The Fundamental Theorem on Symmetric Polynomials: History's First Whiff of Galois Theory

摘要

We describe the Fundamental Theorem on Symmetric Polynomials (FTSP), exposita classical proof, and offer a novel proof that arose out of an informal courseon group theory. The paper develops this proof in tandem with the pedagogicalcontext that led to it. We also discuss the role of the FTSP both as a lemma inthe original historical development of Galois theory and as an early example ofthe connection between symmetry and expressibility that is described by thetheory.