The invention of algebra is primarily credited to Muhammad ibn Musa al- Khwarizmi, a Persian mathematician of the Islamic Golden Age. He wrote a seminal work titled Al-Jabr wal-Muqabala ("The Compendious Book on Calculation by Completion and Balancing") around 820 AD, which systematically presented the solution of linear and quadratic equations and introduced fundamental algebraic concepts such as "reduction" and "balancing" (transposing terms across an equation)
. Al-Khwarizmi is often called the "father of algebra" because he was the first to treat algebra as an independent discipline and teach it in an elementary and systematic form for its own sake, rather than as a tool for solving specific problems. His work marked a revolutionary shift from the Greek focus on geometry to an abstract algebraic approach, allowing a broader development of mathematics
. While earlier mathematicians like Diophantus contributed to algebraic methods, their work was more problem-specific and syncopated, whereas Al- Khwarizmi's algebra was fully rhetorical and generalized. Some historians debate the title, but Al-Khwarizmi's text is considered the first true algebra book still extant and foundational for the discipline
. In summary, Muhammad ibn Musa al-Khwarizmi invented algebra as a formal mathematical discipline, and the very word "algebra" derives from the title of his influential treatise Al-Jabr
