The Mathematical Work of Jon Kleinberg Find the Mathematics; Then Solve the Problem

The Rolf Nevanlinna Prize is awarded by the International Mathematical Union for “outstanding contributions in mathematical aspects of information sciences”. Jon Kleinberg, the 2006 recipient of the Nevanlinna Prize, was cited by the prize committee for his “deep, creative, and insightful contributions to the mathematical theory of the global information environment”. Our purpose is to present an overall perspective on Kleinberg’s work as well as a brief summary of three of his results: • the “hubs and authorities” algorithm, based on structural analysis of link topology, for locating high-quality information on the World Wide Web; • methods for discovering short chains in large social networks; and • techniques for modeling, identifying, and analyzing bursts in data streams. Kleinberg’s Nevanlinna citation includes two other areas in which he has made important contributions: theoretical models of community growth in social networks and the mathematical theory of clustering. Readers interested in learning more about his work on these topics should consult the list of papers given on his home page [8].