Harold W. Kuhn

July 29, 1925 – July 2, 2014

Brief Biography

An important figure in mathematical programming and game theory, Harold Kuhn was born in Santa Monica, California. He completed his undergraduate education at California Institute of Technology – an education that was interrupted by service in the U. S. Army. After proving his linguistic abilities, Kuhn was trained to be a Japanese interpreter during the war crime trials but was discharged due to a knee operation that left him unable to travel abroad. His bachelor’s was followed by a masters and PhD in mathematics from Princeton University, where he would eventually teach and conduct research for 37 years

Inspired by George Dantzig's U. S. Air Force-sponsored research that produced the simplex method in linear programming, Princeton Professor Albert W. Tucker obtained funding from the Office of Naval Research (ONR) to launch his own research project. Tucker’s project would further explore duality relationships in mathematical programming. He convinced Kuhn and David Gale to join the team, which led to Kuhn's first contributions to OR theory at Princeton.

Kuhn's involvement in the ONR project shifted his interests to optimization and decision theory as the group studied John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior (1944) and other seminal work. Questions regarding the relationship between linear programming and the theory of electrical networks developed into an investigation by Tucker and Kuhn of duality in quadratic programming, and eventually in general nonlinear programming. At a RAND conference in 1950 they showed conditions for the relationship between primal and dual nonlinear programming (NLP) problems. Gale, Tucker, and Kuhn eventually received the John von Neumann Theory Prize in 1980 for their work.

In addition to his work on duality in NLP, Kuhn is also known for the development of the Hungarian Method, an algorithm for the problem of assigning of workers to tasks, which he published in the Naval Research Logistics Quarterly in 1955. The Hungarian Method was later shown to be the first algorithm of polynomial complexity for a large class of linear programs. In 2005, the Naval Research Logistics journal recognized Kuhn's 1955 publication as the best paper in the 50 years since its founding.

Kuhh was a very influential instructor. His courses (varying on such topics from game theory, managerial economics, and nonlinear programming) were highly praised by students and faculty alike. He pushed promising undergraduates such as John Birge and David Shmoys to take the courses that established their career directions.

 Kuhn is popularly known for his relation with fellow graduate student and colleage John Nash. Kuhn edited Nash's papers and was instrumental in the award to Nash of the 1994 Prize in Economic Sciences in Memory of Alfred Nobel. Kuhn served as a consultant on the biopic of Nash’s life, A Beautiful Mind (2001). Beyond his teaching, Kuhn served as Scientific Director and Board Member for Mathematica, Inc. from 1961 to 1983 and held a number of administrative posts at Princeton. Professor Harold Kuhn died July 2, 2014.

Other Biographies

Profiles in Operations Research: Harold W. Kuhn
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Wikipedia Entry for Harold W. Kuhn

(2004) INFORS' Operational Research Hall of Fame Harold W. Kuhn. International Transactions in Operations Research, 11: 714-718. (link)


California Institute of Technology, BS 1947

Princeton University, MS 1948

Princeton University, PhD 1950 (Mathematics Genealogy)


Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS

Application Areas

Oral Histories

Interview of Harold Kuhn at his home in Princeton, New Jersey, by Irv Lustig (then with ILOG), July 16, 2001.

NOTE: The video chapter transcripts are searchable, with search results displayed as marks on the time bar above the search box.  Click a mark to jump to the search word or phrase in the video and transcript, or click on any word in the transcript to jump to that point in the video.

Jump to Chapters

Chapter 1: Initial Introductions to Optimization
Chapter 2: Initial Computational Work
Chapter 3: Mathematical Programming and Optimization
Chapter 4: Pure and Applied Mathematics
Chapter 5: Early Career in Math Programming
Chapter 6: John von Neumann and Al Tucker
Chapter 7: Applications of Optimization
Chapter 8: Teaching Students
Chapter 9: Some Early "Stories of Practice"
Chapter 10: Symposium Zero
Chapter 11: The Future of Optimization
Chapter 12: Communication in the Early Days
Chapter 13: The Traveling Salesman Problem
Chapter 14: The Nobel Prize and Concluding Remarks

Memoirs and Autobiographies


Harold W. Kuhn in Wikimization

Kuhn H. W. (1991) Nonlinear Programming: A Historical Note. History of Mathematical Programming: A Collection of Personal Reminiscences, Lentra JK, AHG Rinnooy Kan and A Schriver, eds.  pp 19-31  North-Hollland  pp. 82-96

Kuhn H. W. (1991) On the Origin of the Hungarian Method.  History of Mathematical Programming: A Collection of Personal Reminiscences, Lentra JK, AHG Rinnooy Kan and A Schriver, eds.  pp 19-31  North-Holland pp. 77-81


Hotchkiss M. (2014) Harold Kuhn, Princeton mathematician who advanced game theory, dies at 88, July 5. Princeton University News. (link)

SIAM News. Obituaries: Harold Kuhn (1925-2014). Accessed December 20, 2014. (link)


Harold Kuhn Papers on the Committee on the Structure of the University, Mudd Manuscript Library, Princeton University (link)

Awards and Honors

John von Neumann Theory Prize 1980

The Institute for Operations Research and the Management Sciences Fellow 2002

International Federation of Operational Research Societies' Hall of Fame 2004

Professional Service

Society for Industrial and Applied Mathematics (SIAM), President 1954-5

Selected Publications

Kuhn H. W. & Tucker A., eds. (1950) Contributions to the Theory of Games,Volume I. Annals of Mathematical Studies 24. Princeton University Press: Princeton, NJ.

Gale D., Kuhn H. W., & Tucker A. (1951) Linear programming and the theory of games. Koopmans, T. C., ed. in Activity analysis of production and allocation, 317-329. Wiley: New York.

Kuhn H. W. & Tucker A. W. (1951) Nonlinear Programming. Neyman J, ed. in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 481-491. University of California Press: Berkeley.

Kuhn H. W. (1955) The Hungarian method for the assignment problem. Naval Research Logistics Quarterly 2(1-2): 83-97.

Kuhn H. W. (1956) Solvability and consistency for linear equations and inequalities. American Mathematical Monthly, 63: 217-232.

Kuhn H. W. (1968) Simplicial approximation of fixed points. Proceedings of the National Academy of Sciences, 61: 1238-1242.

Kuhn H. W. (1982) Nonlinear programming: a historical view. ACM SIGMAP Bulletin, (31): 6-18.

Kuhn H. W. (1991) On the Origin of the Hungarian Method. Lenstra J. K., Rinnooy Kan A. H. G., & Schrijver A., eds. in History of Mathematical Programming: A Collection of Personal Reminiscences I, 77-81. CWI/North Holland: Amsterdam.

Kuhn H. W., ed. (1997) Classics in Game Theory. Princeton University Press: Princeton, NJ. 

Kuhn H. W., Nasar S., & Nash J. (2007) The Essential John Nash. Princeton University Press: Princeton, NJ.