The science of mathematics, which began its journey in the world at a very early stage within the ancient civilizations of Mesopotamia, experienced what could be described as a golden age in the medieval Islamic world. For Islamic scholars, mathematics held great significance. In particular, the use of geometric forms in all areas of life, such as employing geometry to adorn mosque walls, calculating religious holidays, measuring land, and determining inheritance shares, led to a strong focus on numerical studies and ultimately gave rise to algebra.
Moreover, these scholarly endeavors illuminated not only the Islamic lands but also had a profound impact on the entire globe. A concrete example can be seen in medieval Europe, where science was often regarded with suspicion amid a gloomy and stifling intellectual climate. The door opened by the Renaissance would provide a means of escape and relief and without question, the refreshing intellectual atmosphere that revitalized Europe would come from the Islamic lands.
Not only mathematics but many other branches of science, over time, continued their journey that began in ancient times, passing through Egypt, India, and Babylon, within the realm of Islamic civilization. From there, this knowledge transferred to Europe and ultimately continued its course in the Americas during the modern era. The scientific heritage of Antiquity, which rightfully belonged to all of humanity, was severely neglected in the regions dominated by the Roman Empire during its decline. Scholars were persecuted, and intellectual curiosity was stifled. However, unlike the Roman and Byzantine emperors, the Islamic caliphs, across the vast regions united through the conquests of the Islamic armies, including Central Asia, the Middle East, North Africa, and Spain, honored science and seated it upon a throne of respect. They encouraged intellectual curiosity, and as a result, the dimming light of the world was rekindled by the illumination that emerged from the Islamic lands.
One of these scientific disciplines was, indeed, mathematics. In the intellectual climate shaped by figures such as Pythagoras and Euclid, mathematics had once been neglected. However, in the early 9th century, a scholar born in Khorasan would devote his life to this science and, through his contributions, propel it like an arrow toward the scholars of future generations. That individual was Muhammad ibn Musa al-Khwarizmi.
Al-Khwarizmi is recognized as one of the most brilliant minds of Islamic civilization. He is believed to have been born in the city of Khwarazm, in the region of Khorasan, and to have died in Baghdad. He spent most of his life devoted entirely to the pursuit of knowledge in Baghdad, where he conducted his most significant and productive work during the reign of the Abbasid Caliph al-Ma’mun. During that period, he worked alongside many renowned scholars at Bayt al-Hikmah, the most prestigious scientific academy in the Islamic world. Al-Khwarizmi’s acceptance into Bayt al-Hikmah came as a result of his substantial contributions to the fields of science and mathematics. He became so well-known in Baghdad that he was appointed to lead a scientific delegation sent from Baghdad to India. Moreover, he was entrusted with overseeing the team at the Qasioun Observatory located near Damascus.
Al-Khwarizmi conducted studies in five scientific disciplines. He studied Indian numerals and compiled astronomical tables. These tables, later reviewed by the Muslims of al-Andalus, served as a vital reference for astronomers across a vast region from Spain to China for centuries. He also prepared the earliest known geometric tables. Additionally, by the order of Caliph alMa’mun, he collaborated with sixty-nine scholars to compile a geographical encyclopedia. This work, known in Islamic history as “Kitab al-Jughrafiya” (The Book of Geography), provided the coordinates of cities and specific regions. The geographical areas were described in seven zones, and the work included the names of cities, mountains, seas, islands, the central points of certain regions, and rivers. These works reflect al-Khwarizmi’s brilliant intellect and boundless curiosity. Moreover, he remained committed to the principles of responsibility and accuracy in his research, emphasizing the importance of supporting sound and exemplary methods in scholarly endeavors.
In addition to being a mathematician, alKhwarizmi was also an astronomer, and in his astronomical studies, he made use of Indian numerals. These numerals would later be developed further by al-Khwarizmi himself and would come to be known in the West as Arabic numerals. His work introduced a completely new method to mathematical studies in Europe, which had become cumbersome due to the limitations of Roman numerals. His book Kitab al-Hisab al-Hindi (Book of Indian Computation) was translated into Latin in the 12th century by Gerard of Cremona under the title Algoritmi de numero Indorum (On Hindu Numerals). The first word of this Latin translation, Algoritmi, eventually evolved into the term “algorithm” or “algorism”, which came to refer to a numerical calculation system based on the decimal system.
Another one of his works, titled Kitab al-Mukhtasar fi Hisab al-Jabr wa’lMuqabalah, was the first mathematical book to include the word “al-jabr” (algebra) in its title. With this work, the science of algebra was, for the first time, separated from the science of arithmetic and established as an independent discipline within the sciences.
Thus, al-Khwarizmi came to be known in the history of science as “the Father of Algebra”. This title was attributed to him because he was the first to use the term “al-jabr” and the scholar who developed systematic methods for solving equations.
In this book, al-Khwarizmi classified the solutions to quadratic equations and provided geometric methods for completing the square. Notably, he did not use symbols in his work; instead, he expressed the squares and square roots of numbers through words.
However, without a doubt, the aspect of alKhwarizmi that brought him the most recognition is that we owe to him the introduction of the number “0,” representing the concept of nothingness in mathematics, as well as laying the foundation for what would later become the mathematical symbol “x”. Al-Khwarizmi introduced the mathematical heritage of Indian civilization to the Middle East and, in particular, through his use of zero, made significant contributions to the advancement of mathematics.
The story of zero is indeed a fascinating one. While al-Khwarizmi and his students used the decimal number system without fractions, they proposed the practice of placing a small circle beside the numbers to maintain the correct positional order. This small circle was referred to as “sifr”, meaning “empty” or “void”. Those who were students of Muslim scholars in the field of mathematics introduced this term to the West as “chiffre”, meaning “digit” or “numeral.” Meanwhile, in translations from Arabic into Latin, Western scholars referred to “sifr” as “zephyrum”. The Italians eventually shortened this term to “zero”, which remains used today.
Western scholars who study the history of science with seriousness and fairness now regard it as more than mere opinion; it is a historical reality: just as the Greek world is recognized as the birthplace of geometry, the Islamic world is acknowledged as the birthplace of algebra. In this context, al-Khwarizmi is rightfully accepted as the father of algebra.
Muslim mathematicians, led by al-Khwarizmi, studied the mathematical traditions of ancient Greece and India, further developed them, and introduced new mathematical concepts and techniques. Their work also had a profound influence on the development of Western mathematics. Thanks to these contributions by Muslim mathematicians, significant advancements were eventually made in various fields, including civil engineering, astronomy, and commerce.
