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The word "algebra" is named after the Arabic word "al-jabr" from the title of the book [al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala' , (The book of Summary Concerning Calculating by Transposition and Reduction), a book written by the Muslim mathematician, Muhammad ibn Mūsā al-Khwārizmī in 820. The word Al-Jabr means "reunion. In fact, many ancient civilizations developed some sort of algebraic methods of solving problems, as far back as the Babylonians, Diophantus of Alexandria and the Indian mathematicians such as Brahmagupta, but Al-Khwarizmi is considered by many to be the "father of algebra" because some of his techniques on solving quadratic equations are still in use today. He was the first to solve equations using general methods. He solved the linear indeterminate equations, quadratic equations, second order indeterminate equations and equations with multiple variable. 
J. J. O'Conner and E. F. Robertson wrote in the MacTutor History of Mathematics archive:

"Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.

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