The history of algebra itself is broken into several sub-categories, and has been expanded upon by several hundred of the world greatest mathematicians. Some of the sub-categories include the Fundamental Theorem of Algebra, abstract linear spaces, as well as quadratic, cubic and quartic equations.
Not only can Algebra be divided into sub-categories as subjects, but the groups that studied, or developed them can also categorize them. Egyptian Algebra, Babylonian Algebra, Greek Geometric Algebra, Diophantine Algebra, Hindu Algebra, Arabic Algebra, European Algebra since 1500, and modern Algebra are the most popular categories. All the different theories within Algebra each have been worked millions of times, checked and rechecked for their validity