aljabr

Aljabr, more commonly known in English as algebra, is a branch of mathematics that studies rules for manipulating symbols representing numbers, variables, and expressions. The term algebra derives from the Arabic al-jabr, meaning "reunion of broken parts" or "completion," a key idea in solving equations. The word entered Western mathematics from al-Khwarizmi's 9th-century treatise Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala, translated in the 12th century as The Compendious Book on Calculation by Completion and Balancing.

Al-Khwarizmi's work presented systematic procedures for solving linear and quadratic equations, using methods described as completing the square and balancing. The approach emphasized reducing complex problems to simpler ones and restoring missing terms to restore a balance between sides of an equation. Early algebra was practical, aimed at problems in commerce, land measurement, and astronomy, and relied on geometric interpretations of quantities.

During the medieval Islamic world, other scholars expanded algebra beyond equations to include polynomial relations and algorithmic techniques. In Europe, translations of Arabic texts in the 12th century helped lay the groundwork for a symbolic algebraic tradition that developed over the following centuries and culminated in the modern use of symbols to express general relationships.

In modern times, algebra encompasses diverse areas from elementary algebra to abstract algebra, including linear algebra, polynomial algebra, and algebraic geometry. It remains fundamental in science, engineering, economics, and beyond, reflecting its origins in early Islamic mathematics and the work of al-Khwarizmi and his successors.