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On Algebra-Part 2


Prof. Ibrahim B. Syed


Islamic Research Foundation International, Inc.

Louisville, Kentucky




Arabic Mathematics Worldwide

   In the 11th century, the Arab mathematical foundation was one of the strongest in the world. The Muslim mathematicians had invented geometrical algebra and had taken it to advanced levels, capable of solving third and fourth degree equations. The world witnessed a new stage in the development of mathematical science, driven by the numerous translated works from Arabic into European languages.

Unquestionably, Al-Khwarizmi was very influential with his methods on arithmetic and algebra which were translated into much of southern Europe. Again, these translations became popular as algorismi – a term which is derived from the name of Al-Khwarizmi. Not all went smoothly nonetheless. The Arabic numerals introduced by Al-Khwarizmi, like much of new mathematics, were not welcomed wholeheartedly. In fact, in 1299 there was a law in the commercial center of Florence (Italy) forbidding the use of such numerals. Initially, only universities dared use them, but later they became popular with merchants, and eventually became commonly used.

In time, Europe realized the great potential value of the Arab mathematical contributions and put into popular use all that seemed practical. The sciences, with mathematics as their essence, flourished and developed into the disciplines we know today. None would have been the same though, had it not been for that book on restoration, or had the zero not been invented, or had the Arabic numerals not made their way to Europe. That “fondness of science,” which inspired an early Arab mathematician to propose calculating by al-jabr and al-muqabala, did much to make the world run as we know it today.

The 10th millennium saw Muslim mathematical study concentrated in three main sub-disciplines. These were the ongoing progress in algebra, the development of arithmetic algorithms, and the increasing complexity in geometry. In addition, the introduction of the zero was destined to revolutionize mathematics as it allowed for key innovations. It was proposed by Muhammad Bin Ahmad in 967 AD. Zero arrived in the West much later, in 13th century.

In the field of Mathematics the number Zero (0) and the decimal system was introduced to Europe, which became the basis for the Scientific revolution. The Arabic numerals were also transferred to Europe, this made mathematical tasks much easier, problems that took days to solve could now be solved in minutes. The works of Al-Khwarizmi (his Latin name was Alghorismus) were translated into Latin.  Al-Khwarizmi (Alghorismus), from whom the mathematical term algorism was derived, wrote Sindh Ind, a compilation of astronomical tables. He, more importantly, laid the ground work for algebra and found methods to deal with complex mathematical problems, such as square roots and complex fractions. He conducted numerous experiments, measured the height of the earth's atmosphere and discovered the principle of the magnifying lens. Many of his books were translated into European languages. Trigonometric work by Alkirmani of Toledo was translated into Latin (from which we get the sine and cosine functions) along with the Greek knowledge of Geometry by Euclid. Along with mathematics, masses of other knowledge in the field of physical science was transferred.

High tech, 1000 CE

The high technology in the world of 1000 CE included paper, the printing press, the crossbow, gunpowder, the iron-chain suspension bridge, the kite, the magnetic compass, the wheelbarrow and the rotary fan. A millennium ago, these items were used extensively in China - and were practically unknown elsewhere. Globalization spread them across the world, including Europe.

A similar movement occurred in the Eastern influence on Western mathematics. The decimal system emerged and became well developed in India between the 2nd and 6th centuries. It was used by Arab mathematicians soon thereafter.


These mathematical innovations reached Europe mainly in the last quarter of the 10th century and began having an impact in the early years of the last millennium, playing an important part in the scientific revolution that helped to transform Europe.

East to Europe


The agents of globalization are neither European nor exclusively Western, nor are they necessarily linked to Western dominance. Indeed, Europe would have been a lot poorer - economically, culturally and scientifically - had it resisted the globalization of mathematics, science and technology at that time.


And today, the same principle applies, though in the reverse direction (from West to East). To reject the globalization of science and technology because it represents Western influence and imperialism would not only amount to overlooking global contributions - drawn from many different parts of the world - that lie solidly behind so-called Western science and technology, but would also be quite a daft practical decision, given the extent to which the whole world can benefit from the process.

