View source for Albert W. Tucker

{{Short description|Canadian mathematician (1905–1995)}}
{{Infobox scientist
| name              = Albert W. Tucker
| image             = Albert W. Tucker.gif
| image_size        = 200
| birth_name        = Albert William Tucker
| birth_date        = {{birth date|1905|11|28|df=y}}
| birth_place       = [[Oshawa, Ontario]], Canada
| death_date        = {{death date and age|1995|1|25|1905|11|28|df=y}}
| death_place       = [[Hightstown, New Jersey]], U.S.
| nationality       = Canadian <br /> American
| field             = [[Mathematician]]: <br /> [[Combinatorial topology]] <br /> [[Optimization (mathematics)|Optimization]]
| work_institution  = [[Princeton University]]
| alma_mater        = [[University of Toronto]] ([[Bachelor of Arts|BA]], [[Master of Arts|MA]])<br>[[Princeton University]] ([[PhD]])
| thesis_title      = An Abstract Approach to Manifolds
| thesis_year       = 1932<ref name="math">{{MathGenealogy|id=8581}}</ref>
| thesis_url        = https://www.proquest.com/docview/301815335/
| doctoral_advisor  = [[Solomon Lefschetz]]<ref name="math"/>
| doctoral_students = [[David Gale]]<br />[[John R. Isbell]]<br />[[Marvin Minsky]]<br />[[John Forbes Nash]]<br />[[Torrence Parsons]]<br />[[Lloyd Shapley]]
<!--<br />
[[Marjorie Stein]]<br />
[[Emmet Whittlesey]]<br />
[[Michel Balinski]]<br />
[[Alan Goldman]]<br />
[[John Isbell]]<br />
[[Stephen Maurer]]-->
| known_for         = [[Tucker's lemma]]<br />[[Karush–Kuhn–Tucker conditions]]<br />[[Prisoner's dilemma]]<br />[[oriented matroid|Combinatorial linear algebra]]
| prizes            = {{no wrap|[[John von Neumann Theory Prize]] (1980)}}
| footnotes         =
}}
'''Albert William Tucker''' (28 November 1905 – 25 January 1995) was a Canadian [[mathematician]] who made important contributions in [[topology]], [[game theory]], and [[non-linear programming]].<ref>{{citation
 | last1 = Cervone | first1 = Barbara Tucker
 | last2 = Duren | first2 = Bill
 | last3 = Kohn | first3 = J. J.
 | last4 = Snell | first4 = J. Laurie
 | last5 = Stein | first5 = Marjorie L.
 | issue = 10
 | journal = Notices of the American Mathematical Society
 | mr = 1350012
 | pages = 1143–1147
 | title = A. W. Tucker: some reminiscences
 | volume = 42
 | year = 1995}}</ref>

==Early life and education==
Albert Tucker was born in [[Oshawa, Ontario]], Canada, and earned his [[Bachelor of Arts|B.A.]] at the [[University of Toronto]] in 1928 and his [[Master of Arts|M.A.]] at the same institution in 1929.<ref>{{Cite book | last1 = Gass | first1 = Saul I. | chapter = Albert W. Tucker | doi = 10.1007/978-1-4419-6281-2_6 | title = Profiles in Operations Research | series = International Series in Operations Research & Management Science | volume = 147 | pages = 95–11 | year = 2011 | isbn = 978-1-4419-6280-5 }}</ref> In 1932, he earned his [[Doctor of Philosophy|Ph.D.]] at [[Princeton University]] under the supervision of [[Solomon Lefschetz]], with a dissertation entitled ''An Abstract Approach to Manifolds''.<ref name="thesis-tucker-1932">{{cite thesis |url=https://www.proquest.com/docview/301815335/ |title=An abstract approach to manifolds |date=1932 |publisher=[[Princeton University]] |type=Ph.D. |last=Tucker |first=Albert William |id={{ProQuest|301815335}} |url-access=subscription |oclc=775707046}}</ref>  In 1932–33 he was a National Research Fellow at [[Cambridge]], [[Harvard]], and then [[University of Chicago]].

==Career==
Tucker then returned to Princeton to join the faculty in 1933, where he stayed until 1974. He chaired the mathematics department for about twenty years, one of the longest tenures. His extensive relationships within the field made him a great source for oral histories of the mathematics community.

In 1950, Albert Tucker gave the name and interpretation "[[prisoner's dilemma]]" to [[Merrill M. Flood]] and [[Melvin Dresher]]'s model of cooperation and conflict, resulting in the most well-known game theoretic paradox.{{sfn|Poundstone|1993|pp=8, 117}} He is also well known for the [[Karush–Kuhn–Tucker conditions]], a basic result in non-linear programming, which was published in conference proceedings, rather than in a journal.

In the 1960s, he was heavily involved in mathematics education, as chair of the [[Advanced Placement Program|AP]] Calculus committee for the College Board (1960–1963), through work with the Committee on the Undergraduate Program in Mathematics (CUPM) of the [[Mathematical Association of America|MAA]] (he was president of the MAA in 1961–1962), and through many [[National Science Foundation|NSF]] summer workshops for high school and college teachers.  [[George B. Thomas|George B. Thomas Jr.]] acknowledged Tucker's contribution of many exercises to Thomas's classic textbook, ''Calculus and Analytic Geometry.''<ref>George B. Thomas Jr., ''Calculus and Analytic Geometry'', 4th ed. (Reading, MA, Menlo Park, CA, London, and Don Mills, Ontario: Addison-Wesley Publishing Company, 1968), p. vii.</ref>

In the early 1980s, Tucker recruited Princeton history professor [[Charles Coulston Gillispie]] to help him set up an oral history project to preserve stories about the Princeton mathematical community in the 1930s. With funding from the [[Sloan Foundation]], this project later expanded its scope. Among those who shared their memories of such figures as [[Albert Einstein|Einstein]], [[John von Neumann|von Neumann]], and [[Kurt Gödel|Gödel]] were computer pioneer [[Herman Goldstine]] and Nobel laureates [[John Bardeen]] and [[Eugene Wigner]].

