View source for George Dantzig

{{Short description|American mathematician (1914–2005)}}
{{Infobox scientist
| image             = George B. Dantzig at National Medal of Science Awards Ceremony, 1976.jpg
| image_size        = 280px
| caption           = Dantzig with President [[Gerald Ford]] in 1976
| birth_name        = George Bernard Dantzig
| birth_date        = {{birth date|1914|11|8}}
| birth_place       = [[Portland, Oregon]], US
| death_date        = {{death date and age|2005|5|13|1914|11|8}}
| death_place       = [[Stanford, California]], US
| fields            = [[Mathematics]]<br />[[Operations research]] <br />[[Industrial engineering]] <br />[[Computer science]]<br />[[Economics]] <br />[[Statistics]]
| workplaces        = U.S. Air Force Office of Statistical Control<br />[[RAND Corporation]]<br />[[University of California, Berkeley]]<br />[[Stanford University]]
| alma_mater        = [[University of Maryland, College Park|University of Maryland]] ([[Bachelor of Science|BS]])<br />[[University of Michigan]] ([[Master of Science|MS]])<br>[[University of California, Berkeley]] ([[Doctor of Philosophy|PhD]])
| doctoral_advisor  = [[Jerzy Spława-Neyman]]
| 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 /> -->[[Alfredo Noel Iusem]]<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 />  -->
| notable_students  =
| known_for         = [[Linear programming]] <br /> [[Quadratic programming]]<br />[[Stochastic programming]] <br /> [[Linear complementarity problem]] <br />[[Max-flow min-cut theorem#Linear program formulation|Max-flow min-cut theorem of networks]]<br />[[Pseudoforest]]<br>[[Vehicle routing problem]]<br>[[Simplex algorithm|Dantzig's simplex algorithm]] <br /> [[Dantzig–Wolfe decomposition]]
| awards            = {{no wrap|[[John von Neumann Theory Prize]] <small>(1975)</small>}} [[National Medal of Science]] <small>(1975)</small><br>[[Harvey Prize]] <small>(1985)</small><br>[[Harold Pender Award]] <small>(1995)</small>
| signature         = <!--(filename only)-->
| footnotes         =  
}}

'''George Bernard Dantzig''' ({{IPAc-en|ˈ|d|æ|n|t|s|ɪ|ɡ}}; November 8, 1914–May 13, 2005) was an American [[mathematical sciences|mathematical scientist]] who made contributions to [[industrial engineering]], [[operations research]], [[computer science]], [[economics]] and [[statistics]].

Dantzig is known for his development of the [[simplex algorithm]],<ref>{{Cite book | last1 = Gass | first1 = Saul I. | chapter = George B. Dantzig | doi = 10.1007/978-1-4419-6281-2_13 | title = Profiles in Operations Research | series = International Series in Operations Research & Management Science | volume = 147 | pages = 217–240 | year = 2011 | isbn = 978-1-4419-6280-5 }}</ref> an algorithm for solving [[linear programming]] problems, and for his other 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 by Polish mathematician-statistician [[Jerzy Spława-Neyman]].<ref name="JH05">Joe Holley (2005). [https://supernet.isenberg.umass.edu/photos/gdobit.html "Obituaries of George Dantzig"]. In: ''Washington Post'', May 19, 2005; B06</ref>

At his death, Dantzig was professor emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at [[Stanford University]].

==Early life==
Born to [[Jewish]] parents 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"] {{Webarchive|url=https://web.archive.org/web/20060830160736/http://news-service.stanford.edu/news/2006/june7/memldant-060706.html |date=2006-08-30 }}. Stanford Report, June 7, 2006.</ref><ref name="mmp">{{cite book |chapter=George B. Dantzig |title=More Mathematical People |editor1-first=Donald J. |editor1-last=Albers |editor2-first=Gerald L. |editor2-last=Alexanderson |editor2-link=Gerald L. Alexanderson |editor3-first=Constance |editor3-last=Reid |editor3-link=Constance Reid |publisher=Harcourt Brace Jovanovich |year=1990 |pages=[https://archive.org/details/moremathematical0000unse/page/60 60–79] |isbn=978-0-15-158175-7 |chapter-url=https://archive.org/details/moremathematical0000unse/page/60 }}</ref> His father, [[Tobias Dantzig]], was a mathematician and linguist, and his mother, Anja Dantzig (née Ourisson), was a Russian-born linguist of [[French people|French]]-[[Lithuanians|Lithuanian]] origin. Dantzig's parents met during their study at the [[University of Paris]], where Tobias studied mathematics under [[Henri Poincaré]], after whom Dantzig's brother was named.<ref name="mmp"/> The Dantzigs emigrated to the United States, where they settled in Portland, Oregon.

