Kantorovich’s Early Life and Education
Leonid Vitalyevich Kantorovich (1912–1986) was born in St. Petersburg (later Leningrad) into a Russian-Jewish family. His father was a physician.
Kantorovich has stated that some of his earliest childhood memories are of the February and October Revolutions in 1917. He fled with his family to Byelorussia (now Belarus) for a year during the height of the subsequent Russian Civil War.
Kantorovich’s father died in 1922, when the boy was ten years old.
Kantorovich was a mathematical prodigy. In 1926, at the age of 14, he was accepted as a student in the Faculty of Mathematics and Mechanics at Leningrad State University.
In 1930, Kantorovich received his bachelor’s degree from Leningrad State University.
In 1935, Kantorovich received his doctoral degree in physico-mathematical sciences from the same university.
Kantorovich’s Career
In 1932, at the age of 20 and even before earning his doctorate, Kantorovich was appointed a full professor at his alma mater.
In 1939, Kantorovich became a professor at the Military Engineering-Technical University in Leningrad. During the war years and the Siege of Leningrad, he was heavily involved in defense work.
For instance, Kantorovich helped with the calculations that established safe routes across frozen Lake Ladoga during the winter—routes which became known as the Road of Life. He even helped walk vehicles laden with supplies for the starving city across the ice beneath a German bombardment.
For his heroic war work, Kantorovich was awarded several of his country’s highest military decorations.
After the war, around 1948, Kantorovich also became involved for a time in the Soviet Union’s nuclear weapons program.
Kantorovich eventually returned to work as a professor at Leningrad State University, where he taught until 1960.
From 1961 until 1971, Kantorovich served as head of the Department of Mathematics and Economics in the recently established Siberian branch of the USSR Academy of Sciences, which was located in the city of Novosibirsk, more than 2000 miles east of Moscow. He also helped to found the Department of Computational Mathematics at Novosibirsk State University.
From 1971 until 1976, Kantorovich served as head of the Institute of National Economic Planning’s research laboratory, located in Moscow.
In 1975, Kantorovich shared the Nobel Memorial Prize in Economic Sciences with Tjalling C. Koopmans.
Kantorovich’s Nobel Lecture, “Mathematics in Economics: Achievements, Difficulties, Perspectives,” was published in the American Economic Review, but not until 14 years later, in 1989 (see below).
Kantorovich’s Ideas
Kantorovich made highly significant contributions to both mathematics and economics.
In fact, many scholars who did not know Kantorovich personally assumed his works to have been authored by two separate individuals with the same name—one a mathematician and the other an economist.
Kantorovich’s earliest publications were in pure mathematics.
He published two books in Russian, on conformal mapping and variational analysis, during the early 1930s, culminating in Approximate Methods of Higher Analysis (in Russian), co-authored by V.I. Krylov and published in 1936 (see “Selected Works Authored or Co-authored by Kantorovich” below).
However, it was in 1939 that Kantorovich had the insight for which he is principally known and which led to his Nobel Prize.
In that year, Kantorovich published a pamphlet in Russian entitled Mathematical Methods of Organizing and Planning Production. This seminal work was published in an English translation 21 years later, in 1960 (see below).
In this text, Kantorovich laid the mathematical foundations for the field that is now known as “linear programming.”
Linear programming is a method of calculation designed to achieve the optimal solution for a class of problems whose mathematical models can be represented by linear relationships.
For example, under certain specified conditions linear programming may provide a rigorous technique for solving the problem of the optimal allocation of resources.
More technically, linear programming is an optimization technique for a system characterized by a linear objective function and linear constraints. The objective function defines the quantity to be optimized, while the goal of the calculation is to determine the extremal values of its variables.
After his 1939 breakthrough pamphlet, Kantorovich wrote several more articles and monographs applying linear programming to economic problems, sometimes working alone and sometimes with collaborators.
Nevertheless, for the most part, it was left to others to more thoroughly develop the economic implications of Kantorovich’s mathematical insights.
For Kantorovich always remained a mathematician at heart—one, moreover, who continued throughout his career to do cutting-edge work in pure mathematics (which we pass over here).
Selected Works Authored or Co-authored by Kantorovich
Approximate Methods of Higher Analysis, with V.I. Krylov (in Russian) (1936); English translation: Approximate Methods of Higher Analysis, with V.I. Krylov. Mineola, NY: Dover Books (1958).
Mathematical Methods of Organizing and Planning Production (in Russian) (pamphlet) (1939); English translation: “Mathematical Methods of Organizing and Planning Production,” Management Science, 6: 366–422 (1960).
“A New Method of Solving of Some Classes of Extremal Problems” (in Russian), Proceedings of the National Academy of Sciences of the USSR, 28: 211–214 (1940).
“On the Translocation of Masses” (in Russian), Proceedings of the National Academy of Sciences of the USSR, 37: 227–230 (1942).
“Functional Analysis and Applied Mathematics” (in Russian), Russian Mathematical Surveys, 3: 89–185 (1948).
Functional Analysis in Partially Ordered Spaces, with B.Z. Vulikh and A.G. Pinsker (in Russian) (1950).
The Best Use of Economic Resources (in Russian) (1959); English translation: The Best Use of Economic Resources. Oxford: Pergamon Press (1965).
Functional Analysis in Normed Spaces, with G.P. Akilov (1959).
Variational Methods for the Study of Nonlinear Operators, with M.M. Vainberg and G.P. Akilov (1964).
Seismic Design Decision Analysis: Seismic Risk and Principles of Seismic Zoning (out of print) (1974).
Problems of Application of Optimization Methods in Industry (out of print) (1976).
Essays in Optimal Planning (1976).
Functional Analysis, second edition (1982).
“My Journey in Science” (in Russian), Russian Mathematical Surveys, 42: 233–270 (1987); reprinted as “My Journey in Science,” in Lev J. Leifman, ed., Functional Analysis, Optimization, and Mathematical Economics: A Collection of Papers Dedicated to the Memory of Leonid Vital’evich Kantorovich. Oxford: Oxford University Press; pp. 8–45 (1990).
“Mathematics in Economics: Achievements, Difficulties, Perspectives,” American Economic Review, 79: 18–22 (1989).
Selected Works About Kantorovich
Boldyrev, Ivan and Till Düppe, “Programming the USSR: Leonid V. Kantorovich in Context,” British Journal for the History of Science, 35: 255–278 (2020).
Boyd, John P., “Correcting Three Errors in Kantorovich & Krylov′s Approximate Methods of Higher Analysis,” American Mathematical Monthly, 123: 241–257 (2016).
Cockshott, W. Paul, “Von Mises, Kantorovich and in-natura Calculation,” European Journal of Economics and Economic Policies: Intervention, 7: 167–199 (2010).
Gardner, Roy, “L.V. Kantorovich: The Price Implications of Optimal Planning,” Journal of Economic Literature, 28: 638–648 (1990).
Katsenelinboigen, Aron, “L.V. Kantorovich: The Political Dilemma in Scientific Creativity,” Journal of Post Keynesian Economics, 1: 129–147 (1978–1979).
Kutateladze, S.S., “Mathematics and Economics of Leonid Kantorovich,” Siberian Mathematical Journal, 53: 975–985 (2012).
Leifman, Lev J., ed., Functional Analysis, Optimization, and Mathematical Economics: A Collection of Papers Dedicated to the Memory of Leonid Vital’evich Kantorovich (1990).
Petrosyan, Leon A., Joseph V. Romanovsky, and David Wing-kay Yeung, eds., Advances in Economics and Optimization: Collected Scientific Papers Dedicated to the Memory of L.V. Kantorovich (2014).