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The development of algebra can be represented as Egyptian algebra, Babylonian algebra, Greek geometric algebra, Diophantine algebra, Hindu algebra, Arabic algebra, European algebra since 1500 and modern algebra. The development of algebraic notation progressed through three stages: the rhetorical (or verbal) stage, the syncopated stage (in which abbreviated words were used) and the symbolic stage, with which we are all familiar. Since algebra grows out of arithmetic, recognition of new numbers – irrationals, zero, negative numbers and complex numbers – is an important part of its history.

Classical algebra was first developed by the ancient Babylonians, who had a system similar to our algebra. They were able to solve for unknown quantities (variables) and had formulas and equations. This may seem elementary, but many advanced civilizations solved such problems geometrically because it was more visual. This is similar to the idea of graphing two linear equations to see where they intersect rather than directly solving for the solution. The Chinese began to publish their own algebra writings around 100 BC.

The history of algebra is split into two basic kinds of algebra. One is called Classical Algebra (equation solving or "find the unknown number" problems) and another is called Modern, or Abstract Algebra (the study of groups, rings and fields). Classical algebra has been developed over a period of 4000 years. Abstract algebra has only appeared in the last 20.

Modern Algebra has come into existence much more recently, emerging over the past 200 years. This is a very complicated study of abstract ideas that are useful for mathematicians and scientists. It also includes some more basic topics like Boolean algebra and matrix multiplication.

The word ²Algebra² was first used around 800AD by the Arabic scholars and literally means the re-union of broken parts. While in ancient civilizations the basics of algebra were only studied by advanced mathematicians and scientists, now it is taught routinely to 7^th and 8^th graders. That is why it is important to know the history of algebra in order to identify the present status of modern day mathematics. Of course, you first need a good knowledge of arithmetic and logic to master algebra. However, algebra is the fundamental language of math that actually allows you to "do" anything.

The history of algebra is closely connected with such names as the Alexandrian mathematicians Hero of Alexandria and Diophantus, the Arab mathematician al-Khwarizmi, the Egyptian mathematician Abu Kamil, the Persian mathematician, astronomer and poet Omar Khayyam, the great Italian mathematician Leonardo Fibonacci, the Italian mathematicians Scipione del Ferro, Niccolò Tartaglia and Gerolamo Cardano, the Norwegian mathematician Niels Abel and the French mathematician Evariste Galois, the French philosopher and mathematician René Descartes, the German mathematician Carl Friedrich Gauss.

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