. He also wrote Kitab Al-Tarikh and his book on sun-dials was captioned Kitab Al-Rukhmat, but both of them have been lost.

Zīj al-Sindhind (Astronomical tables of Sind and Hind) is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of sine values.

A Servant of God

Al-Khawarizmi emphasised that he wrote his algebra book to serve the practical needs of the people concerning matters of inheritance, legacies, partition, law suits and commerce. He considered his work as worship to God.