Breaking boundaries

Certainly, the Renaissance, the Enlightenment and the Industrial Revolution were great achievements  -  and they occurred mainly in Europe and, later, in America. Yet many of these developments drew on the experience of the rest of the world, rather than being confined within the boundaries of a discrete Western civilization.


Our global civilization is a world heritage - not just a collection of disparate local cultures. When a modern mathematician in Boston invokes an algorithm to solve a difficult computational problem, he/she may not be aware that he/she is helping to commemorate the Arab mathematician Mohammad Ibn Musa-al-Khwarizmi, who flourished in the first half of the ninth century. (The word algorithm is derived from the name al-Khwarizmi.)


The square root of math itself

There is a chain of intellectual relations that link Western mathematics and science to a collection of distinctly non-Western practitioners, of whom al-Khwarizmi was one. (The term algebra is derived from the title of his famous book Al-Jabr wa-al-Muqabilah.)

Indeed, al-Khwarizmi is one of many non-Western contributors whose works influenced the European Renaissance and, later, the Enlightenment and the Industrial Revolution. The West must get full credit for the remarkable achievements that occurred in Europe and Europeanized America, but the idea of an immaculate Western conception is an imaginative fantasy.

Modern prosperity, with all its improvement in welfare, has been delivered to humanity by science and technology. In the last two centuries especially, science has delivered better lives for people, longer lives, and for larger populations. The key to unlocking the source of these benefits was scientific method, the relentless search for truth through observation, theorizing and experimentation.

In the 13th century the Muslim world, with its development of the culture of philosophy, science, mathematics, astronomy, physics, chemistry and medicine, led the world. The Muslim world once possessed in its hands the keys to the future prosperity that technology could deliver. Not only that, but with the invention of double entry bookkeeping, it possessed in its hands the blueprint of the plans for the modern corporation. Eventually, after several hundred years, Europe was able to absorb this knowledge and overthrow the dark constraint of its own religion to unlock the mysteries of science and discover the path to prosperity. If the Muslim world had been able to continue on the Qur'anic commands on scientific research, the cause of human progress would have been advanced by about five hundred years.


In conclusion algebra and algorithms are enabling the building of computers, and the creation of encryption. The modern technology industry would not exist without the contributions of Muslim mathematicians like Al-Khwarizmi.

Ms. Carly Fiorina, Hewlett-Packard's Chairman and CEO delivered a speech in Minneapolis, Minnesota on September 26, 2001. The title of her speech was 'TECHNOLOGY, BUSINESS AND OUR WAY OF LIFE: WHAT'S NEXT". She said "There was once a civilization that was the greatest in the world." ……."And this civilization was driven more than anything, by invention. Its architects designed buildings that defied gravity. Its mathematicians created the algebra and algorithms that would enable the building of computers, and the creation of encryption. Its doctors examined the human body, and found new cures for disease. Its astronomers looked into the heavens, named the stars, and paved the way for space travel and exploration."  "When other nations were afraid of ideas, this civilization thrived on them, and kept them alive.  When censors threatened to wipe out knowledge from past civilizations, this civilization kept the knowledge alive, and passed it on others."

"While modern Western civilization shares many of these traits, the civilization I'm talking about was the Islamic world from the year 800 to 1600, which included the Ottoman Empire and the courts of Baghdad, Damascus and Cairo, and enlightened rulers like Suleiman the Magnificent."

"Although we are often unaware of our indebtedness to this other civilization, its gifts are very much part of our heritage. The technology industry would not exist without the contributions of Arab mathematicians.  Sufi poet-philosophers like Rumi challenged our notions of self and truth.  Leaders like Suleiman contributed to our notions of tolerance and civic leadership. And perhaps we can learn a lesson from his example: It was leadership based on meritocracy, not inheritance.  It was leadership that harnessed the full capabilities of a very diverse population-that included Christianity, Islamic and Jewish traditions."










11. From The Islamic Herald, March 1995.        



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