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
Lev S. Pontryagin, c. 1950

Chapter 7 · Decisions in Time

Lev S. Pontryagin

1908 – 1988

Photograph: Unknown photographer; Moscow State University / Wikimedia Commons, Lev Pontryagin, c. 1950, CC BY 4.0. Shown toned. File and licence

The problem on the desk

Pontryagin’s group sought necessary conditions for choosing the best controlled motion. In pursuit games he later studied constructions with convex sets that guarantee capture in specified linear systems.1,2

A life in moments

  1. 1908

    Moscow

    Born on 3 September.3

  2. 1929

    Moscow State University · Moscow

    Graduated from the university.3

  3. 1934

    Steklov Mathematical Institute · Moscow

    Joined the institute.3

  4. mid-1950s

    Steklov Mathematical Institute · Moscow

    Worked with Boltyanskii and Gamkrelidze on optimal processes and the maximum principle.2

  5. 1980

    Moscow

    Published the full treatment Linear Differential Games of Pursuit.1

  6. 1988

    Died on 3 May.3

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

A story

A principle developed together

Gamkrelidze’s retrospective identifies the work of Pontryagin, Boltyanskii and himself at Steklov in the mid-1950s. It gives a collaborative history of the maximum principle.2

Around Pontryagin

  • co-author Revaz Gamkrelidze Gamkrelidze worked with Pontryagin and Boltyanskii on the maximum principle.2

Recorded as advisor Pavel Sergeevich Aleksandrov Recorded as students Vladimir Grigorievich Boltyanskii, Revaz Valerianovich Gamkrelidze, Evgenii Frolovich Mishchenko Mathematics Genealogy Project record

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

Two desks

Pontryagin and Isaacs Controlling motion when objectives compete. The same problem from two desks →

The card in the book

Mathematician at the Steklov Institute in Moscow, blind from the age of fourteen. He first worked in topology — duality theorems, topological groups, characteristic classes — and from the 1950s turned to control, leading the group whose maximum principle became the foundation of optimal control theory; he later developed linear differential games of pursuit and evasion, pursuing the subject independently of Isaacs' line.

Main works Topological Groups (1938); The Mathematical Theory of Optimal Processes, with V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko (Russian 1961; English 1962); “Linear differential games of pursuit” (in Russian, Matematicheskii Sbornik, 1980).

To read further

Sources (3)
  1. Linear differential games of pursuit, L. S. Pontryagin, 1980; Matematicheskii Sbornik 112(154), pp. 307–330; author abstract
  2. On the history of discovery of the maximum principle, R. V. Gamkrelidze, 2019; Abstract; pp. 1–7
  3. Lev Semenovich Pontryagin (obituary), 1989; Opening page

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.