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
Leonid V. Kantorovich, 1975

Chapter 0 · Mathematical Foundations

Leonid V. Kantorovich

1912 – 1986

Photograph: Leonid Kantorovich, 1975. Photograph by Andrey Bogdanov, via Wikimedia Commons, CC BY 3.0 (https://creativecommons.org/licenses/by/3.0/). Indicate any crop or colour treatment. Shown toned. File and licence

The problem on the desk

In 1938 the Leningrad plywood combine asked how to allocate its equipment efficiently. Kantorovich turned a factory scheduling question into a general optimisation method: choose a feasible production plan and use resolving multipliers to test its optimality.1

A life in moments

  1. 1912

    Petersburg

    Born on 19 January.2

  2. 1926

    Leningrad University · Leningrad

    Entered the university at fourteen.2

  3. 1930

    Leningrad University · Leningrad

    Graduated in mathematics.2

  4. 1934

    Leningrad University · Leningrad

    Was confirmed in the rank of professor.3

  5. 1939

    Leningrad University · Leningrad

    Published his booklet on organising and planning production.1

  6. 1960

    Institute of Mathematics, Siberian Branch · Novosibirsk

    Moved with his Leningrad laboratory group to form the Department of Mathematical Economics.4

  7. 1975

    Shared the economics prize with Tjalling Koopmans for resource-allocation theory.5

  8. 1986

    Died on 7 April.2

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 was able to indicate a relatively simple general method for solving this group of problems

Мне удалось указать сравнительно простой общий метод решения этой группы проблем

Математические методы организации и планирования производства [Mathematical methods of organising and planning production], 1939; translation ours6

A story

A factory question became a general method

The 1939 booklet grew from lectures on industrial planning. It ranged beyond the original equipment problem to fuel, materials, transport and land use, using the same optimisation ideas.1

Around Kantorovich

  • shared a prize Tjalling C. Koopmans Shared the 1975 economics prize with Koopmans.5
  • correspondence Tjalling C. Koopmans In 1956, responding to Koopmans’s request for his transport paper, Kantorovich also sent his 1939 planning booklet.7

Recorded as advisors Grigorii Mihailovich Fikhtengol’ts, Vladimir Ivanovich Smirnov Recorded as students Gleb Akilov, Victor Havin, Gennady Rubinshtein Mathematics Genealogy Project record

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

Two desks

Kantorovich and Koopmans Allocating scarce resources under competing demands. The same problem from two desks →

The card in the book

Educated at Leningrad University, he became a professor there in 1934, moved to Novosibirsk in 1960 and to Moscow in 1971. He worked on ordered vector spaces, approximation theory and numerical methods. A problem of allocating machine capacity in plywood production, brought to him in 1938, led to his 1939 work on what is now called linear programming, with its resolving multipliers; in 1942 he formulated the mass-transport problem as an optimisation problem. He shared the 1975 Nobel Memorial Prize in Economic Sciences with Tjalling Koopmans for contributions to the theory of optimum allocation of resources.

Main works Mathematical Methods of Organizing and Planning Production (in Russian, 1939); “On the translocation of masses” (in Russian, DAN SSSR 37, 1942); The Best Use of Economic Resources (Russian 1959; English 1965); Functional Analysis in Normed Spaces, with G. P. Akilov (Russian 1959; English 1964).

To read further

Sources (7)
  1. Leonid Vital’evich Kantorovich (on his seventieth birthday), Russian Mathematical Surveys, collective anniversary article, 1982; p. 232
  2. L. V. Kantorovich, Institute for System Analysis, Russian Academy of Sciences; Biographical opening
  3. Leonid Vital’evich Kantorovich (on his seventieth birthday), Russian Mathematical Surveys, collective anniversary article, 1982; p. 229
  4. Leonid Vital’evich Kantorovich (on his seventieth birthday), Russian Mathematical Surveys, collective anniversary article, 1982; p. 234
  5. The Prize in Economics 1975: press release, Royal Swedish Academy of Sciences, 1975; 14 October 1975; award statement and Optimum Allocation of Resources
  6. Математические методы организации и планирования производства [Mathematical methods of organising and planning production], L. V. Kantorovich, 1939; Leningrad University edition, Introduction, printed p. 6 (PDF page 4, left page), second paragraph, opening clause
  7. Leonid V. Kantorovich, INFORMS; Brief Biography, paragraph on correspondence with Koopmans in 1956

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.