the bait al-hikmah became one of the Muslim world’s most famous and influential libraries and centres of research under Caliph al-Ma’mun’s patronage. He went out of his way to recruit some of the most talented philosophers, scientists, geographers and mathematicians of his time to this institute in order to teach and conduct advanced research in science, mathematics and philosophy. As expected, al-Khwarizmi occupied a prominent position in bait al-hikmah, where he studied and conducted research in a host of disciplines including astronomy, geography, history, music and mathematics, which was his most favourite subject. Deeply impressed by al-Khwarizmi’s mathematical abilities, the Caliph personally asked him to head the department of astronomical research at bait al-hikmah. He not only excelled in astronomy, he also went on to make seminal contributions in a number of other scientific subjects, and authored an influential book on history entitled Kitab al-Tarikh (The Book of History), which later inspired celebrated Muslim historians like Abul Hasan al-Mas’udi and al-Tabari to produce their own works on the subject.
It was under Caliph Harun al-Rashid’s patronage that pioneering Muslim scholars and translators like Hajjaj ibn Yusuf ibn Matar al-Hasib and Abu Yahya al-Batriq first began to translate the philosophical and scientific contributions of the ancient Greeks into Arabic. The Muslim scientists and mathematicians not only translated and preserved ancient Greek intellectual heritage (such as Euclid’s Elements, Ptolemy’s Almagest and the vast corpus of Aristotelian logic for the benefit of posterity), they also explored and analysed the intellectual and cultural contribution of other ancient civilisations, including those of Persia, India and China. Their thirst for knowledge and wisdom inspired them to learn, assimilate and refine the works of the ancients and make their own original contributions in all the branches of knowledge. According to some historians, al-Khwarizmi’s quest for knowledge took him all the way to India, where he mastered traditional Indian science and mathematics. It was also during his stay in India that he became familiar with the zero-based decimal system for the first time. Although it is not clear how long he stayed in India, he lived there for long enough to have gained proficiency in Sanskrit, the lingua franca of ancient India, as he was thoroughly familiar with this language. During this period al-Khwarizmi discovered that the ancient Indians used a blank space to denote ‘nothing’ or ‘nil’ (sunya), which inspired him to coin the Arabic word sifr meaning ‘nothing’, just as its Latin equivalent, ciphrium, later came to denote ‘zero’. However, according to other historians, there is no credible evidence to suggest that al-Khwarizmi visited India. On the contrary, they argue that he became familiar with Indian arithmetic and astronomy from translated manuscripts which were available in Baghdad at the time. Either way, his discovery of the concept of ‘zero’ enabled him to lay the foundations of a new decimal system, which is today widely known as Arabic numerals, and in so doing he revolutionised the study of mathematics forever.
By all accounts, al-Khwarizmi’s contribution to mathematics was both unique and unprecedented. In addition to systematically analysing the geometric algebra of the Greeks and the arithmeticised algebra of the Indians, he also conducted research into Babylonian algebra. His complete mastery of Greek, Indian and Babylonian mathematics enabled him to critically evaluate the contribution of the ancients before he went onto develop his own fresh ideas and thoughts on the subject. The originality of his mathematical contribution is most evident from the fact that the word ‘algebra’ was derived directly from the title of his famous book on the subject, entitled Kitab al-Mukhtasar fi Hisab al-Jabr wa’l Muqabalah (The Summarised Treatise on the Process of Calculation for Integration and Equation). This book was one of the first of its kind written by a Muslim. In this book, he systematically defined and developed algebra for the first time in the history of mathematics (it was later translated into Latin by Robert of Chester, under the title of Liber Algebras et al-Mucabala). Known popularly as Hisab al-Jabr wa’l Muqabalah, this seminal mathematical treatise was divided into five chapters, in each of which the author rigorously and systematically examined and analysed different dimensions of algebra.
In the first chapter, al-Khwarizmi discussed the nature of linear and quadratic equations, and showed how they could be explained and resolved without providing any demonstrative proof. He also divided quadratic equations into six categories in order to highlight their separate geometrical configurations. During his investigations, he discovered that quadratic equations had two different roots, one being positive which he accepted, and the other being negative which he rejected. In so doing, he developed a fresh approach to the study and exploration of such equations. In the next chapter, al-Khwarizmi showed how quadratic equations could be resolved in a demonstrative way by utilising geometric methods. In the third and fourth chapters, he analysed and explored problems posed by multiplication and explained how differences between sums, squares and methods of locating square roots of hidden or unknown quantities in equations could be resolved. In the fifth and final chapter of the book, he developed solutions for a host of mathematical problems using different algebraic formulae. As expected, these mathematical problems were complex and multi-layered, and they required original and imaginative solutions, but al-Khwarizmi was able to define and resolve them, one by one, in a masterly fashion. Indeed, he used around eight hundred different demonstrative equations to show how calculations of integration and equation could be performed.
Al-Khwarizmi’s work in the field of arithmetic and algebra was of such a high standard that it would not be an exaggeration to say that he was the pioneer, or father, of these important branches of mathematics. His book on arithmetic entitled Kitab al- Jam’ wa’l Tafriq bi’l Hisab al-Hindi (The Book of Aggregation and Division in Indian Mathematics) was not only a pioneering mathematical contribution, it also became a hugely influential book. After Bon Compagni translated it into Latin in 1157, it became a popular textbook on arithmetic throughout medieval Europe. A copy of this translation is still extant to this day in Rome. The book also introduced Arabic numerals and the concept of ‘zero’ or ‘cipher’ into the Western world for the very first time, and in so doing it helped to popularise the application of basic arithmetic into every area of modern life. Al-Khwarizmi’s scholarship had such a pervasive influence on Western science and technology that he became known as ‘Algorithm’ across Europe, and throughout the centuries his Latinised name became synonymous with the word ‘arithmetic’ in the West. Today ‘algorithm’ refers to a technique which is used in the field of computer science for carrying out analysis using recurring methods. Without al-Khwarizimi’s seminal contributions in arithmetic, algebra, trigonometry and other branches of mathematics, it would not have been possible for Copernicus, Kepler, Galileo, Newton and others to achieve as much as they did in the field of astronomy, physics, mathematics and chemistry. Thanks also to al-Khwarizmi, today man can travel to space; fly aeroplanes; watch satellite television, and also count up to a zillion without any problems or difficulties. By revolutionising the study of mathematics, he completely revolutionised our vision of ourselves and, indeed, our vision of the future for the benefit of whole humanity.
If scientists like Sir Issac Newton were a rare breed, then geniuses like al-Khwarizmi were even rarer. His contribution to mathematics aside, al-Khwarizmi was also a brilliant astronomer and geographer. Once, when Caliph al-Ma’mun commissioned him to measure the meridian from a location close to the Euphrates, he accomplished the task by inventing an astronomical device which was far superior to anything the Greeks had produced. In fact, he not only accurately measured and determined the sphericity of the earth, he also suggested ways in which the process could be made easier in the future, by improving the device he had invented. Towards the end of his life he authored a book on geography entitled Kitab Surat al-Ard (The Book on the Shape of the Earth). In this book, he went to great lengths to correct Ptolemy’s misconceptions about different aspects of geography, geology and other related sciences. The publication of this book also marked the beginning of the science of geography in the Muslim world. All subsequent Muslim scientists and geographers (such as Abu Kamil, Sind ibn Ali, Sinan ibn Fath and Abul Wafa al-Bujazani) were one way or another influenced by this pioneering book. In total, al-Khwarizmi authored more than a dozen books on all the sciences of his time. He died at the age of sixty-seven and was laid to rest in Baghdad.
