Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and his work with linear programming. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman.
Born in Portland, Oregon, George Bernard Dantzig was named after George Bernard Shaw, the Irish writer. His father, Tobias Dantzig, was a Baltic German mathematician and linguist, and his mother, Anja Dantzig (née Ourisson), was a French linguist. Dantzig's parents met during their study at the Sorbonne University in Paris, where Tobias studied mathematics under Henri Poincaré, after whom Dantzig's brother was named. The Dantzigs immigrated to the United States, where they settled in Portland, Oregon.
Early in the 1920s the Dantzig family moved from Baltimore to Washington. His mother became a linguist at the Library of Congress, and his father became a math tutor at the University of Maryland, College Park, George attended Powell Junior High School and Central High School; one of his friends there was Abraham Seidenberg, who also became a professional mathematician. By the time he reached high school he was already fascinated by geometry, and this interest was further nurtured by his father, challenging him with complicated problems, particularly in projective geometry.
George Dantzig earned bachelor's degrees in mathematics and physics from the University of Maryland in 1936, and his master's degree in mathematics from the University of Michigan in 1938. After a two-year period at the Bureau of Labor Statistics, he enrolled in the doctoral program in mathematics at the University of California, Berkeley, where he studied statistics under Jerzy Neyman.
With the outbreak of World War II, George took a leave of absence from the doctoral program at Berkeley to join the U.S. Air Force Office of Statistical Control. In 1946, he returned to Berkeley to complete the requirements of his program and received his Ph.D. that year. Although he had a faculty offer from Berkeley, he returned to the Air Force as mathematical advisor to the comptroller.
In 1952 Dantzig joined the mathematics division of the RAND Corporation. By 1960 he became a professor in the Department of Industrial Engineering at UC Berkeley, where he founded and directed the Operations Research Center. In 1966 he joined the Stanford faculty as Professor of Operations Research and of Computer Science. A year later, the Program in Operations Research became a full-fledged department. In 1973 he founded the Systems Optimization Laboratory (SOL) there. On a sabbatical leave that year, he headed the Methodology Group at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. Later he became the C. A. Criley Professor of Transportation Sciences at Stanford, and kept going, well beyond his mandatory retirement in 1985.
He was a member of the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences. George was the recipient of many honors, including the first John von Neumann Theory Prize in 1974, the National Medal of Science in 1975, an honorary doctorate from the University of Maryland, College Park in 1976. The Mathematical Programming Society honored Dantzig by creating the George B. Dantzig Prize, bestowed every three years since 1982 on one or two people who have made a significant impact in the field of mathematical programming.
One day in 1939, Dantzig arrived late for class taught by Professor Neyman and mistakenly thought that two unsolved problems in statistics that Neyman had written on the board were homework problems. After a few days of struggling, he solved them and returned them to Neyman as homework. Dantzig described the event in his own word:
During my first year at Berkeley I arrived late one day to one of Neyman's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework - the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever.
About six weeks later, at 8 a.m. on a Sunday morning, he and Anne were awakened by Neyman banging on their front door who said, "I have just written an introduction to one of your papers. Read it so I can send it out right away for publication." The solution to the second homework problem became part of a joint paper with Abraham Wald who proved it in 1950, unaware that Dantzig had solved it. Neyman suggested Dantzig to submit his answers to the "homework" problems as his doctoral dissertation when he was looking for area for research for his doctorate. These experiences ended up as a sermon for a Lutheran minister and the basis for the film, "Good Will Hunting."
Freund wrote further that "through his research in mathematical theory, computation, economic analysis, and applications to industrial problems, [Dantzig] has contributed more than any other researcher to the remarkable development of linear programming".
Dantzig's seminal work allows the airline industry, for example, to schedule crews and make fleet assignments. Based on his work tools are developed "that shipping companies use to determine how many planes they need and where their delivery trucks should be deployed. The oil industry long has used linear programming in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. It is used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas".
