Saddle Point
Back to the cover

Part I · Foundations

  1. 0 Mathematical Foundations
  2. 1 Observation, Beliefs, and Decision

Part II · Engines

  1. 2 Competing for Allocation: The Blotto Game
  2. 3 Bargaining, Commitment, and Repeated Cooperation
  3. 4 Signals, Disclosure, and Persuasion
  4. 5 Different Models of One Game
  5. 6 Leadership and Rules: Inspection
  6. 7 Decisions in Time
  7. 8 Many Agents
  8. 9 Networks, Dependence, and Resilience
  9. 10 Aggregating Information

Part III · Systems

  1. 11 Architecture of Decision Support
  2. 12 Simulation and Wargaming with AI Agents

Part IV · Limits

  1. 13 Where the Mathematics Stops
George B. Dantzig, 1936

Chapter 0 · Mathematical Foundations

George B. Dantzig

1914 – 2005

Photograph: George B. Dantzig, c. 1936. The Terrapin yearbook (1936), p. 54; photographer unknown; via Wikimedia Commons. Public domain in the United States, as recorded on the file page. Shown toned. File and licence

The problem on the desk

Air Force planning involved many interdependent activities and scarce resources. Dantzig needed a computable way to select an entire feasible programme, rather than apply separate planning rules. In 1947 this work produced the linear-programming formulation and simplex method.1

A life in moments

  1. 1914

    Portland

    Born on 8 November.1

  2. 1946

    University of California, Berkeley · Berkeley

    Completed his doctorate under Jerzy Neyman.2

  3. 1947

    US Air Force · Washington, D.C.

    Developed the simplex method for linear programming.1

  4. 1952

    RAND Corporation · Santa Monica

    Joined RAND.3

  5. 1960

    University of California, Berkeley · Berkeley

    Became professor of operations research.1

  6. 1966

    Stanford University · Stanford

    Moved to Stanford.1

  7. 1974

    Systems Optimization Laboratory · Stanford

    Founded the laboratory with Richard Cottle.4

  8. 2005

    Stanford

    Died on 13 May.5

Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.

In their own words

I didn’t discover the linear programming model all in a flash. It evolved.

An Interview with George B. Dantzig: The Father of Linear Programming, 19867

A story

The problems on the blackboard

Dantzig recalled arriving late to Neyman’s class and copying two problems as homework. Only later did he learn that they were unsolved research problems. Neyman accepted the results as the basis of his dissertation.6

Firsthand recollection recorded in 1984 and published in 1986; no overnight solution or magical “positive thinking” claim is added.

Around Dantzig

  • exchange John von Neumann Discussed linear programming with von Neumann in October 1947.8
  • co-author Abraham Wald Dantzig recalled that Wald added him as co-author after discovering overlap with his dissertation result.9
  • co-author Thomas L. Saaty Co-authored Compact City with Thomas Saaty.5

Advisor in the record Jerzy Neyman Students in the record Richard Cottle, Roger Wets, Yinyu Ye Mathematics Genealogy Project record

The genealogy lists only what the database records; a missing name is not a missing teacher.

The card in the book

Born in Portland, Oregon, he earned his Berkeley doctorate under Jerzy Neyman in 1946. As mathematical adviser to the US Air Force comptroller he formulated linear programming and, in 1947, the simplex method. He then worked at the RAND Corporation and at the University of California, Berkeley, and from 1966 at Stanford, where in 1974 he and Richard Cottle founded the Systems Optimization Laboratory. His later work includes decomposition methods for large structured programs and stochastic programming.

Main works Linear Programming and Extensions (1963); “Decomposition principle for linear programs”, with P. Wolfe (Operations Research 8, 1960); Linear Programming, with M. N. Thapa: vol. 1, Introduction (1997), vol. 2, Theory and Extensions (2003).

To read further

Sources (9)
  1. Who Was George B. Dantzig?, INFORMS; Biographical narrative
  2. An Interview with George B. Dantzig: The Father of Linear Programming, Donald J. Albers with Constance Reid; interviewee George B. Dantzig, 1986; pp. 301–302
  3. An Interview with George B. Dantzig: The Father of Linear Programming, Donald J. Albers with Constance Reid; interviewee George B. Dantzig, 1986; p. 310
  4. Operations Research at Stanford, Stanford University, Management Science and Engineering; Timeline: 1974
  5. George B. Dantzig, operations research professor, dies at 90, Stanford Report, 2005; Opening paragraph; paragraph on Compact City
  6. An Interview with George B. Dantzig: The Father of Linear Programming, Donald J. Albers with Constance Reid; interviewee George B. Dantzig, 1986; pp. 300–302
  7. An Interview with George B. Dantzig: The Father of Linear Programming, Donald J. Albers with Constance Reid; interviewee George B. Dantzig, 1986; p. 306
  8. An Interview with George B. Dantzig: The Father of Linear Programming, Donald J. Albers with Constance Reid; interviewee George B. Dantzig, 1986; pp. 308–310
  9. An Interview with George B. Dantzig: The Father of Linear Programming, Donald J. Albers with Constance Reid; interviewee George B. Dantzig, 1986; p. 301

The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.