==Students and legacy==
Tucker's Ph.D. students include [[Michel Balinski]], [[David Gale]], [[Alan J. Goldman]], [[John Isbell]], [[Stephen Maurer]], Turing Award winner [[Marvin Minsky]], Nobel Prize winner [[John Forbes Nash|John Nash]], [[Torrence Parsons]], Nobel Prize winner [[Lloyd Shapley]], Robert Singleton, and [[Marjorie Stein]]. Tucker advised and collaborated with [[Harold W. Kuhn]] on a number of papers and mathematical models.

Tucker noticed the leadership ability and talent of a young mathematics graduate student named [[John George Kemeny|John G. Kemeny]], whose hiring Tucker suggested to [[Dartmouth College]]. Following Tucker's advice, Dartmouth recruited Kemeny, who became Chair of the Mathematics Department and later College President. Years later, Dartmouth College recognized Albert Tucker with an honorary degree.

Tucker died in [[Hightstown, New Jersey|Hightstown, N.J.]] in 1995 at age 89. His sons, [[Alan Tucker]] and [[Thomas W. Tucker]], and his grandson [[Thomas J. Tucker]] are all also professional mathematicians.

===Tucker Prize===
At each (triennial) International Symposium of the [[Mathematical Optimization Society]] (MOS) the [[Tucker Prize]], in honour of A. W. Tucker, is given for outstanding thesis in the area of [[discrete mathematics]].<ref>{{Cite web|url=http://www.mathopt.org/?nav=tucker|title = Mathematical Optimization Society}}</ref>

==Works==
* with H. W. Kuhn (eds.): ''Contributions to the theory of games'', Annals of Mathematical Studies 1950
* with H. W. Kuhn (eds.): ''Linear inequalities and related systems'', Annals of Mathematical Studies 1956
* with Allan Gewirtz, Harry Sitomer: ''Constructive linear algebra'', Englewood Cliffs 1974
* with Evar Nering: ''Linear Programs and related problems'', Academic Press 1993

== References ==
{{reflist}}

===Bibliography===
* {{cite book | last=Poundstone | first=William | title=Prisoner's Dilemma | publisher=Anchor | publication-place=New York | date=1993 | isbn=0-385-41580-X}}

==Further reading==
* {{Cite news |url=https://www.nytimes.com/1995/01/27/obituaries/albert-w-tucker-89-pioneering-mathematician.html |title=Albert W. Tucker, 89, Pioneering Mathematician |first=Sylvia |last=Nasar |author-link=Sylvia Nasar |date=January 27, 1995 |newspaper=[[The New York Times]] }}
* {{MacTutor Biography|id=Tucker_Albert|title=Albert Tucker}}

== External links ==
{{Wikiquote}}
* [https://www.princeton.edu/pr/news/95/q1/0126tucker.html News from PRINCETON UNIVERSITY]
* {{MathGenealogy|id=8581}}
* [http://www.lib.utexas.edu/taro/utcah/00301/cah-00301.html#a0 A Guide to Albert William Tucker Papers]
* [http://www.economics.utoronto.ca/osborne/MathTutorial/TUCKER.HTM Extract from an obituary]
* [http://www.economics.utoronto.ca/osborne/MathTutorial/KTCF.HTM Kuhn-Tucker conditions]
* [https://web.archive.org/web/20150309172454/http://www.princeton.edu/~mudd/finding_aids/mathoral/pm02.htm The Princeton Mathematics Community in the 1930s] An oral history project initiated by Tucker, also contains a series of interviews with Tucker.
* [http://purl.umn.edu/107690 Oral History Interview with Albert W. Tucker], [[Charles Babbage Institute]], University of Minnesota.
* [https://www.informs.org/content/view/full/271234 Biography of Albert W. Tucker] from the Institute for Operations Research and the Management Sciences

{{s-start}}
{{s-aca}}
{{succession box
|  before=[[Emil Artin]]
|  title=Dod Professor of Mathematics at [[Princeton University]]
|  years=1954–1974
|  after=[[Elias Stein]]
}}
{{s-end}}

{{John von Neumann Theory Prize recipients}}
{{Authority control}}

{{DEFAULTSORT:Tucker, Albert W.}}
[[Category:1905 births]]
[[Category:1995 deaths]]
[[Category:20th-century Canadian mathematicians]]
[[Category:Topologists]]
[[Category:Game theorists]]
[[Category:University of Toronto alumni]]
[[Category:Harvard University staff]]
[[Category:University of Chicago people]]
[[Category:John von Neumann Theory Prize winners]]
[[Category:People from Oshawa]]
[[Category:Princeton University alumni]]
[[Category:Princeton University faculty]]
[[Category:Presidents of the Mathematical Association of America]]
[[Category:Canadian emigrants to the United States]]
[[Category:Oral history]]