Mathematics is the key to understanding the universe and its contents, events and phenomena. The significance of this science is comparable to that of the basic necessities of life. Mathematics is often understood as a study that deals with quantities, magnitudes, and the relations between numbers and symbols. In science, the study of a particular substance or an event, which usually include the study of its structure, order, and other properties, evolved from elemental practices of counting, measuring, and description of the substance or event. Thus, mathematics can be thought of as a science that deals with logical reasoning and quantitative calculation. Over the years, its development has involved an increasing degree of idealisation and abstraction of its subject.
Mathematics embraces three main subject matters: arithmetic, geometry, and analytical mathematics. Each of these divisions is then divided into either pure or abstract, wherein abstract mathematics considers magnitude or quantity abstractly, without relation to matter. On the other hand, pure mathematics treats magnitude as subsisting in material bodies, and is consequently interwoven with physical considerations. Arithmetic is the most useful of all sciences, and probably no other branch of human knowledge is more widely spread among the masses. Arithmetic is related to the use of integers, rational numbers, real numbers, or complex numbers under the operations of addition, subtraction, multiplication, and division. It is the foundation of all mathematics, pure or applied.
In the seventh century A.D., the Prophet Muhammad (S.A.W.) was sent to the people of Arabia. Within a decade of his death, Muslims had conquered all of the Arabian Peninsula. Within a century, Islam had spread from Al Hamrah in Spain to the borders of China. Islam unified science, theology, and philosophy. Muslims were commanded to study, seek knowledge, and learn and benefit from experiences of others by Allah (S.W.T.) in the holy Quran and by the Prophet Muhammad (S.A.W.) in the Sunnah. It was this that inspired Muslims to great heights in sciences, medicine, mathematics, astronomy, chemistry, philosophy, art and architecture.
The glorious ear of Islamic civilisation emerged with the work of many Muslim scholars in various fields, but particularly in mathematics, led by al-Khwarizmi (780-850), Thabit bin Qurrah (826–901), Abu al-Karaji (953-1029), al-Hazen (965–1040), and Omar Khayyam (1048–1131).
The development of mathematical science was significant in the reign of the Abbasid empire. In this period, Islamic civilisation forged a golden age, particularly after the establishment of the Bayt al-Hikmah (House of Wisdom) by Caliph Ma‘mun, who ruled during 813-833.
The Bayt al-Hikmah, which would last more than 200 years, carried out translation of many ancient works from Greek manuscripts which were obtained through treaties. By the end of the 9th century, the major works of the Greeks had been translated. In addition, they learned the mathematics of the Babylonians and the Hindus.
Al Khwarizmi worked in the ninth century under the patronage of the Caliph Al Ma’mun in Baghdad. He became a member of Dar-ul Hikme, which means the House of wisdom, an academy of scientists founded in Baghdad most probably by Caliph Kharun Rhasid. But the academy owes its pre-eminence to Al Ma’mun, a great patron of learning and scientific investigation. At the time of Al Ma’mun, not only the science of mathematics but also other sciences lived a golden age. Early in his career, Al Khwarizmi went to Afghanistan and then to India, he met Indian scholars. After coming back to Baghdad, he introduced Hindu mathematics and astronomy. At that time, he wrote an astronomical table which is known in Arabic as Sindhind. In this period, he taught addition, subtraction, multiplication, and division for traders, survey officers, and finance officers at Dar-ul Hikme. He taught some particular calculations that were important for Cadis (Islamic lawyers) to implement the law of heritage in Islam.
While teaching at Dar-ul Hikme, Al Khwarizmi published his most popular book, Al Kitab Al Jabr Wa’al Muqabelah, which was written in Arabic in 830. This book made him famous in the east and west. Al Kitab Al Jabr Wa’al Muqabelah has been translated into English as The Book of Restoration and Balancing. In his algebra, Al Khwarizmi did not use symbols but expressed everything in words: For the unknown quantity he employs the word shay (thing or something). For the second power of the quantity he employs the word mal (wealthy). For the unit he uses dirham. The idea of root was explained as a line x1. There is a duality in the measuring of jadh (root) because an area corresponds to the first power x. Thus jadh as the side of a square (x) multiplied by the square unit x1. Al Kitab Al Jabr Wa’al Muqabelah includes forty different problems. The book consists of one preference, appendix and five main chapters.
The Babylonians were capable of solving particular instances of quadratic problems. Al-Khwarizmi, however, gave general solutions for these problems. This was a huge step forwards. A Babylonian who was good at Mathematics would have to carefully consider each new quadratic problem (‘new’ meaning ‘having different numbers’). Al-Khwarizmi, meanwhile, could simply apply his method. This was guaranteed to work, was less prone to mistakes, and was easier and faster. Mathematicians are actually lazy: they like looking for general solutions, rather than having to think every time a new instance of the problem comes along.
About the quadratic formula, among other things, Al-Khwarizmi wrote ‘The Compendious Book on Calculation by Completion and Reduction’. The book was so useful that it was later translated into Latin, so that West European scientists could read it. Some Arabic words, however, were apparently hard to translate. For example, the Arabic word pronounced as ‘al-jabr’ means something like ‘completion’ or ‘restoration’. The translator for some reason did not actually translate it, but instead created a new Latin word with a similar pronunciation: ‘algebra’. Because of this, the readers thought that ‘algebra’ was a word that described the techniques used by Al-Khwarizmi, so that’s where we get the word algebra from. In a similar way, the name ‘Al-Khwarizmi’ became ‘Algorismus’ In Latin, from which our word ‘algorithm’ is derived.
—The writer is studying for a Masters at JK Institute of Mathematical Sciences, Srinagar.