Early in the 1920s the Dantzig family moved from [[Baltimore]] to [[Washington, D.C.]] His mother became a linguist at the [[Library of Congress]], and his father became a math tutor at the [[University of Maryland, College Park]].

==Education==
Dantzig attended Powell Junior High School and [[Cardozo Education Campus|Central High School]]. 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"/>

George Dantzig received his B.S. from [[University of Maryland]] in 1936 in mathematics and physics. He earned his master's degree in mathematics from the [[University of Michigan]] in 1937. After working as a junior statistician at the Bureau of Labor Statistics from 1937 to 1939,<ref>{{cite web |url=https://news.stanford.edu/pr/2005/pr-dantzigobit-052505.html |title=George B. Dantzig, operations research giant, dies at 90 |author=Dawn Levy |date=May 25, 2005 |publisher=[[Stanford University]] News Service |access-date=February 22, 2021 |archive-date=February 26, 2021 |archive-url=https://web.archive.org/web/20210226053552/https://news.stanford.edu/pr/2005/pr-dantzigobit-052505.html |url-status=dead }}</ref> he enrolled in the doctoral program in mathematics at the [[University of California, Berkeley]], where he studied statistics under [[Jerzy Spława-Neyman]].

During his study in 1939, Dantzig solved two unproven statistical theorems due to a misunderstanding. Near the beginning of a class, Professor Spława-Neyman wrote two problems on the blackboard. Dantzig arrived late and assumed that they were a homework assignment. According to Dantzig, they "seemed to be a little harder than usual", but a few days later he handed in completed solutions for both problems, still believing that they were an assignment that was overdue.<ref name="mmp"/><ref name=snopes>{{cite web |url=http://www.snopes.com/college/homework/unsolvable.asp |publisher=Snopes |title=The Unsolvable Math Problem |date=June 28, 2011}}</ref> Six weeks later, an excited Spława-Neyman eagerly told 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.<ref>{{cite journal|last1=Dantzig|first1=George|title=On the non-existence of tests of "Student's" hypothesis having power functions independent of σ|journal=The Annals of Mathematical Statistics|date=1940|doi=10.1214/aoms/1177731912|volume=11|issue=2|pages=186–192|doi-access=free}}</ref> This story began to spread and was used as a motivational lesson demonstrating the power of positive thinking. Over time, some 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]]''.<ref name=snopes/>

Dantzig recalled in a 1986 interview in the ''[[College Mathematics Journal]]'', "A year later, when I began to worry about a thesis topic, Spława-Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis."<ref name=AB>{{cite journal |url=http://rev-inv-ope.univ-paris1.fr/fileadmin/rev-inv-ope/files/26305/IO-26305-1.pdf |title=Professor George Bernard Dantzig, Life & Legend |first1=Sira M. |last1=Allende |first2=Carlos N. |last2=Bouza |journal=Revista Investigación Operacional |year=2005 |volume=26 |issue=3 |pages=205–11 |access-date=2019-03-24 |archive-date=2018-04-21 |archive-url=https://web.archive.org/web/20180421052355/http://rev-inv-ope.univ-paris1.fr/fileadmin/rev-inv-ope/files/26305//IO-26305-1.pdf |url-status=dead }}</ref>

Years later, another researcher, [[Abraham Wald]], was preparing to publish a paper where he had arrived at a conclusion for the second problem when he learned of Dantzig's earlier solution. When Dantzig suggested publishing jointly, Wald simply added Dantzig's name as co-author.<ref name="mmp"/><ref name=AB/><ref>{{cite journal|last1=Dantzig|first1=George|last2=Wald|first2=Abraham|title=On the Fundamental Lemma of Spława-Neyman and Pearson|journal=The Annals of Mathematical Statistics|date=1951|url=http://projecteuclid.org/euclid.aoms/1177729695|access-date=14 October 2014|doi=10.1214/aoms/1177729695|volume=22|pages=87–93|doi-access=free}}</ref>

== Career ==
With the outbreak of [[World War II]], Dantzig took a leave of absence from the doctoral program at Berkeley to work as a civilian for the [[United States Army Air Forces]]. From 1941 to 1946, he became the head of the combat analysis branch of the Headquarters Statistical Control for the Army Air Forces.<ref name= "JH05"/> In 1946, he returned to Berkeley to complete the requirements of his program and received his [[PhD]] 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"/>

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 managed 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 University]].<ref name = "SR06"/>

