The word “algebra” comes from the Arabic word “al-jabr”, which was used in the year 830 by the Muslim Mathematician Muhammad ibn Mūsā al-Khwārizmī in the thesis named Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing. According to some history sources, the word “al-jabr” meant the transposition of subtracted terms to the other side of the equation, which is used to bring balance within the equation. In other words, it meant cancellation of the similar terms on the opposite sides of an equation.
Even though it can be said that Musa al-Khawarizmi set the pillars of algebra and paved the road for the future algebraists, the origins of algebra can be tracked back to the ancient Babylonians, who were highly interested in approximations for solving their rhetorical algebraic equations. This is the main reason why they developed a positional number system. The origins of Algebra can also be traced in Egypt where, the most extensive Egyptian Mathematical document is found. This document dates 1650 BC and was written by Ahmes.
Compared to both Babylonian and Egyptian algebra, Greek algebra was taken to a different stage as mathematicians of the time created Geometric algebra. In this kind of algebra, the terms were expressed by geometric objects, which were used to solve equations. Interestingly, the equations were solved using a process that the Greek mathematicians invented, named “the application of areas”. It can be surely said that Greek mathematicians (especially Euclid) have highly contributed in bringing algebra to a higher level, compared to their predecessors from Babylonia and Egypt.
Algebra was a science which also attracted mathematicians from other parts of the world like China and India. The oldest Chinese mathematics document dates to at least 300 BCE, while the oldest Indian mathematics documents dates to around the 6th century BCE. Most of the Indian mathematics books suggest that number systems were the area of their study.
Nonetheless, algebra reached its peak in the second half of the 8th century, when Islam became a worldwide culture and research in mathematics highly increased. It was at this time when Muslim scholars began translating almost every Greek works, including Euclid’s Elements and Ptolemy’s Almagest. The importance of knowledge became significant in the Muslim world to the point that Byzantine Empire would give Muslims the Greek works in exchange for treaties. Therefore, Muslim scholars were influenced by Hindu, Mesopotamian, and Greek scholars.
Influenced by great scholars, Muslim mathematicians bring algebra to the level which we know today. It is Muhammad ibn Mūsā al-Khwārizmī that, according to Angela Armstrong, “he introduced us to the idea of an equation which does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems.” It is this great mathematician that introduces us to the fundamental concept of reduction and balancing which we use even today when solving equations.