**Albert** **W**. **Tucker**

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

Born | Albert William Tucker28 November 1905 |

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

Nationality | Canadian American |

Alma mater | University of Toronto, Princeton University |

Known for | Prisoner's dilemma Karush–Kuhn– Tucker conditionsCombinatorial 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^{}[1] (1932) |

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]}

## Biography[edit]

**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 till 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 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.

## Works[edit]

- 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

**Tucker** Prize[edit]

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]}

## References[edit]

- ^
^{a}^{b}**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".

## Further reading[edit]

- 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

## External links[edit]

- 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

- 1905 births
- 1995 deaths
- 20th-century mathematicians
- Topologists
- Game theorists
- University of Toronto alumni
- Harvard University staff
- University of Chicago people
- John von Neumann Theory Prize winners
- People from Oshawa
- Princeton University alumni
- Princeton University faculty
- Presidents of the Mathematical Association of America