Vol. 7, Issue 2, Part C (2025)

The study of algebra, one of the fundamental branches of mathematics, traces its origins from ancient civilizations to modern computational applications. Algebra’s history can be divided into key phases, beginning with the Babylonians, who developed rudimentary methods for solving linear and quadratic equations around 2000 BCE. Ancient Greek mathematicians further contributed by formalizing geometric approaches to problems that are algebraic in nature. The significant advancement occurred during the Islamic Golden Age, where scholars like Al-Khwarizmi introduced systematic techniques and symbolic representation, laying the groundwork for modern algebra. During the European Renaissance, algebra evolved rapidly with the introduction of symbolic notation and the development of solutions to cubic and quartic equations. The 19^th and 20^th centuries saw a shift from solving specific equations to studying abstract structures such as groups, rings, and fields, giving rise to modern abstract algebra. Today, algebra plays a crucial role in various disciplines, including computer science, physics, and economics, demonstrating its enduring significance and versatility. This paper provides a comprehensive review of algebra’s historical milestones, key contributors, and conceptual developments, highlighting how ancient practices have influenced contemporary mathematical thought and applications. By tracing algebra’s evolution, the study emphasizes the cumulative nature of mathematical knowledge and its continuous adaptation to solve increasingly complex problems. Understanding this historical progression not only deepens appreciation for algebra but also informs its teaching, research, and application in diverse scientific fields.