  Major Percy A. MacMahon's first paper on plane partitions included a
conjectured generating function for symmetric plane partitions. This conjecture
was proven almost simultaneously by George Andrews and Ian Macdonald, Andrews
using the machinery of basic hypergeometric series and Macdonald employing his
knowledge of symmetric functions. The purpose of this paper is to simplify
Macdonald's proof by providing a direct, inductive proof of his formula which
expresses the sum of Schur functions whose partitions fit inside a rectangular
box as a ratio of determinants.
