Dated: Thursday, April 18, 2013

by Salma Mansoor

Modern mathematics owes much of its existence to Islam. One of the early Islamic mathematicians of the middle ages developed many of the fundamental cornerstones of modern mathematics. The word algebra comes from the Arabic al-jabr, “restoration”. The field of algebra was developed by Muslim mathematicians in the Middle East and India.

Algorithms, the processes of mathematics and computer science, are named after the great Arabic mathematician al-Khwarizmi.

Our modern number system is called Hindu-Arabic in recognition of its origins in the number systems of India and Arabia. Our number system depends fundamentally on the number 0 (zero) which was invented by Arab mathematicians. A numeral is sometimes called a cipher (hence encipher, decipher) from the Arabic word sifr meaning zero.

Abu Ja’far Mohammed ibn Musa Al-Khwarizmi

The most distinguished of the Arabic mathematicians was the ninth century scholar Abu Ja’far Mohammed ibn Musa Al-Khwarizmi, who was an astronomer to the caliph at Baghdad. His name indicates that he was from the town of Khwarizm (now Khiva), on the Amu Darya river, south of the Aral Sea in what is now Uzbekistan. (Khwarizm was part of the Silk Route, a major trading pathway between Europe and the East.) Al-Khwarizmi’s full name can be translated as “Father of Ja’far, Mohammed, son of Moses, native of the town of Al-Khwarizmi”.

Al-Khwarizmi wrote several books that were to be enormously influential. In particular, his book describing how to write numbers and compute with them using the place-value decimal system that came out of India would, when translated into Latin three hundred years later, prove to be a major source for Europeans who wanted to learn the new system.

In fact, Al-Khwarizmi’s book on arithmetic with the Hindu-Arabic numbers was so important; it appears to have been translated several times.

Kitab al jabr w’al-muqabala

Another of Al-Khwarizmi’s manuscripts was called Kitab al jabr w’al-muqabala, which translates roughly as “restoration and compensation”. The book is essentially an algebra text. It starts off with a discussion of quadratic equations, then goes on to some practical geometry, followed by simple linear equations, and ending with a long section on how to apply mathematics to solve inheritance problems. The Englishman Robert of Chester translated Al-Khwarizmi’s algebra book from Arabic into Latin in 1145. The part dealing with quadratic equations eventually became famous. Such was the influence of this work that the Arabic phrase al jabr in the book’s title gave rise to our modern word “algebra”.

After Al-Khwarizmi, algebra became an important part of Arabic mathematics. Arabic mathematicians learned to manipulate polynomials, to solve certain algebraic equations, and more. For modern readers, used to thinking of algebra as the manipulation of symbols, it is important to realize that the Arabic mathematicians did not use symbols at all. Everything was done in words.

In addition to the translations of Al-Khwarizmi’s works, of particular note was the appearance in 1202 of Fibonacci’s book Liber abaci, which described the Hindu-Arabic place-value system for representing numbers, and explained how to compute with them. Fibonacci’s treatment was so good that it arguably had more influence than any other source on the eventual acceptance of the new number system around the world, including Al-Khwarizmi’s writings that had come much earlier.

Umar Al-Khayammi

One of the most famous Arabic mathematicians was ‘Umar Al-Khayammi, known in the West as Omar Khayyam, who lived approximately from 1048 to 1131. Although remembered today primarily as a poet, in his time he was also famous as a mathematician, scientist, and philosopher, doing major work in all those fields.