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
John von Neumann, 1956

Chapter 0 · Mathematical Foundations

John von Neumann

1903 – 1957

Photograph: John von Neumann, 1956. ENERGY.GOV / U.S. Department of Energy, via Wikimedia Commons. Public domain in the United States. Shown toned. File and licence

The problem on the desk

Can random choices give each player a guaranteed value in a finite two-person zero-sum game? Von Neumann’s 1928 minimax theorem answered this mathematical question; his later collaboration with Oskar Morgenstern connected games with economic behaviour.1

A life in moments

  1. 1903

    Budapest

    Born on 28 December.2

  2. 1926

    University of Budapest · Budapest

    Received his doctorate for work on axiomatic set theory.3

  3. 1928

    Published his paper on games, including the finite minimax theorem.1

  4. 1930

    Princeton University · Princeton

    Began a visiting professorship.4

  5. 1933

    Institute for Advanced Study · Princeton

    Joined the permanent faculty.4

  6. 1944

    Princeton University Press · Princeton

    Published Theory of Games and Economic Behavior with Oskar Morgenstern.5

  7. 1957

    Died on 8 February.6

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

Some of the best inspirations of modern mathematics (I believe, the best ones) clearly originated in the natural sciences.

The Mathematician, 19478

A story

A visit about linear programming

Dantzig recalled visiting von Neumann on 3 October 1947. Their discussion connected linear programming with zero-sum games and duality.7

A documented retrospective account by Dantzig, not a contemporaneous transcript.

Around Neumann

  • co-author Oskar Morgenstern Co-authored Theory of Games and Economic Behavior in 1944.1
  • exchange George B. Dantzig Discussed linear programming with Dantzig in October 1947.7

Advisor in the record Leopold (Lipót) Fejér Students in the record Donald Gillies, Israel Halperin, Maurice Pryce Mathematics Genealogy Project record

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

Two desks

Neumann and Borel Randomisation in adversarial games. The same problem from two desks →

The card in the book

Born in Budapest, he studied mathematics there and chemical engineering in Zurich, taught in Berlin and Hamburg, and moved to Princeton in 1930; in 1933 he joined the first faculty of the Institute for Advanced Study. His work spans set theory, operator algebras, the mathematical foundations of quantum mechanics, ergodic theory, numerical analysis and the logical design of stored-program computers. In 1928 he proved the minimax theorem for finite two-person zero-sum games; with the economist Oskar Morgenstern he later wrote Theory of Games and Economic Behavior.

Main works Zur Theorie der Gesellschaftsspiele (Math. Annalen 100, 1928); Mathematische Grundlagen der Quantenmechanik (1932); Theory of Games and Economic Behavior, with O. Morgenstern (1944).

To read further

Sources (8)
  1. John von Neumann, INFORMS; Brief Biography, paragraphs on 1928 and Morgenstern; Selected Publications
  2. John von Neumann, 1903–1957, Salomon Bochner, 1958; p. 442
  3. John von Neumann, 1903–1957, Salomon Bochner, 1958; p. 443
  4. John von Neumann, 1903–1957, Salomon Bochner, 1958; p. 444
  5. John von Neumann, INFORMS; Selected Publications
  6. John von Neumann, 1903–1957, Salomon Bochner, 1958; p. 438
  7. 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
  8. The Mathematician, John von Neumann, 1947; Paragraph beginning “Most people, mathematicians and others” (original: The Works of the Mind, pp. 180–196)

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.