An event in Dantzig's life became the origin of a famous story in 1939 while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.
Six weeks later, Dantzig received a visit from an excited professor Neyman, who was eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics. He had prepared one of Dantzig's solutions for publication in a mathematical journal. As Dantzig told it in a 1986 interview in the College Mathematics Journal:
A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.
Years later another researcher, Abraham Wald, was preparing to publish a paper which arrived at a conclusion for the second problem, and included Dantzig as its co-author when he learned of the earlier solution.
This story began to spread, and was used as a motivational lesson demonstrating the power of positive thinking. Over time Dantzig's name was removed and facts were altered, but the basic story persisted in the form of an urban legend, and as an introductory scene in the movie Good Will Hunting.
Linear programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming arose as a mathematical model developed during World War II to plan expenditures and returns in order to reduce costs to the army and increase losses to the enemy. It was kept secret until 1947. Postwar, many industries found its use in their daily planning.
The founders of this subject are Leonid Kantorovich, a Russian mathematician who developed linear programming problems in 1939, Dantzig, who published the simplex method in 1947, and John von Neumann, who developed the theory of the duality in the same year.
Dantzig's original example of finding the best assignment of 70 people to 70 jobs exemplifies the usefulness of linear programming. The computing power required to test all the permutations to select the best assignment is vast; the number of possible configurations exceeds the number of particles in the universe. However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the Simplex algorithm. The theory behind linear programming drastically reduces the number of possible optimal solutions that must be checked.
In 1963, Dantzig’s Linear Programming and Extensions was published by Princeton University Press. Rich in insight and coverage of significant topics, the book quickly became “the bible” of linear programming.
Books by George Dantzig:
- 1953. Notes on linear programming. RAND Corporation.
- 1956. Linear inequalities and related systems. With others. Edited by H.W. Kuhn and A.W. Tucker. Princeton University Press.
- 1963. Linear programming and extensions. Princeton University Press and the RAND Corporation. pdf from RAND
- 1966. On the continuity of the minimum set of a continuous function. With Jon H. Folkman and Norman Shapiro.
- 1968. Mathematics of the decision sciences. With Arthur F. Veinott, Jr. Summer Seminar on Applied Mathematics 5th : 1967 : Stanford University. American Mathematical Society.
- 1969. Lectures in differential equations. A. K. Aziz, general editor. Contributors: George B. Dantzig and others.
- 1970. Natural gas transmission system optimization. With others.
- 1973. Compact city; a plan for a liveable urban environment. With Thomas L. Saaty.
- 1974. Studies in optimization. Edited with B.C. Eaves. Mathematical Association of America.
- 1985. Mathematical programming : essays in honor of George B. Dantzig. Edited by R.W. Cottle. Mathematical Programming Society.
- 1997. Linear programming 1: Introduction. G.B.D. and Mukund N. Thapa. Springer-Verlag.
- 2003. Linear programming 2: Theory and Extensions. G.B.D. and Mukund N. Thapa. Springer-Verlag.
- 2003. The Basic George B. Dantzig. Edited by Richard W. Cottle. Stanford Business Books, Stanford University Press, Stanford, California.
- Dantzig, George B. (1960), "General convex objective forms", in Arrow, Kenneth J.; Karlin, Samuel; Suppes, Patrick, Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium, Stanford mathematical studies in the social sciences, IV, Stanford, California: Stanford University Press, pp. 151–158, ISBN 9780804700214.
Articles, a selection:
- Dantzig, George B. (June 1940). "On the Non-Existence of Tests of 'Student's' Hypothesis Having Power Functions Independent of σ". The Annals of Mathematical Statistics 11 (2): 186–92. doi:10.1214/aoms/1177731912. JSTOR 2235875.
- Wood, Marshall K.; Dantzig, George B. (1949). "Programming of Interdependent Activities: I General Discussion". Econometrica 17 (3/4): 193–9. JSTOR 1905522.
