Leonid Kantorovich

We continue our collection of stories about Great Petersburgers. Now he is considered the creator of the so-called mathematical economics. But during his life he was better known as a man who put “mathematics in the service of socialist construction.” That is exactly what was written in the program documents of the Leningrad Physics and Mathematics Society, which he reorganized in the early 30s of the last century. However, the methods of production planning that he had created turned out to be more applicable in countries that had never been involved in socialist construction. And in 1975, he received the Nobel Prize for his work. We are talking about the Soviet scientist Leonid Kantorovich.

1Leonid Vitaliyevich Kantorovich was born on January 19, 1912 (January 6, according to the old Russian style) in Saint Petersburg to a family of a doctor. He was a prodigy and so his talent revealed itself very early. In 1926, just at the age of 14, he entered St. Petersburg (then Leningrad) University (SPU).  A year later he started participating in the seminars of V.I. Smirnov, G.M. Fichtenholtz and B.N. Delone. It is natural that the first academic years formed his lifetime environment: D. K. Faddeev, I. P. Natanson, S. L. Sobolev, S. G. Mikhlin, and a few others with whom Kantorovich was friendly all his life also participated in Fikhtengolts’s circle. The first works of Leonid Vitalievich were mainly performed in 1927–1929. They were related to the descriptive theory of functions and sets. The theory of functions of a real variable and set theory occupied one of the central places in mathematics and had a significant impact on the development of other branches of mathematics. Kantorovich managed to solve a number of difficult and fundamental problems in this area.

After graduation from SPU in 1930, Kantorovich started teaching, combining it with intensive scientific research.  Since 1932 he worked as an assistant professor at SPU. From 1934 Kantorovich was a full professor at his alma mater.  He had written practically all of his major mathematical works in his Leningrad period. Moreover, in the 1930s he mostly published articles on pure mathematics, whereas the 1940s became his season of computational mathematics in which he was soon acknowledged as an established and acclaimed leader.

Soon after the publication of the fundamental monograph of S. Banach “Theory of Linear Operations”, one of the first national schools on functional analysis began to form at Leningrad University. Already in 1934, in a series of works by L. V. Kantorovich, important results were obtained on the theory of functionals and operators in Banach spaces

L. V. Kantorovich stood at the origins of the formation of modern computational mathematics. The first works on approximate methods of conformal mappings, variational methods, quadrature formulas, numerical methods for solving integral equations and partial differential equations were performed in the early 30s, when computational mathematics had not yet become an independent scientific discipline. Kantorovich has for a number of years been interested in the application of mathematics to a programming problem. He published an extensive monograph in 1939 entitled “Mathematical Methods in the Organization and Planning of Production”. Kantorovich should be credited with being the first to recognize that certain important broad classes of production problems had well-defined mathematical structures which, he believed, were amenable to practical numerical evaluation and could be numerically solved.

An important role in the development of computational mathematics was played by the book by L. V. Kantorovich and V. I. Krylov “Methods for the approximate solution of partial differential equations” (1936). This book, later called “Approximate Methods of Higher Analysis”, has been reprinted several times, translated into English, German, Hungarian, Romanian and is still widely used by specialists all over the world.

Speaking about his Leningrad period, we should name also the Higher Military Engineering School. During the years of World War II, Kantorovich was drafted into the armed forces, and teaching in this school was his main business. Professor L.V. Kantorovich was solving the problem of reducing risks and ensuring the safety of the Road of Life. This ice road winter transport route across the frozen Lake Ladoga provided the only access to the besieged city of Leningrad while the perimeter in the siege was actively maintained by the German Army. At this time, he wrote the original course “Probability Theory” (1946), intended for military schools and reflecting the specific military applications of this science. The Higher Military Engineering School, now called the Military Engineering-Technical University, still keeps the memory of the work of L.V. Kantorovich, and in 1999 a memorial plaque appeared on its building in St. Petersburg.

The necessity for development of modern effective numerical methods for analyzing of various applied problems has become especially acute in the last prewar and during the war years. And in 1948, in connection with the need to carry out important applied calculations, L. V. Kantorovich headed the Department of approximate calculations created at the Steklov Mathematical Institute in Leningrad. He understood that the further development of numerical methods should be based on the fundamental results of the theoretical branches of mathematics, and proceeded to research in this direction. The main results of these studies were summarized by him in his works of 1947–1948: “On the General Theory of Approximate Methods of Analysis”, “On the Newton Method for Functional Equations”, “Functional Analysis and Applied Mathematics”, awarded in 1949 by Stalin prize.

At the beginning of the 1950s, at the initiative of L. V. Kantorovich, the first specialization in computational mathematics in our country was organized at the Faculty of Mathematics and Mechanics of Leningrad University. Later this specialization became a department headed by V. I. Krylov, a co-author of Kantorovich. Leonid Vitaliyevich emphasized the importance of functional analysis as the theoretical basis of computational mathematics. Therefore, among the employees and graduates of the department of computational mathematics, there have always been many analytical specialists.

The work on computational mathematics is associated with the direct participation of L. V. Kantorovich in the development of computer technology. He led the design of new computing devices; he owns a number of inventions in this area. Together with his students, he developed original principles of machine programming for numerical calculations and, which was completely unusual in those years, for conducting complex analytical calculations.

2In 1957 Kantorovich was invited to join the Siberian Division of the Academy of Sciences to be constructed in the picturesque suburbs of Novosibirsk. He agreed and soon was elected a corresponding member of the Division of Economics of the Academy of Sciences of the USSR. Since then his major publications were devoted to economics, with the exception of the celebrated course of functional analysis. Already in 1942, he wrote the first version of his famous monograph, The Best Uses of Economic Resources. However, this work was so ahead of time and so inconsistent with the dogmas of the existing political economy that its publication became possible only in 1959. Then the pioneering ideas of L. V. Kantorovich were recognized and began to be used in economic practice.  The 1960s became the decade of his recognition. In these years he vigorously propounded and maintained his views of the interplay between mathematics and economics and exerted great efforts to instill the ideas and methods of modern science into the top economic management of the Soviet Union. In 1964 he was elected a full member of the Department of Mathematics of the Academy of Sciences of the USSR, and in 1965, the research of L. V. Kantorovich in the field of economic and mathematical methods was awarded the Lenin Prize. In 1975 the Nobel prize in economics was awarded to him and Tjalling C. Koopmans “for their contributions to the theory of optimum allocation of resources”.

 At the beginning of the 1970s Kantorovich left Novosibirsk for Moscow where he was still engaged in economic analysis, not seizing his efforts to influence the everyday economic practice and decision making in the national economy. Although he never resumed proving theorems, his impact on the mathematical life of Russia increased sharply due to the sweeping changes in the Moscow academic life.

Cancer terminated his path in science on April 7, 1986. He was buried at Novodevichy Cemetery in Moscow.