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| {{Infobox scientist
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| |name = George Bernard Dantzig
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| |image =
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| |image_size = 210px
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| |caption = <!--(not needed as image is straightforward portrait)-->
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| |birth_date = {{birth date|1914|11|8}}
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| |birth_place = [[Portland, Oregon]]
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| |death_date = {{death date and age|2005|5|13|1914|11|8}}
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| |death_place = [[Stanford, California]]
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| |citizenship = [[United States of America|American]]
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| |fields = [[Mathematician]]<br />[[Operations research]] <br />[[Computer science]]<br />[[Economics]] <br />[[Statistics]]
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| |workplaces = U.S. Air Force Office of Statistical Control<br />[[RAND Corporation]]<br />
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| [[University of California, Berkeley]]<br />[[Stanford University]]
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| |alma_mater = [[Bachelor's degrees]] - [[University of Maryland, College Park|University of Maryland]]<br />[[Master's degree]] - [[University of Michigan]]<br />[[Doctor of Philosophy]] - [[University of California, Berkeley]]
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| |doctoral_advisor = [[Jerzy Neyman]]
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| |doctoral_students = <!-- [[Philip Abrahamson]]<br />[[Jeffrey Adachi]]<br /> Ilan Adler <br /> [[Muhamed Aganagic]] <br /> Kurt Anstreicher <br /> [[Earl Bell, Jr.]]<br />[[James Bigelow]]<br /> John Birge <br /> Richard W. Cottle <br /> [[Ronald Davis]]<br />[[Pierre De Mazancourt]]<br />[[Gregory Dobson]] <br /> B. Curtis Eaves <br />[[Mostafa El Agizy]]<br />[[Robert Entriken]] --> <br /> [[Robert Fourer]] <br /> <!-- Saul Gass <br />[[Eric Horvitz]]<br />[[Hui Hu]] <br /> Alfredo Iusem <br />[[Peter Jackson]] <br /> --> [[Ellis L. Johnson]] <br /> <!-- [[Stepan Karamardian]]<br />[[Edward Klotz]] <br /> Hiroshi Konno <br /> [[Alamuru Krishna]]<br />[[Robert Leary]] <br />Stephanie Leichner <br /> Irvin Lustig <br /> --> [[Thomas Magnanti]] <br /> <!-- [[Steven Maier]] <br /> S. Thomas McCormick, V <br /> David Morton <br />[[Vincent Nicholson]] <br /> André Perold <br /> [[John Pisa]]<br />[[Mark Prindiville]]<br />[[Paul Rech]]<br />[[Dan Scott]]<br />[[Samirendra Sinha]] <br /> [[John Stone]] <br /> Mukund Thapa <br /> Craig Tovey <br /> Alan Tucker <br /> Richard Van Slyke <br /> --> [[Roger J-B Wets]] <!-- <br /> [[Carlos Winkler-Piwenka]] <br /> Robert Wittrock <br /> [[Richard Wollmer]] --> <br /> [[Yinyu Ye]] <!-- <br /> [[Chang Yu]] <br /> -->
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| |notable_students =
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| |known_for = [[Linear programming]] <br /> [[Simplex algorithm]] <br /> [[Dantzig–Wolfe decomposition|Dantzig-Wolfe decomposition principle]] <br /> Generalized linear programming <br /> Generalized upper bounding <br /> [[Max-flow min-cut theorem#Linear program formulation|Max-flow min-cut theorem of networks]] <br />[[Quadratic programming]] <br /> Complementary pivot algorithms <br /> Linear complementary problem <br />[[Stochastic programming]]
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| |awards = [[John von Neumann Theory Prize]] [1974]<br />
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| [[National Medal of Science]] (USA) in Mathematical, Statistical, and Computational Sciences [1975]<br> [[Harvey Prize]] [1985]
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| |religion =
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| |influences = [[Wassily Leontief]] <br /> [[John von Neumann]] <br /> Marshal K. Wood
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| |influenced = [[Kenneth J. Arrow]] <br /> Robert Dorfman <br /> [[Leonid Hurwicz]] <br /> [[Tjalling C. Koopmans]] <br /> [[Thomas L. Saaty]] <br /> [[Paul Samuelson]] <br /> [[Philip Wolfe (mathematician)|Philip Wolfe]]
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| |signature = <!--(filename only)-->
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| |footnotes =
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| }}'''George Bernard Dantzig''' (November 8, 1914 – May 13, 2005) was an [[United States|American]] [[mathematical sciences|mathematical scientist]] who made important contributions to [[operations research]], [[computer science]], [[economics]], and [[statistics]].