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]]. Dantzig was the recipient of many honors, including the first [[John von Neumann Theory Prize]] in 1974, the [[National Medal of Science]] in 1975,<ref>[https://www.nsf.gov/od/nms/recip_details.cfm?recip_id=95 National Science Foundation – The President's National Medal of Science]</ref> and 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. He was elected to the 2002 class of [[Fellow]]s of the [[Institute for Operations Research and the Management Sciences]].<ref>{{citation|url=https://www.informs.org/Recognizing-Excellence/Fellows/Fellows-Alphabetical-List|title=Fellows: Alphabetical List|publisher=[[Institute for Operations Research and the Management Sciences]]|access-date=2019-10-09|archive-url=https://web.archive.org/web/20190510220119/https://www.informs.org/Recognizing-Excellence/Fellows/Fellows-Alphabetical-List|archive-date=2019-05-10|url-status=dead}}</ref>

=== Research ===
Freund wrote further that "through his research in mathematical theory, computation, economic analysis, and applications to industrial problems, Dantzig 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"] {{Webarchive|url=https://web.archive.org/web/20090416184457/http://www.stanford.edu/group/SOL/dantzig.html |date=2009-04-16 }}. In: ''SIAM News'', November 1994.</ref>

Dantzig's 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".<ref name= "JH05"/>

====Linear programming====
[[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 algorithm|simplex method]] in 1947, and [[John von Neumann]], who developed the theory of the [[duality (optimization)|duality]] in the same year.

Dantzig was asked to work out a method the Air Force could use to improve their planning process.<ref>{{Cite web|title=Biographical Profiles: Dantzig, George B.|url=https://www.informs.org/Explore/History-of-O.R.-Excellence/Biographical-Profiles/Dantzig-George-B|access-date=2020-10-30|website=INFORMS|language=en-US}}</ref>  This led to his original example of finding the best assignment of 70 people to 70 jobs, showing 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]]. The book quickly became a standard text in linear programming.

== Personal life ==
Dantzig married Anne S. Shmuner in 1936.<ref>{{Cite web|url=https://news.stanford.edu/news/2005/may25/dantzigobit-052505.html|title = George B. Dantzig, operations research professor, dies at 90|date = 25 May 2005}}</ref><ref>{{Cite web|url=https://www.telegraph.co.uk/news/obituaries/1490820/George-Dantzig.html |archive-url=https://ghostarchive.org/archive/20220112/https://www.telegraph.co.uk/news/obituaries/1490820/George-Dantzig.html |archive-date=2022-01-12 |url-access=subscription |url-status=live|title = George Dantzig|date=27 May 2005 }}{{cbignore}}</ref>  He died on May 13, 2005, in his home in [[Stanford, California]], of complications from [[diabetes]] and [[cardiovascular disease]]. He was 90 years old.<ref name="JH05" /> His children were named David, Paul, and Jessica. 

== Presidential award ==

On October 18, 1976, President [[Gerald Ford]] presented Dantzig with the [[National Medal of Science]]. The award was given "For inventing linear programming and discovering methods that led to wide-scale scientific and technical applications to important problems in logistics, scheduling, and network optimization, and to the use of computers in making efficient use of the mathematical theory."<ref>{{Cite web|url=https://www.nsf.gov/od/nms/recip_details.jsp?recip_id=95|title = The President's National Medal of Science: Recipient Details}}</ref>

==Publications==
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. ''[https://books.google.com/books?id=2j46uCX5ZAYC Linear programming and extensions]''. Princeton University Press and the RAND Corporation. [https://www.rand.org/pubs/reports/R366/ pdf from RAND]
* 1966. ''On the continuity of the minimum set of a continuous function''. With [[Jon Folkman|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.<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=https://www.ams.org/journals/bull/2011-48-01/S0273-0979-2010-01303-3/|doi=10.1090/S0273-0979-2010-01303-3|doi-access=free}}</ref>

Book chapters:
* {{citation | last1 = Dantzig | first1 = George B. | contribution = General convex objective forms | editor-last1 = Arrow | editor-first1 = Kenneth J. | editor-last2 = Karlin | editor-first2 = Samuel | editor-last3 = Suppes | editor-first3 = Patrick | editor-link1 = Kenneth Arrow | editor-link2 = Samuel Karlin | editor-link3 = Patrick Suppes | title = Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium | pages = 151–158 | publisher = Stanford University Press | location = Stanford, California | series = Stanford mathematical studies in the social sciences, IV | year = 1960 | postscript = .}} {{isbn|9780804700214}}.

