  The Fundamental Lemma is a somewhat obscure combinatorial identity introduced
by Robert P. Langlands as an ingredient in the theory of automorphic
representations. After many years of deep contributions by mathematicians
working in representation theory, number theory, algebraic geometry, and
algebraic topology, a proof of the Fundamental Lemma was recently completed by
Ngo Bao Chau, for which he was awarded a Fields Medal. Our aim here is to touch
on some of the beautiful ideas contributing to the Fundamental Lemma and its
proof. We highlight the geometric nature of the problem which allows one to
attack a question in p-adic analysis with the tools of algebraic geometry.
