Proof of the Alternating Sign Matrix Conjecture

The number of n × n matrices whose entries are either $-1$, $0$, or $1$, whose row- and column- sums are all $1$, and such that in every row and every column the non-zero entries alternate in sign, is proved to be [1!4! (3n-2)!] [n!(n+1)! (2n-1)!], as conjectured by Mills, Robbins, and Rumsey.