Articles, a selection:
*{{cite journal |first1=George B. |last1=Dantzig |date=June 1940 |title=On the Non-Existence of Tests of 'Student's' Hypothesis Having Power Functions Independent of σ |journal=The Annals of Mathematical Statistics |volume=11 |issue=2 |pages=186–92 |jstor=2235875 |doi=10.1214/aoms/1177731912|doi-access=free }}
*{{cite journal |first1=Marshall K. |last1=Wood |first2=George B. |last2=Dantzig |year=1949 |title=Programming of Interdependent Activities: I General Discussion |journal=Econometrica |volume=17 |issue=3/4 |pages=193–9 |jstor=1905522 |doi=10.2307/1905522}}
* {{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 | jstor = 1905523 }}
* {{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 | jstor = 1910385 }}

==See also==
{{Portal|Systems science}}
{{div col}}
* [[Dantzig–Wolfe decomposition]]
* [[Knapsack problem]]
* [[Maximum flow problem]]
* [[Optimization (mathematics)]]
* [[Travelling salesman problem]]
* [[Shadow price]]
* [[List of Jewish American mathematicians]]
{{colend}}

==Notes==
{{Reflist|30em}}

==Further reading==
*{{cite journal |last1=Cottle |first1=Richard |last2=Johnson |first2=Ellis |last3=Wets |first3=Roger |url=https://www.ams.org/notices/200703/fea-cottle.pdf |title=George B. Dantzig (1914–2005) |journal=Notices of the American Mathematical Society |volume=54 |issue=3 |date=March 2007 |pages=344–62}}
* [http://www.stanford.edu/group/SOL/dantzig.html "Professor George Dantzig: Linear Programming Founder Turns 80"] {{Webarchive|url=https://web.archive.org/web/20090416184457/http://www.stanford.edu/group/SOL/dantzig.html |date=2009-04-16 }}, ''[[Society for Industrial and Applied Mathematics|SIAM]] News'', November 1994
* {{MacTutor Biography|id=Dantzig_George}}
*{{cite journal |first1=George B. |last1=Dantzig |year=1990 |title=The Diet Problem |journal=Interfaces |volume=20 |issue=4 |pages=43–7 |jstor=25061369 |doi=10.1287/inte.20.4.43}}
* {{cite journal|last=Cottle|first=Richard W.|year=2005|title=George B. Dantzig: a legendary life in mathematical programming|journal=Mathematical Programming|volume=105|issue=1|pages=1–8|issn=0025-5610|doi=10.1007/s10107-005-0674-4|s2cid=207054446}}

==External links==
{{Wikiquote}}
* {{MacTutor Biography|id=Dantzig_George}}
*[https://web.stanford.edu/group/SOL/GBD/Dantzig-Khachiyan.pdf  Tributes to George Dantzig and Leonid Khachiyan]
*[https://web.archive.org/web/20060113014322/http://supernet.som.umass.edu/photos/gdobit.html Obituaries of George Dantzig]
*[http://www.personal.psu.edu/ecb5/Courses/M475W/WeeklyReadings/Week%2015/An_Interview_with_George_Dantzig.pdf Interview with George B. Dantzig: The Father of Linear Programming – The College Mathematical Journal, 1986] {{Webarchive|url=https://web.archive.org/web/20211115103142/http://www.personal.psu.edu/ecb5/Courses/M475W/WeeklyReadings/Week%2015/An_Interview_with_George_Dantzig.pdf |date=2021-11-15 }} {{JSTOR|2686279}}
*[https://web.archive.org/web/20071009161640/http://www2.informs.org/History/dantzig/ INFORMS George Dantzig Memorial Website]
* {{MathGenealogy|id=32292}}
* [https://www.informs.org/content/view/full/262887 Biography of George Dantzig] from the Institute for Operations Research and the Management Sciences (INFORMS)
* An Interview with Nobel Laureate Harry M. Markowitz [https://doi.org/10.2469/faj.v73.n4.3]

{{Systems science}}
{{Winners of the National Medal of Science|math-stat-comp}}
{{John von Neumann Theory Prize recipients}}
{{Authority control}}

{{DEFAULTSORT:Dantzig, George}}
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[[Category:2005 deaths]]
[[Category:20th-century American mathematicians]]
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[[Category:American people of French-Jewish descent]]
[[Category:American statisticians]]
[[Category:American systems scientists]]
[[Category:Deaths from diabetes in California]]
[[Category:Fellows of the Econometric Society]]
[[Category:General equilibrium theorists]]
[[Category:Jewish American scientists]]
[[Category:John von Neumann Theory Prize winners]]
[[Category:Mathematical economists]]
[[Category:Mathematicians from Oregon]]
[[Category:Fellows of the Institute for Operations Research and the Management Sciences]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:National Medal of Science laureates]]
[[Category:Numerical analysts]]
[[Category:People from Stanford, California]]
[[Category:RAND Corporation people]]
[[Category:Stanford University School of Engineering faculty]]
[[Category:United States Air Force civilians]]
[[Category:University of California, Berkeley alumni]]
[[Category:UC Berkeley College of Engineering faculty]]
[[Category:University of Maryland, College Park alumni]]
[[Category:University of Michigan College of Literature, Science, and the Arts alumni]]
[[Category:United States Army Air Forces personnel of World War II]]
[[Category:United States Army civilians]]
[[Category:20th-century American Jews]]
[[Category:21st-century American Jews]]
[[Category:Scientists from Portland, Oregon]]