Alan J Hoffman was born on May 30, 1924 in New York City. After military service, he graduated from Columbia College in 1947, and received his PhD in 1950 from Columbia University with a dissertation "On the Foundations of Inversion Geometry". He spent a year at the Institute for Advanced Study, and has worked at the National Bureau of Standards, the Office of Naval Research (London), and Management Consultation Services, General Electric Company. Until his recent retirement, he worked 41 years at the IBM T J Watson Research Center. He has also held adjunct and visiting professorships at City University of New York, Yale, Stanford, Technion, Georgia Institute of Technology, and Rutgers. His exuberance and enthusiasm in research and teaching is legendary.

• The Variation of the Spectrum of a Normal Matrix (with H W Wielandt) - Integral Boundary Points of Convex Polyhedra (with J Kruskal) - On Moore Graphs with Diameters 2 and 3 (with R R Singleton) - Cycling in the Simplex Algorithm - On Approximate Solutions of Systems of Linear Inequalities - On the Polynomial of a Graph - Some Recent Applications of the Theory of Linear Inequalities of Extremal Combinatorial Analysis - On Simple Linear Programming Problems - Self-Orthogonal Latin Squares (with R K Brayton & D Coppersmith) - On the Nonsingularity of Complex Matrices (with P Camion) - A Generalization of Max Flow-Min Cut - A Characterization of Comparability Graphs and of Interval Graphs (with P C Gilmore) - and 33 other papers

Alan J Hoffman was born on May 30, 1924 in New York City. After military service, he graduated from Columbia College in 1947, and received his PhD in 1950 from Columbia University with a dissertation "On the Foundations of Inversion Geometry". He spent a year at the Institute for Advanced Study, and has worked at the National Bureau of Standards, the Office of Naval Research (London), and Management Consultation Services, General Electric Company. Until his recent retirement, he worked 41 years at the IBM T J Watson Research Center. He has also held adjunct and visiting professorships at City University of New York, Yale, Stanford, Technion, Georgia Institute of Technology, and Rutgers. His exuberance and enthusiasm in research and teaching is legendary.

• The Variation of the Spectrum of a Normal Matrix (with H W Wielandt) - Integral Boundary Points of Convex Polyhedra (with J Kruskal) - On Moore Graphs with Diameters 2 and 3 (with R R Singleton) - Cycling in the Simplex Algorithm - On Approximate Solutions of Systems of Linear Inequalities - On the Polynomial of a Graph - Some Recent Applications of the Theory of Linear Inequalities of Extremal Combinatorial Analysis - On Simple Linear Programming Problems - Self-Orthogonal Latin Squares (with R K Brayton & D Coppersmith) - On the Nonsingularity of Complex Matrices (with P Camion) - A Generalization of Max Flow-Min Cut - A Characterization of Comparability Graphs and of Interval Graphs (with P C Gilmore) - and 33 other papers

Alan J Hoffman was born on May 30, 1924 in New York City. After military service, he graduated from Columbia College in 1947, and received his PhD in 1950 from Columbia University with a dissertation "On the Foundations of Inversion Geometry". He spent a year at the Institute for Advanced Study, and has worked at the National Bureau of Standards, the Office of Naval Research (London), and Management Consultation Services, General Electric Company. Until his recent retirement, he worked 41 years at the IBM T J Watson Research Center. He has also held adjunct and visiting professorships at City University of New York, Yale, Stanford, Technion, Georgia Institute of Technology, and Rutgers. His exuberance and enthusiasm in research and teaching is legendary.

• The Variation of the Spectrum of a Normal Matrix (with H W Wielandt) - Integral Boundary Points of Convex Polyhedra (with J Kruskal) - On Moore Graphs with Diameters 2 and 3 (with R R Singleton) - Cycling in the Simplex Algorithm - On Approximate Solutions of Systems of Linear Inequalities - On the Polynomial of a Graph - Some Recent Applications of the Theory of Linear Inequalities of Extremal Combinatorial Analysis - On Simple Linear Programming Problems - Self-Orthogonal Latin Squares (with R K Brayton & D Coppersmith) - On the Nonsingularity of Complex Matrices (with P Camion) - A Generalization of Max Flow-Min Cut - A Characterization of Comparability Graphs and of Interval Graphs (with P C Gilmore) - and 33 other papers