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The roots of algebra began with the ancient Babylonians, who developed an advanced arithmetical system with which they were able to do calculations in an algorithmic fashion. The Greeks provided the foundation, whereby the solutions of individual problems could be gathered and applied in a more general fashion. Indian mathematicians continued to build on the traditions laid down by the Babylonians, Egyptians, and Greeks. However, it is in the Islamic world where modern algebra began to take form.

Although several cultures helped shape algebra, one man is credited with writing down many of the rules known today. Al-Khwarizmi, known as the father of algebra, was a Muslim mathematician who, around 820, compiled these rules in a book called The Compendious Book on Calculation by Completion and Balancing. The word “algebra” is derived from al-jabr, one of the two operations Al-Khwarizmi used to solve quadratic equations. The word “algorithm” stems from the Latin form of his name.

Al-Khwarizmi's book established algebra as a mathematical discipline independent of geometry and arithmetic. The volume presented the various ways polynomial equations could be solved, and demonstrated how transferring subtracted terms to the other side of an equation and cancelling similar terms on opposite sides of an equation could result in its being solved. The Compendious Book was also noteworthy because it was written in ordinary language, which meant the average person could potentially understand the mathematical concepts.

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