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 (BA, MA) Princeton University (PhD) |

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 |

**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.

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.^{[ 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.

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 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 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.

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] }

- 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

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

**John Forbes Nash, Jr.**, known and published as **John Nash**, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Memorial Prize in Economics. In 2015, he and Louis Nirenberg were awarded the Abel Prize for their contributions to the field of partial differential equations.

**Thomas Eugene Kurtz** is a retired Dartmouth professor of mathematics and computer scientist, who along with his colleague John G. Kemeny set in motion the then revolutionary concept of making computers as freely available to college students as library books were, by implementing the concept of time-sharing at Dartmouth College. In his mission to allow non-expert users to interact with the computer, he co-developed the BASIC programming language and the Dartmouth Time Sharing System during 1963 to 1964.

**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. 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.

**Lloyd Stowell Shapley** was an American mathematician and Nobel Memorial 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 jointly 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, and for developing Kuhn poker. He described the Hungarian method for the assignment problem, but a paper by Carl Gustav Jacobi, published posthumously in 1890 in Latin, was later discovered that had described the Hungarian method a century before Kuhn.

**Jeffrey Renwick Weeks** is an American mathematician, a geometric topologist and cosmologist. Weeks is a 1999 MacArthur Fellow.

* 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.

**Colin Conrad Adams** is a mathematician primarily working in the areas of hyperbolic 3-manifolds and knot theory. His book, *The Knot Book*, has been praised for its accessible approach to advanced topics in knot theory. He is currently Francis Christopher Oakley Third Century Professor of Mathematics at Williams College, where he has been since 1985. He writes "Mathematically Bent", a column of math for the *Mathematical Intelligencer*. His nephew is popular American singer Still Woozy.

**Karen Keskulla Uhlenbeck** ForMemRS 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.

**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.

**Alan J. Goldman** (1932–2010) was an American expert in operations research.

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

The **Archives of American Mathematics,** located at the University of Texas at Austin, aims to collect, preserve, and provide access to the papers principally of American mathematicians and the records of American mathematical organizations.

**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".

- Nasar, Sylvia (January 27, 1995). "Albert W. Tucker, 89, Pioneering Mathematician".
*The New York Times*. - O'Connor, John J.; Robertson, Edmund F., "Albert Tucker",
*MacTutor History of Mathematics Archive*, University of St Andrews

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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