Algebra has been developed over thousands of years in several different countries. The earliest methods for solving mathematical problems with one or more unknown quantities come from ancient Egypt. The word "algebra" itself is derived from the title of Baghdad mathematician Al-Kwarizmi's 9th century book, "Hidab al-jabr wal-muqubala."

The ancient Babylonians and Greeks also had methods for solving equations with unknown quantities. The 2nd century Greek Diophantus continued the Greek tradition with his work "Arithmetica;" however, he had no generalized method for solving equations. After the fall of Rome, progress in the development of algebra continued in India, Egypt and Iraq (then known as Persia).

Hindu mathematicians were the first to discover that quadratic equations have two roots. Islamic math was influential in the development of Western European mathematical techniques. Knowledge of algebra trickled into Europe starting in the 12th century with a translation of Al-Kwarimi's work, and received fuller development starting in the 1500s. Abstract or modern algebra is a 19th-century British development of the field.