- Dantzig, George B. (1949). "Programming of Interdependent Activities: II Mathematical Model". Econometrica 17 (3): 200–211. doi:10.2307/1905523.
- Dantzig, George B. (1955). "Optimal Solution of a Dynamic Leontief Model with Substitution". Econometrica 23 (3): 295–302. doi:10.2307/1910385.
- Dantzig-Wolfe decomposition
- Knapsack problem
- Maximum flow problem
- Optimization (mathematics)
- Travelling salesman problem
- Gass, Saul I. (2011). "George B. Dantzig". Profiles in Operations Research. International Series in Operations Research & Management Science 147. pp. 217–240. doi:10.1007/978-1-4419-6281-2_13. ISBN 978-1-4419-6280-5.
- Joe Holley (2005). "Obituaries of George Dantzig". In: Washington Post, May 19, 2005; B06
- Richard W. Cottle, B. Curtis Eaves and Michael A. Saunders (2006). "Memorial Resolution: George Bernard Dantzig". Stanford Report, June 7, 2006.
- Albers, Donald J.; Alexanderson, Gerald L.; Reid, Constance, eds. (1990). "George B. Dantzig". More Mathematical People. Harcourt Brace Jovanovich. pp. 60–79. ISBN 978-0-15-158175-7.
- National Science Foundation - The President's National Medal of Science
- Albers, Donald. More Mathematical People Contemporary Conversations. 1990: Harcourt Brace Jovanovich. ISBN 978-0151581757.
- Albers and Reid (1986). "An interview with George B. Dantzig : the father of linear programming". The College Mathematics Journal 17: 293–314.
- "The Life and Times of the Father of Linear Programming".
- "The Unsolvable Math Problem".
- Robert Freund (1994). "Professor George Dantzig: Linear Programming Founder Turns 80". In: SIAM News, November 1994.
- "The Unsolvable Math Problem". Snopes. June 28, 2011.
- Dantzig, George (1940). "On the non-existence of tests of" Student's" hypothesis having power functions independent of σ". The Annals of Mathematical Statistics. doi:10.1214/aoms/1177731912.
- Allende, Sira M.; Bouza, Carlos N. (2005). "Professor George Bernard Dantzig, Life & Legend" (PDF). Revista Investigación Operacional 26 (3): 205–11.
- Dantzig, George; Wald, Abraham (1951). "On the Fundamental Lemma of Neyman and Pearson". The Annals of Mathematical Statistics. Retrieved 14 October 2014.
- Todd, Michael J. (2011). "Review: The Basic George B. Dantzig, by Richard W. Cottle". Bull. Amer. Math. Soc. (N.S.) 48 (1): 123–129. doi:10.1090/S0273-0979-2010-01303-3.
- Cottle, Richard; Johnson, Ellis; Wets, Roger (March 2007). "George B. Dantzig (1914–2005)" (PDF). Notices of the American Mathematical Society 54 (3): 344–62.
- "Professor George Dantzig: Linear Programming Founder Turns 80", SIAM News, November 1994
- O'Connor, John J.; Robertson, Edmund F., "George Dantzig", MacTutor History of Mathematics archive, University of St Andrews.
- Dantzig, George B. (1990). "The Diet Problem". Interfaces 20 (4): 43–7. doi:10.1287/inte.20.4.43. JSTOR 25061369.
- Cottle, Richard W. (2005). "George B. Dantzig: a legendary life in mathematical programming". Mathematical Programming 105 (1): 1–8. doi:10.1007/s10107-005-0674-4. ISSN 0025-5610.
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- Works by or about George Dantzig in libraries (WorldCat catalog)
- O'Connor, John J.; Robertson, Edmund F., "George Dantzig", MacTutor History of Mathematics archive, University of St Andrews.
- Obituaries of George Dantzig
- Interview with George B. Dantzig: The Father of Linear Programming - The College Mathematical Journal, 1986
- INFORMS George Dantzig Memorial Website
- George Dantzig at the Mathematics Genealogy Project