We describe the Fundamental Theorem on Symmetric Polynomials (FTSP), exposit
a classical proof, and offer a novel proof that arose out of an informal course
on group theory. The paper develops this proof in tandem with the pedagogical
context that led to it. We also discuss the role of the FTSP both as a lemma in
the original historical development of Galois theory and as an early example of
the connection between symmetry and expressibility that is described by the
theory.Comment: 15 pages, 1 figure. Corrected a misattributio