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| Dantzig is known for his development of the [[simplex algorithm]],<ref>{{cite doi|10.1007/978-1-4419-6281-2_13}}</ref> an algorithm for solving [[linear programming]] problems, and his work with linear programming. In [[mathematical statistics|statistics]], Dantzig solved two [[open problem]]s in [[statistical theory]], which he had mistaken for homework after arriving late to a lecture of [[Jerzy Neyman]].<ref name= "JH05">Joe Holley (2005). [http://supernet.som.umass.edu/photos/gdobit.html "Obituaries of George Dantzig"]. In: ''Washington Post'', May 19, 2005; B06</ref>
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| Dantzig was the Professor Emeritus of Transportation Sciences and Professor of [[Operations Research]] and of [[Computer Science]] at [[Stanford]].
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| ==Biography==
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| Born in [[Portland, Oregon]], George Bernard Dantzig was named after [[George Bernard Shaw]], the Irish writer.<ref name = "SR06">Richard W. Cottle, B. Curtis Eaves and Michael A. Saunders (2006). [http://news-service.stanford.edu/news/2006/june7/memldant-060706.html "Memorial Resolution: George Bernard Dantzig"]. Stanford Report, June 7, 2006.</ref><ref name="mmp">{{Cite book|contribution=George B. Dantzig|title=More Mathematical People|editor1-first=Donald J.|editor1-last=Albers|editor2-first=Gerald L.|editor2-last=Alexanderson|editor3-first=Constance|editor3-last=Reid|publisher=Harcourt Brace Jovanovich|year=1990|pages=60–79|postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}.</ref> His father, [[Tobias Dantzig]], was a [[Baltic region|Baltic]] [[Germans|German]] mathematician and linguist, and his mother, Anja Dantzig (née Ourisson), was a [[French people|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.<ref name="mmp"/> The Dantzigs immigrated to the [[United States]], where they settled in Portland, Oregon.
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| Early in the 1920s the Dantzig family moved from [[Baltimore]] to [[Washington, D.C.|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.<ref name="mmp"/> 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]].<ref name= "JH05"/><ref name="mmp"/>
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| George Dantzig earned [[bachelor's degrees]] in mathematics and physics from the [[University of Maryland, College Park|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]].
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| 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.<ref name = "SR06"/> Although he had a faculty offer from Berkeley, he returned to the Air Force as mathematical advisor to the comptroller.<ref name="mmp"/>
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| In 1952 Dantzig joined the mathematics division of the [[RAND Corporation]]. By 1960 he became a professor in the [[University of California, Berkeley College of Engineering|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.<ref name = "SR06"/>
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| He was a member of the [[United States National Academy of Sciences|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,<ref>[http://www.nsf.gov/od/nms/recip_details.cfm?recip_id=95 National Science Foundation - The President's National Medal of Science]</ref> 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.
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| Dantzig died on May 13, 2005, in his home in [[Stanford, California]], of complications from [[diabetes]] and [[cardiovascular disease]]. He was 90 years old.
