Galois Theory I: An Historical Perspective

Abstract

Galois theory sits atop a structure of work began about 4000 years ago on the question of how to solve polynomial equations algebraically by radicals, that is, how to solve equations of the form

$$ a_n x^n + a_{n - 1} x^{n - 1} + ... + a_0 = 0 $$

by applying the four basic arithmetical operations (addition, subtraction, multiplication and division), and the taking of roots, to the coefficients of the equation and to other “known” quantities (such as elements of the base field).