Middle Ages Technologies

Muslim Algebra

by Ricia Elwell-Socci

Al’ Khwarizmi’s stories illustrate how much the Muslim Community and government supported local mathematicians and the invention of algebra.

Harun al-Rashid was the 5 th Caliph of Abbasid dynasty on 14 September 786 around the time that Al Khwarizmi was born. He had two sons. When he died his sons fought over the rule and eventually the younger one defeated his brother and took over his fathers rule. Al-Mamun continued his father’s desire for learning and built the House of Wisdom, Bayt Al-Hikma, in Baghdad . He also built a library that housed significant manuscripts, many about astronomy, from the Byzantine Empire and beyond and observatories for Muslim astronomers so that they could expand the knowledge of earlier scholars. Muhammad said “He who travels in search of knowledge, travels along Allah’s path of Paradise .”

At the House of Wisdom, Greek philosophical and scientific works were translated. Scholars from all around the world came to study at the House of Wisdom. The most famous students at the House of Wisdom at this time were, Al’ Khwarizmi, who studied algebra, geometry and astronomy and three brothers, the Banu Musa who studied geometry and celestial mechanics

Al’ Khwarizmi was the man who first discovered algebra. The first great advance in the Muslim world was the introduction to Arabic numerals. It first originated in India and it was simplified and made the development of algebra possible. “In al-Khwarizmi's time, algebra was a practical system for solving all kinds of problems in cases of inheritance, contracts, surveying, tax collection, 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.”

In the absence of mathematics, collecting taxes was harsh and unfair. Collecting taxes was usually done by “tax farmers”, who usually were able to extort, intimidate and confiscate property. In the 13 th century, the Muslim community used mathematical advances to create centralized bureaucracy; the taxes were then fair, predictable and orderly. An organized government could do things for its people such as building roads and make informed decisions about what to do with the collected tax money.

With algebra, business was booming. Using mathematics, they were able to use banks where you could exchange a letter of credit from Bagdad in have it be accepted in places like Samarkand in Central Asia or Kairouan in North Africa.

They frequently used imported goods from one country, to export to another, such as horses and camels, from the Arabian Peninsula , cloth and pearls from the Gulf. They also traded medicines, paper and sugar.

Mathematics made trading with people in India , the Philippines , Malaya , the East Indies , and China possible. Between the 8 th and the 11 th century, they traded what people needed, metals, grains and woods. They exported, too. They frequently used imported goods from one country, to export to another, such as horses and camels, from the Arabian Peninsula , cloth and pearls from the Gulf. They also traded medicines, paper and sugar.

Al’ Khwarizmi wrote many books on math, but his most famous book is al-jabra w’al muabala or in English, The Comprehension Book on Calculation by Completion and Balancing. From the title of his book, they got al-jabra which is our algebra. This shows that the Muslim community was doing wonderful things and was technologically advanced. They were able to use what was invented in hat time. Algebra literally means ‘restoration of balance.’ Other than algebra, applications and how to find area and volume were in his book. The longest section of his book consists only of solved problems that come up during legacies and inheritances. Al’ Khwarizmi said: “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.”

Before algebra, the Muslim community used the numbers used the numbers invented by the Gupta’s. Since the invention of algebra there have been new improvements such as using abbreviations and using the multiplication, division, addition and subtraction (X, /, +, -) in the 16 th century. Before abbreviations were used, people wrote out the equations using words. For example: Area of a Circle = pi multiplied by the radius squared, now it’s written as A= π R 2. Here is an example from his book: “ If the instance be, 'ten and thing to be multiplied by thing less ten,' then this is the same as 'if it were said thing and ten by thing less ten. You say, therefore, thing multiplied by thing is a square positive; and ten by thing is ten things positive; and minus ten by thing is ten things negative. You now remove the positive by the negative, then there only remains a square. Minus ten multiplied by ten is a hundred, to be subtracted from the square. This, therefore, altogether, is a square less a hundred dirhems.” Now we don’t even use the symbols! Algebra can be used in many real life times, such as knowing how many right answers you need to pass a test. It is used to order stock and plan budgets.

Algebra was a wonderful innovation and was and still is used all the time. Thanks to Al-Mamun, the House of Wisdom was built, allowing algebra, among other things, to be created. It was created because of Arabic numerals and is a simplified version of something that originated out of India . There have been improvements like using symbols and abbreviations to make algebra easier.

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