Arabic algebra refers to the mathematical tradition stemming from the work of Arabic and Islamic scholars during the Golden Age of Islam, most notably the contributions of Muḥammad ibn Mūsā al-Khwārizmī. Al-Khwārizmī's 9th-century treatise, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala ("The Compendious Book on Calculation by Completion and Balancing"), laid the foundations for what we now recognize as algebra.
Here's a breakdown of what characterized Arabic algebra:
- Al-Jabr (Completion): This refers to the process of removing negative terms from an equation by adding the same quantity to both sides. For example, transforming x² = 40x - 4x² into 5x² = 40x.
- Al-Muqābala (Balancing): This refers to the process of simplifying an equation by reducing positive terms of the same power when they occur on both sides. For example, transforming 50 + x² = 29 + 10x into 21 + x² = 10x.
- Focus on Solving Equations: Arabic algebra heavily emphasized finding solutions to practical problems involving equations, particularly linear and quadratic equations.
- Rhetorical Algebra: Al-Khwarizmi's algebra was primarily "rhetorical," meaning that equations were expressed in words rather than symbols. Symbolic algebra developed later.
- Systematic Approach: Al-Khwarizmi provided systematic methods for solving various types of equations, categorizing them and offering step-by-step procedures. He identified six canonical forms for linear and quadratic equations, which he then solved.
- Practical Applications: While theoretical, the development of algebra was motivated by practical applications in areas such as inheritance calculations, trade, land surveying, and construction.
While Al-Khwarizmi is often credited as the "father of algebra", it is important to acknowledge that his work built upon earlier mathematical traditions from the Greeks (Diophantus), Indians, and Babylonians. Arabic scholars preserved, translated, and expanded upon this knowledge, making significant advancements and transmitting it to Europe, where it further developed into the modern algebra we know today. The very word "algebra" is derived from "al-jabr," underscoring the profound influence of this period.
In essence, Arabic algebra represents a crucial stage in the development of algebra as a distinct branch of mathematics, characterized by its systematic approach to solving equations and its emphasis on practical applications.
