A History of Abstract Algebra

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For about three millennia, until the early nineteenth century, “algebra” meant solving polynomial equations, mainly of degree four or less. Questions of notation for such equations, the nature of their roots, and the laws governing the various number systems to which the roots belonged, were also of concern in this connection. All these matters became known as classical algebra. (The term “algebra” was only coined in the ninth century AD.) By the early decades of the twentieth century, algebra had evolved into the study of axiomatic systems. The axiomatic approach soon came to be called modern or abstract algebra. The transition from classical to modern algebra occurred in the nineteenth century.

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