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| ==Work==
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| 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".<ref name="RF94">Robert Freund (1994). [http://www.stanford.edu/group/SOL/dantzig.html "Professor George Dantzig: Linear Programming Founder Turns 80"]. In: ''SIAM News'', November 1994.</ref>
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| 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's used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas".<ref name= "JH05"/>
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| ===Mathematical statistics===
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| 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.<ref name="mmp"/><ref>[http://www.snopes.com/college/homework/unsolvable.asp Snopes urban legend reference on the legend to which Dantzig gave rise]</ref>
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| 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.<ref name= "JH05"/><ref name="mmp"/> 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]]'':<ref>{{cite journal | url=http://rev-inv-ope.univ-paris1.fr/files/26305/IO-26305-1.pdf | title=Professor George Bernard Dantzig, Life & Legend | author=Sira M. Allende & Carlos N. Bouza, Universidad de La Habana | journal=Revista Investigación Operacional | year=2005 | volume=26 | issue=3}}</ref>
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| <blockquote>A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two
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| problems in a binder and he would accept them as my thesis.</blockquote>
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| 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.<ref name="mmp"/>
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| 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]]''.
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| ===Linear programming===
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| [[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.
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| The founders of this subject are [[Leonid Kantorovich]], a Russian mathematician who developed linear programming problems in 1939, Dantzig, who published the [[Simplex algorithm|simplex method]] in 1947, and [[John von Neumann]], who developed the theory of the [[duality (optimization)|duality]] in the same year.
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| 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.
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| 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.
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| ==Publications==
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| Books by George Dantzig:
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| * 1953. ''Notes on linear programming''. RAND Corporation.
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| * 1956. ''Linear inequalities and related systems''. With others. Edited by H.W. Kuhn and A.W. Tucker. Princeton University Press.
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| * 1963. ''[http://books.google.com/books?id=2j46uCX5ZAYC&printsec=frontcover Linear programming and extensions]''. Princeton University Press and the RAND Corporation. [http://www.rand.org/pubs/reports/R366/ pdf from RAND]
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| * 1966. ''On the continuity of the minimum set of a continuous function''. With [[Jon Folkman|Jon H. Folkman]] and Norman Shapiro.
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| * 1968. ''Mathematics of the decision sciences''. With Arthur F. Veinott, Jr. Summer Seminar on Applied Mathematics 5th : 1967 : Stanford University. American Mathematical Society.
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| * 1969. ''Lectures in differential equations''. A. K. Aziz, general editor. Contributors: George B. Dantzig and others.
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| * 1970. ''Natural gas transmission system optimization''. With others.
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| * 1973. ''[[Compact city]]; a plan for a liveable urban environment''. With Thomas L. Saaty.
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| * 1974. ''Studies in optimization''. Edited with B.C. Eaves. Mathematical Association of America.
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| * 1985. ''Mathematical programming : essays in honor of George B. Dantzig''. Edited by R.W. Cottle. Mathematical Programming Society.
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| * 1997. ''Linear programming 1: Introduction''. G.B.D. and Mukund N. Thapa. Springer-Verlag.
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| * 2003. ''Linear programming 2: Theory and Extensions''. G.B.D. and Mukund N. Thapa. Springer-Verlag.
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| * 2003. ''The Basic George B. Dantzig''. Edited by Richard W. Cottle. Stanford Business Books, Stanford University Press, Stanford, California.<ref>{{cite journal|author=Todd, Michael J.|title=Review: ''The Basic George B. Dantzig'', by Richard W. Cottle|journal=Bull. Amer. Math. Soc. (N.S.)|year=2011|volume=48|issue=1|pages=123–129|url=http://www.ams.org/journals/bull/2011-48-01/S0273-0979-2010-01303-3/|doi=10.1090/S0273-0979-2010-01303-3}}</ref>
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| Articles, a selection:
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| * 1940. "On the non-existence of tests of "Student's" hypothesis having power functions independent of <math>\sigma</math>". ''Annals of Mathematical Statistics'', Volume 11, number 2, pp 186–192. Reprinted in Cottle, ed. ''The Basic George B. Dantzig''.
