Albert W. Tucker
Encyclopedia
Albert William Tucker was a Canadian-born American mathematician
who made important contributions in topology
, game theory
, and non-linear programming.
Albert Tucker was born in Oshawa
, Ontario
, Canada
, and earned his B.A.
at the University of Toronto
in 1928. In 1932, he completed his Ph.D.
at the Princeton University
under the supervision of Solomon Lefschetz
, with the thesis An Abstract Approach to Manifolds.
In 1932–33 he was a National Research Fellow at Cambridge
, Harvard, and the University of Chicago
. He then returned to Princeton to join the faculty in 1933, where he stayed till 1970. 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.
His Ph.D. students include Michel Balinski, David Gale
, Alan Goldman, John Isbell, Stephen Maurer, Marvin Minsky
, Nobel Prize winner John Nash
, Torrence Parsons
, Lloyd Shapley
, Robert Singleton
, and Marjorie Stein. Although he wasn't his dissertation advisor, Tucker did advise and collaborated with Harold W. Kuhn
on a number of papers and models.
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. 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 AP
Calculus committee for the College Board (1960–1963), through work with the Committee on the Undergraduate Program in Mathematics (CUPM) of the MAA
(he was president of the MAA in 1961–1962), and through many NSF
summer workshops for high school and college teachers.
In the early 1980s, Tucker recruited Princeton history professor Charles 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 Einstein
, von Neumann
, and Gödel
were computer pioneer Herman Goldstine and Nobel laureates John Bardeen
and Eugene Wigner.
Albert Tucker noticed the leadership ability and talent of a young mathematics graduate student named 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, Darthmouth College recognized Albert Tucker with an honorary degree. Tucker died in Highstown, N.J.
in 1995 at age 89.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made important contributions in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, and non-linear programming.
Albert Tucker was born in Oshawa
Oshawa
Oshawa is a city in Ontario, Canada, on the Lake Ontario shoreline. It lies in Southern Ontario approximately 60 kilometres east of downtown Toronto. It is commonly viewed as the eastern anchor of both the Greater Toronto Area and the Golden Horseshoe. It is now commonly referred to as the most...
, Ontario
Ontario
Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa....
, Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
, and earned his B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
at the University of Toronto
University of Toronto
The University of Toronto is a public research university in Toronto, Ontario, Canada, situated on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in Upper Canada...
in 1928. In 1932, he completed his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
at the Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
under the supervision of Solomon Lefschetz
Solomon Lefschetz
Solomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.-Life:...
, with the thesis An Abstract Approach to Manifolds.
In 1932–33 he was a National Research Fellow at Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
, Harvard, and the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
. He then returned to Princeton to join the faculty in 1933, where he stayed till 1970. 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.
His Ph.D. students include Michel Balinski, David Gale
David Gale
David Gale was a distinguished American mathematician and economist. He was a Professor Emeritus at University of California, Berkeley, affiliated with departments of Mathematics, Economics, and Industrial Engineering and Operations Research...
, Alan Goldman, John Isbell, Stephen Maurer, Marvin Minsky
Marvin Minsky
Marvin Lee Minsky is an American cognitive scientist in the field of artificial intelligence , co-founder of Massachusetts Institute of Technology's AI laboratory, and author of several texts on AI and philosophy.-Biography:...
, Nobel Prize winner John Nash
John Forbes Nash
John Forbes Nash, Jr. is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life...
, Torrence Parsons
Torrence Parsons
Torrence Douglas Parsons was an American mathematician.He worked mainly in graph theory, and is known for introducing a graph-theoretic view of pursuit-evasion problems . He obtained his Ph.D. from Princeton University in 1966 under the supervision of Albert W. Tucker.-Further reading:Memorial...
, Lloyd Shapley
Lloyd Shapley
Lloyd Stowell Shapley is a distinguished American mathematician and economist. He is a Professor Emeritus at University of California, Los Angeles, affiliated with departments of Mathematics and Economics...
