# The legacy of Al-Khwarizmi

Long back, in parts of the eighth and ninth centuries, there lived a Muslim mathematician and astronomer, Muhammad ibn Musa. Though nothing certain is known about his place of birth, as per the tenth-century bibliographer and biographer Ibn al-Nadim, he was born in Khwarizm, owing to which he came to be popularly known as Muhammad Al-Khwarizmi or simply Al-Khwarizmi. It is pertinent to mention that the word algorithm is derived from Al-Khwarizm.
It was the work of Al-Khwarizmi that set the systematic and foundational basis of what is now popularly known as Algebra. From his work, “al-Kitāb al-Mukhtaṣarfī Ḥisāb al-Jabrwal-Muqābalah” translated into English as “The Compendious Book on Calculation by Completion and Balancing”, the word Algebra came into light. The book expounded upon the basics of transportation of terms and cancelling of like terms, besides the fundamental concepts of reduction and balancing. In the words of Victor Katz, it is the first true algebra text that is still extant. According to Robertus Castrensis, the book was used as the principal textbook in European universities as far as the sixteenth century. This book didn’t just introduce the fundamentals of balancing, but it, at the same time, offered practical answers for land distribution, inheritance rules and salary distribution.
The importance of the book and the contributions of the author are hard to overstate. Al-Khwarizmi’s text was not an emulation of the Babylonians. It was non-routine and out of the ordinary. In the words of R. Rashed and Anjela Armstrong, “Al-Khwarizmi’s text can be seen to be distinct not only from the Babylonian tablets but also from the Diophantus’ Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study.” In the words of J. J. O’Connor and E. F. Robertson, “Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.”
Apart from mathematics, al-Khwarizmi made significant contributions to the study of geography. His contributions to medieval geography, his systematising and correcting Ptolemy’s work on geography, and his findings concerning the shape of the earth are noteworthy. Praiseworthy also to mention that he created, with the help of seventy subordinate geographers, the map of the then known world. His works on the astrolabe and the Jewish calendar speak for themselves.
He is famous for teaching the world the solution of linear and quadratic equations by putting them in six different standard forms. Although al-Khrawizmi confined his discussion of polynomial equations to those of degrees one and two, known as linear and quadratic equations, that is not all he is known for. Calculation of the position of celestial objects such as the sun, the moon besides some other planets, his work on spherical geometry, his work on the tables of sines and tangents and his parallel and eclipse calculations are awe-inspiring.
One of the issues that were a hindrance to his worldwide recognition for his contributions was the fact his works were written in Arabic. The language was a barrier when it came to catering to the needs or intellectual aspirations of a worldwide and world-class audience. Fortunately, his book on algebra, which is for some people the only work they remember him, was translated twice into Latin, once by Gerard of Cremona and then by Robert of Chester in the twelfth century. This resulted in a wider recognition of the book.
Unlike most of the discoveries and inventions of today, algebra was introduced to the Europeans much later, some three-hundred years later, after it made its appearance in the works of al-Khwarizmi. Unfortunately, such contributions seem few and far between now. The Muslim world seems to have given a wide berth to its legacy and it seems to have forgotten its forerunners in the fields of science, art, literature and astronomy. However, the journey of a thousand miles is said to begin with a single step. The legacy can be capitalised upon. Mathematics is not for fun alone. It is, as John Locke said, a way to settle in the mind a habit of reasoning. In the words of Alfred North Whitehead, “Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.” And one must not forget that it is a legacy worth continuing.

—The writer is Assistant Professor at Government Degree College Sopore. [email protected]