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The Alexandrian mathematicians Hero of Alexandria and Diophantus continued the traditions of Egypt and Babylon, but Diophantus's book Arithmetica is on a much higher level and gives many surprising solutions to difficult indeterminate equations. This ancient knowledge of solutions of equations in turn found a home early in the Islamic world, where it was known as the "science of restoration and balancing." (The Arabic word for restoration, al-jabru,is the root of the word algebra.) In the 9th century, the Arab mathematician al-Khwarizmi wrote one of the first Arabic algebras, a systematic exposé of the basic theory of equations, with both examples and proofs. By the end of the 9th century, the Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities of algebra and solved such complicated problems as finding x, y, and z such that x + y + z = 10, x2 + y2 = z2, and xz = y2.

Ancient civilizations wrote out algebraic expressions using only occasional abbreviations, but by medieval times Islamic mathematicians were able to talk about arbitrarily high powers of the unknown x, and work out the basic algebra of polynomials (without yet using modern symbolism). This included the ability to multiply, divide, and find square roots of polynomials as well as a knowledge of the binomial theorem. The Persian mathematician, astronomer, and poet Omar Khayyam showed how to express roots of cubic equations by line segments obtained by...

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...A Brief Look at the Origin of Algebra Connie Beach Professor Clifton E. Collins, Sr. Math 105: Introduction to College Mathematics May 22, 2010 Abstract In this paper we look at the history of algebra and some of its different writers. Algebra originated in ancient Egypt and Babylon around 1650 B.C. Diophantus of Alexandria, a Greek mathematician, and Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī, a Persian mathematician from Baghdad, astronomer and geographer, shared the credit of being the founders of algebra. Diophantus, who is known as the “father of algebra”, carried on the work of the ancient Egyptians and Babylonians, but the word Algebra actually came from the word al-jabr, which is from al-Khwārizmī’s work, Kitab al-Jabr wa-l-Muqabala. The algebraic notation had gone through 3 stages: rhetorical (or verbal), stage, syncopated (use of abbreviated words) stage, and symbolism (the use of letters for the unknown) stage. As a matter of fact, the algebra that we know of today began during the 16th century, even though its history shows that it began almost 4000 years ago. A Brief Look at the Origin of Algebra I have always had a love for math. My favorite math class was Algebra; in fact, I had taken Algebra I, II, III, and IV all through high school, and aced every class. I can just look at a problem and know the answer. Then, I returned to college after 30 years, and took an Intro to College Math class. I wasn’t sure if I still remembered what I had learned...

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