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| * {{cite journal | last = Wood | first = Marshall K. | coauthors = George B. Dantzig | title = Programming of Interdependent Activities: I General Discussion | journal = Econometrica | volume = 17 | year = 1949 | issue = 3 | pages = 193–199 | doi = 10.2307/1905522 }}
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| * {{cite journal | last = Dantzig | first = George B. | title = Programming of Interdependent Activities: II Mathematical Model | journal = Econometrica | volume = 17 | year = 1949 | issue = 3 | pages = 200–211 | doi = 10.2307/1905523 }}
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| * {{cite journal | last = Dantzig | first = George B. | title = Optimal Solution of a Dynamic Leontief Model with Substitution | journal = Econometrica | volume = 23 | year = 1955 | issue = 3 | pages = 295–302 | doi = 10.2307/1910385 }}
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| ==See also==
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| {{Portal|Systems science}}
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| * [[Dantzig-Wolfe decomposition]]
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| * [[Knapsack problem]]
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| * [[Maximum flow problem]]
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| * [[Optimization (mathematics)]]
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| * [[Travelling salesman problem]]
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| ==Notes==
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| {{Reflist}}
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| == Further reading ==
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| * Cottle, Richard; Johnson, Ellis; Wets, Roger, [http://www.stanford.edu/group/SOL/GBD/cottle-johnson-wets-2007.pdf "George B. Dantzig (1914–2005)"], ''Notices of the American Mathematical Society'', v.54, no.3, March 2007.
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| * [http://www.stanford.edu/group/SOL/dantzig.html "Professor George Dantzig: Linear Programming Founder Turns 80"], ''[[Society for Industrial and Applied Mathematics|SIAM]] News'', November 1994
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| * {{MacTutor Biography|id=Dantzig_George}}
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| *[http://dl.dropbox.com/u/5317066/1990-dantzig-dietproblem.pdf "The Diet Problem"] by George Dantzig
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| ==External links==
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| {{Wikiquote}}
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| * {{worldcat id|lccn-n50-37389}}
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| * {{MacTutor Biography|id=Dantzig_George}}
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| *[http://supernet.som.umass.edu/photos/gdobit.html Obituaries of George Dantzig]
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| *[http://www.phpsimplex.com/en/Dantzig_interview.htm Interview with George B. Dantzig: The Father of Linear Programming - The College Mathematical Journal, 1986]
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| *[http://www2.informs.org/History/dantzig/ INFORMS George Dantzig Memorial Website]
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| * {{MathGenealogy|id=32292}}
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| {{Authority control |VIAF=17287797 |LCCN=n/50/37389 }}
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| {{Systems science}}
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| {{Winners of the National Medal of Science|math-stat-comp}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Dantzig, George
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = American mathematician
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| | DATE OF BIRTH = November 8, 1914
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| | PLACE OF BIRTH = [[Portland, Oregon]]
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| | DATE OF DEATH = May 13, 2005
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| | PLACE OF DEATH = [[Stanford, California]]
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| }}
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| {{DEFAULTSORT:Dantzig, George}}
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| [[Category:John von Neumann Theory Prize winners]]
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| [[Category:National Medal of Science laureates]]
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| [[Category:American operations researchers]]
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| [[Category:Numerical analysts]]
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| [[Category:American computer scientists]]
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| [[Category:20th-century mathematicians]]
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| [[Category:American mathematicians]]
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| [[Category:American statisticians]]
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| [[Category:Stanford University School of Engineering faculty]]
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| [[Category:University of California, Berkeley faculty]]
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| [[Category:RAND Corporation people]]
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| [[Category:University of Maryland, College Park alumni]]
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| [[Category:University of Michigan alumni]]
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| [[Category:University of California, Berkeley alumni]]
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| <!-- [[Category:Jewish scientists]] ? -->
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| [[Category:People of Baltic German descent]]
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| [[Category:American people of French descent]]
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| [[Category:Cardiovascular disease deaths in California]]
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| [[Category:Deaths from diabetes]]
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| [[Category:1914 births]]
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| [[Category:2005 deaths]]
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| [[Category:Mathematical economists]]
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| [[Category:Members of the United States National Academy of Sciences]]
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| [[Category:American military personnel of World War II]]
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