King R.B. Beyond the Quartic Equation

Birkhäuser Boston, 1996. - 157 pages.One of the landmarks in the history of mathematics is the proof of the non existence of algorithms based solely on radicals and elementary arithmetic operations (addition, subtraction, multiplication, and division) for solutions of general algebraic equations of degrees higher than four. This proof by the French mathematician Evariste Galois in the early nineteenth century used the then novel concept of the permutation symmetry of the roots of algebraic equations and led to the invention of group theory, an area of mathematics now nearly two centuries old that has had extensive applications in the physical sciences in recent decades.