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What is the history of algebra?

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From the ancient Babylonians to Islamic mathematicians to French philosophers, the history of algebra is the history of solving problems. With the rhetorical algebra of the Babylonians in BCE 2000, working with non-numeric objects using arithmetical operators to solve practical problems finds its roots. In CE 890, the Islamic mathematician Al-Khwarizimi wrote "The Compendious Book on Calculation by Completion and Balancing," in Arabic "Hidab al-jabr wal-muquabala," from which the term algebra derives.

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Although the roots of the word algebra date back to al-Khwarizimi's al-jabr, or "restoration of broken parts," the concepts date back to ancient times. In his work, Al-Khwarizimi translates and formalizes ideas and methods of the Greeks and Indians — ideas that date back to the Babylonians and their work with the quadratic equation. Other mathematicians of the Golden Age of Islam, like Omar Khayyam, built upon Al-Khwarizimi's algebra, solving more complex and more abstract problems including cubic equations without the aid of the modern algebraic symbology known today.

The Italian mathematician Leonardo Fibonacci, who popularized the use of the Hindu-Arabic number system in the West in the early 13th century, extended Khayyam's work on the cubic equation. Other Italian mathematicians in the 16th century solved the cubic equation around the time Rene Descartes, a French philosopher and mathematician, was working on his treatise, "Discours de la methode." In one of the appendices, "La Geometrie," Descartes used the symbols a, b and c for constant values and x, y and z for unknowns in developing algebraic equations to solve problems in geometry. This innovation not only established the symbols and methods for manipulating them commonly seen in algebra today, but it also sparked major advances in many fields of mathematics.

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