How many alternating sign matrices are there? This question generated considerable interest in the early 1980s displaying deep connections to enumerative combinatorics of plane partitions. We shall review the story of this connection (following closely D. Bressoud's excellent book) which ultimately lead to the tour de force answer given by Zeilberger in 1996. In part III of this lecture we focus further on Kuperberg's approach using statistical mechanics. Speaker(s): Thomas Bothner (University of Michigan)