Albert W. Tucker | |
---|---|

Born | Albert William Tucker 28 November 1905 Oshawa, Ontario, Canada |

Died | 25 January 1995 89) Hightstown, New Jersey, U.S. | (aged

Nationality | Canadian American |

Alma mater | University of Toronto, Princeton University |

Known for | Prisoner's dilemma Karush–Kuhn–Tucker conditions Combinatorial linear algebra |

Awards | John von Neumann Theory Prize (1980) |

Scientific career | |

Fields | Mathematician: Combinatorial topology Optimization |

Institutions | Princeton University |

Thesis | An Abstract Approach to Manifolds (1932^{ [1] }) |

Doctoral advisor | Solomon Lefschetz ^{ [1] } |

Doctoral students | David Gale John R. Isbell Marvin Minsky John Forbes Nash Torrence Parsons Lloyd Shapley |

Influenced | Harold W. Kuhn David Gale R. Tyrrell Rockafellar |

**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.^{ [2] }

Albert Tucker was born in Oshawa, Ontario, Canada, and earned his B.A. at the University of Toronto in 1928 and his M.A. at the same institution in 1929.^{ [3] } In 1932, he earned his Ph.D. at Princeton University under the supervision of Solomon Lefschetz, with a dissertation entitled *An Abstract Approach to Manifolds*.^{ [4] } In 1932–33 he was a National Research Fellow at Cambridge, Harvard, and then University of Chicago.

He 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.

His Ph.D. students include Michel Balinski, David Gale, Alan J. Goldman, John Isbell, Stephen Maurer, Turing Award winner Marvin Minsky, Nobel Prize winner 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.

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.^{[ citation needed ]} 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. George B. Thomas Jr. acknowledged Tucker's contribution of many exercises to Thomas's classic textbook, *Calculus and Analytic Geometry.*^{ [5] }

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 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, Dartmouth College recognized Albert Tucker with an honorary degree. Tucker died in 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.

- with Evar Nering: Linear Programs and related problems, Academic Press 1993
- 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

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.^{ [6] }

**George Bernard Dantzig** was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics.

**Leonid Vitaliyevich Kantorovich** was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He is regarded as the founder of linear programming. He was the winner of the Stalin Prize in 1949 and the Nobel Memorial Prize in Economic Sciences in 1975.

**Michael David Spivak** was an American mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. Spivak was the author of the five-volume *A Comprehensive Introduction to Differential Geometry*.

**John George Kemeny** was a Hungarian-born American mathematician, computer scientist, and educator best known for co-developing the BASIC programming language in 1964 with Thomas E. Kurtz and Mary Kenneth Keller. Kemeny served as the 13th President of Dartmouth College from 1970 to 1981 and pioneered the use of computers in college education. Kemeny chaired the presidential commission that investigated the Three Mile Island accident in 1979. According to György Marx he was one of The Martians.

**Serge Lang** was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential *Algebra*. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group.

**Lloyd Stowell Shapley** was an American mathematician and Nobel Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design."

**Harold William Kuhn** was an American mathematician who studied game theory. He won the 1980 John von Neumann Theory Prize along with David Gale and Albert W. Tucker. A former Professor Emeritus of Mathematics at Princeton University, he is known for the Karush–Kuhn–Tucker conditions, for Kuhn's theorem, for developing Kuhn poker as well as the description of the Hungarian method for the assignment problem. Recently, though, a paper by Carl Gustav Jacobi, published posthumously in 1890 in Latin, has been discovered that anticipates by many decades the Hungarian algorithm.

**David Gale** was an American mathematician and economist. He was a professor emeritus at the University of California, Berkeley, affiliated with the departments of mathematics, economics, and industrial engineering and operations research. He has contributed to the fields of mathematical economics, game theory, and convex analysis.

**Luther Pfahler Eisenhart** was an American mathematician, best known today for his contributions to semi-Riemannian geometry.

* Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus* (1965) by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced undergraduates

**Jan Arnoldus Schouten** was a Dutch mathematician and Professor at the Delft University of Technology. He was an important contributor to the development of tensor calculus and Ricci calculus, and was one of the founders of the Mathematisch Centrum in Amsterdam.

**Karen Keskulla Uhlenbeck** is an American mathematician and one of the founders of modern geometric analysis. She is a professor emeritus of mathematics at the University of Texas at Austin, where she held the Sid W. Richardson Foundation Regents Chair. She is currently a distinguished visiting professor at the Institute for Advanced Study and a visiting senior research scholar at Princeton University.

**Frank Morgan** is an American mathematician and the Webster Atwell '21 Professor of Mathematics at Williams College.

**Robert Creighton Buck**, usually cited as R. Creighton Buck, was an American mathematician who, with Ralph Boas, introduced Boas–Buck polynomials. He taught at University of Wisconsin–Madison for 40 years. In addition, he was a writer.

**Philip Starr "Phil" Wolfe** was an American mathematician and one of the founders of convex optimization theory and mathematical programming.

**Michael Eugene Taylor** is an American mathematician, working in partial differential equations.

**Alan Curtiss Tucker** is an American mathematician. He is a professor of applied mathematics at Stony Brook University, and the author of a widely used textbook on combinatorics; he has also made research contributions to graph theory and coding theory. He has had four children, Katie, Lisa, Edward, and James.

**Thomas William Tucker** is an American mathematician, the Charles Hetherington Professor of Mathematics at Colgate University, and an expert in the area of topological graph theory.

**Victor Joseph Katz** is an American mathematician, historian of mathematics, and teacher known for using the history of mathematics in teaching mathematics.

**Donald Lester Kreider** was an American mathematician and educator who served as President of the Mathematical Association of America (1993–1994).

- 1 2 Albert W. Tucker at the Mathematics Genealogy Project
- ↑ Cervone, Barbara Tucker; Duren, Bill; Kohn, J. J.; Snell, J. Laurie; Stein, Marjorie L. (1995), "A. W. Tucker: some reminiscences",
*Notices of the American Mathematical Society*,**42**(10): 1143–1147, MR 1350012 - ↑ Gass, Saul I. (2011). "Albert W. Tucker".
*Profiles in Operations Research*. International Series in Operations Research & Management Science. Vol. 147. pp. 95–11. doi:10.1007/978-1-4419-6281-2_6. ISBN 978-1-4419-6280-5. - ↑ Tucker, Albert William (1932).
*An abstract approach to manifolds*(Ph.D.). Princeton University. OCLC 775707046 – via ProQuest. - ↑ 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. - ↑ "Mathematical Optimization Society".

Wikiquote has quotations related to ** Albert W. Tucker **.

- News from PRINCETON UNIVERSITY
- Albert W. Tucker at the Mathematics Genealogy Project
- 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 Institute, University of Minnesota.
- Biography of Albert W. Tucker from the Institute for Operations Research and the Management Sciences

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