A clique is a subset of vertices in which every pair is connected by an edge. Finding the maximum clique is NP-complete (Karp 1972) and hard to approximate within n^(1-ε) for any ε>0 (Hastad 1996, assuming NP≠ZPP). The Bron-Kerbosch algorithm with pivoting finds all maximal cliques in O(3^(n/3)) time. Max clique underlies social network analysis (finding tightly-knit communities), bioinformatics (protein interaction networks), and coding theory (error-correcting codes via Ramsey theory).