, Robert Singleton
Robert Singleton
Robert Singleton , also known as John, was an English Roman Catholic priest, executed on a treason charge. He is considered a Catholic martyr by Antonio Possevino, in his Apparatus Sacer.-Life:...
, and Marjorie Stein. Although he wasn't his dissertation advisor, Tucker did advise and collaborated with Harold W. Kuhn
Harold W. Kuhn
Harold William Kuhn is an American mathematician who studied game theory. He won the 1980 John von Neumann Theory Prize along with David Gale and Albert W. Tucker...
on a number of papers and models.
In 1950, Albert Tucker gave the name and interpretation "prisoner's dilemma
Prisoner's dilemma
The prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...
" to Merrill M. Flood
Merrill M. Flood
Merrill Meeks Flood was an American mathematician, notable for developing, with Melvin Dresher, the basis of the game theoretical Prisoner's dilemma model of cooperation and conflict while being at RAND in 1950 Merrill Meeks Flood (1908 – 1991) was an American mathematician, notable for...
and Melvin Dresher
Melvin Dresher
Melvin Dresher was a Polish-born American mathematician, notable for developing, with Merrill Flood, the game theoretical model of cooperation and conflict known as the Prisoner's Dilemma while at RAND in 1950 .Dresher came to the United States in 1923...
's model of cooperation and conflict, resulting in the most well-known game theoretic paradox. 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 AP
Advanced Placement Program
The Advanced Placement program is a curriculum in the United States and Canada sponsored by the College Board which offers standardized courses to high school students that are generally recognized to be equivalent to undergraduate courses in college...
Calculus committee for the College Board (1960–1963), through work with the Committee on the Undergraduate Program in Mathematics (CUPM) of the MAA
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
(he was president of the MAA in 1961–1962), and through many NSF
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
summer workshops for high school and college teachers.
In the early 1980s, Tucker recruited Princeton history professor Charles 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 Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
, von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
, and Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
were computer pioneer Herman Goldstine and Nobel laureates John Bardeen
John Bardeen
John Bardeen was an American physicist and electrical engineer, the only person to have won the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the transistor; and again in 1972 with Leon Neil Cooper and John Robert Schrieffer for a...
and Eugene Wigner.
Albert Tucker noticed the leadership ability and talent of a young mathematics graduate student named John G. Kemeny
John George Kemeny
John George Kemeny was a Hungarian American mathematician, computer scientist, and educator best known for co-developing the BASIC programming language in 1964 with Thomas E. Kurtz. Kemeny served as the 13th President of Dartmouth College from 1970 to 1981 and pioneered the use of computers in...
, whose hiring Tucker suggested to Dartmouth College
Dartmouth College
Dartmouth College is a private, Ivy League university in Hanover, New Hampshire, United States. The institution comprises a liberal arts college, Dartmouth Medical School, Thayer School of Engineering, and the Tuck School of Business, as well as 19 graduate programs in the arts and sciences...
. Following Tucker's advice, Dartmouth recruited Kemeny, who became Chair of the Mathematics Department and later College President. Years later, Darthmouth College recognized Albert Tucker with an honorary degree. Tucker died in Highstown, N.J.
Hightstown, New Jersey
Hightstown is a Borough in Mercer County, New Jersey, United States. As of the 2010 United States Census, the borough population was 5,494.Hightstown was incorporated as a borough by an Act of the New Jersey Legislature on March 5, 1853, within portions of East Windsor Township. The borough became...
in 1995 at age 89.
External links
- News from PRINCETON UNIVERSITY
- A Guide to Albert William Tucker Papers
- Extract from an obituary
- Kuhn Tucker conditions
- The Princeton Mathematics Community in the 1930s An oral history project initiated by Tucker, also contains a series of interviews with Tucker.
- Oral History Interview with Albert W. Tucker, Charles Babbage InstituteCharles Babbage InstituteThe Charles Babbage Institute is a research center at the University of Minnesota specializing in the history of information technology, particularly the history since 1935 of digital computing, programming/software, and computer networking....
, University of Minnesota.