Leonid Kantorovich Biography

Leonid Vitalievich Kantorovich Leonid Vitalievich Kantorovich entered the galaxy of the largest scientists of the twentieth century due to his capital contribution to mathematics and economics. The studies of L. Kantorovich in the field of functional analysis, computational mathematics, the theory of extreme tasks, the descriptive theory of functions and the theory of sets have influenced the formation and development of these mathematical disciplines, and served as the basis for the formation of new scientific areas.

Kantorovich is rightfully considered one of the founders of the modern economic and mathematical direction, the core of which is the theory and models of linear extreme tasks. This direction was then reduced and developed in the writings of other scientists, first of all, J. Danzig and was called linear programming. The ideas and methods of this discipline are widely used to set and solve various extreme and variational problems not only in the economy, but also in physics, chemistry, energy, geology, biology, mechanics and management theory.

Linear programming also has a significant impact on the development of computing mathematics and computer technology. It seems to us that no one else did so much to use linear programming in economic theory, as L. Kantorovich was born on January 19, his creative abilities were manifested unusually early. At the age of 14, he entered the Leningrad State University and a year later he began active scientific activities at the seminars V.

Smirnov, G. Fichtengoltz and B. The first works of Leonid Vitalievich belonged to the descriptive theory of functions and sets. Basically, they were made in - gg. The theory of functions of the material variable and the theory of sets then occupied one of the central places in mathematics and had a significant impact on the development of other sections of mathematics.

Kantorovich managed to solve a number of difficult and fundamental problems in this area. At the end of LSU in the city of Leonid Vitalievich taught at higher educational institutions of Leningrad, while continuing active scientific activity. From these educational institutions, in addition to Leningrad University, we will call a particularly higher military engineering and technical school.

During the Great Patriotic War, L. Kantorovich was called up in the armed forces, and teaching in this school was his main business. At this time, he wrote the original course “Probability Theory”, intended for military educational institutions and reflecting the specific military applications of this science. Vitu, now called the Military Engineering University, still stores the memory of L.

Kantorovich, and in the city of Kantorovich worked as a professor, and in January, in G., soon after the release of the fundamental monograph of S. already in the city of Kantorovich, important results were obtained on the theory of functionals and operators in banach spaces that significantly complement the classical studies of I. In the same years, L. Kantorovich put forward the fundamental idea of ​​studying the general functional spaces endowed with the structure of a conditionally complete vector lattice.

The need to attract the structure of order in a functional analysis was realized almost simultaneously by a number of mathematicians F. The rice and somewhat later by M. Crane, G. Birkgof, G. G. L. Kantorovich, a class of ordered vector spaces with ordinal completeness, has a number of fundamentally important specific properties that allowed us to propose new methods of studying functional objects, including classical ones.

The theory of such spaces-they are called the spaces of Cantorovich or K-space-is now one of the main sections of functional analysis. These issues were devoted to the Kantorovich, published in Kantorovich with his students B. Wulich and A. The last quarter of the last century, clearly showed that the so -called expanded or universally complete spaces of Cantorovich are nothing more than images of the field of material numbers in the boulevorant models of the classical theory of the sets of Ceremrelo - Frenkel.

Thus, the spaces of Kantorovich are as inevitable in mathematics as many material numbers. As a curious illustration, we note that in connection with the development of a boulevic analysis, the expanded spaces of Cantorovich were re -opened in the United States under the name of the Bolevs of linear spaces almost half a century after their appearance in Leonid Vitalievich and his students.

Kantorovich stood at the origins of the formation of modern computing mathematics. The first works on close -based methods of conformal display, variational methods, quadrature formulas, numerical methods for solving integrated equations and equations in private derivatives were performed by L. Kantorovich in the early twenties, when computational mathematics has not yet taken shape in an independent scientific discipline.

An important role in the formation of computational mathematics was played by the monograph by L. Kantorovich and V.Krylova “Methods of approximate solution of equations in private derivatives” G. This book, which was subsequently called “Conditioned Methods of Higher Analysis”, was repeatedly reprinted, translated into English, German, Hungarian, Romanian and is still widely used by specialists around the world.

The need to develop modern effective numerical methods for analyzing various applied tasks began to be especially acutely felt in the last pre -war and war years. And in the city of Kantorovich he headed the created at the Mathematical Institute. Steklov and the department of close computing located in Leningrad. He understood that the further development of numerical methods should be based on the fundamental results of theoretical sections of mathematics, and began research in this direction.

The main results of these studies were generalized by him in the work - GG. Stalin State Prize. In the beginning of the 10s, on the initiative of L. Kantorovich at the Mathematician Faculty of Leningrad University, the first specialization in computational mathematics was organized in our country, and later the department, which was originally headed by co-author V. Leonid Vitalievich, always emphasized the importance of functional analysis as the theoretical base of computing mathematics.

Therefore, among the employees and graduates of the departments of computing mathematics in LSU and NSU created by him, there have always been many specialists of the analytical profile. L. Kantorovich’s direct participation in the development of computer technology is associated with the work on computing mathematics. He led the construction of new computing devices, he owns a number of inventions in this area.

Together with students, he developed the original principles of machine programming for numerical calculations and, which was completely unusual in those years, for conducting complex analytical calculations. Kantorovich “Mathematical methods of organization and planning of production”, which recorded the opening of linear programming - a direction that had a great influence on the development of economic science.

In this work, Leonid Vitalievich first gave a mathematical setting of production tasks of optimal planning and suggested effective methods for solving them and the techniques of economic analysis of these problems. Thus, the idea of ​​optimality in the economy was put on a strong scientific foundation. Kantorovich already considered it necessary to continue research in the following areas: the further development of linear programming algorithms and their concretization for individual tasks of tasks; generalization of the proposed methods in order to study the wider classes of extreme tasks with restrictions, including nonlinear tasks and tasks in functional spaces; the application of such methods to the extreme tasks of mathematics, mechanics and technology; the distribution of new methods of economic analysis of individual production tasks for general economic systems; The application of these methods to the tasks of planning and analyzing the structure of economic indicators at the level of the industry, region and the national economy as a whole.

Published in the city of Zalgaller reflects the remarkable experience of authors to use the methods of optimal calculations in the tasks of industrial reverse in the pre -computer period. Some studies in the first two directions by L. Kantorovich were carried out in the prewar years. Now he concentrated the main efforts on the development of the third direction.

However, this work was so ahead of time and did not correspond to the dogmas of the then political economy and it was the dogmas, and not the essence that its publication was possible only in the city of then the pioneering ideas of L. Kantorovich became recognition and began to be used in economic practice. Kantorovich "Economic calculation of the best use of resources." In the future, it was translated into English, French, Japanese, Romanian, Slovak.

At this time, he still continued his mathematical research, and in the same year his book with G. Akilov “Functional analysis in normalized spaces”, which also had several publications and translations. Kantorovich in the field of economic and mathematical methods were awarded the Lenin Prize together with Academician V. Nemchinov and who came to the economy of prof. Novozhilov, and in the city of Kantorovich, together with the American economist T.

Kupmans, was awarded the Nobel Prize for Economics for contribution to the theory of optimal use of resources. Kantorovich was in the first group of scientists invited to work in the Siberian department. In - gg. Nemchinov and L. Kantorovich headed the laboratory for the use of mathematical and statistical methods in economic research and planning of the Siberian branch. Kantorovich moved to Novosibirsk and joined as a mathematical and economic department into the Institute of Mathematics of the Siberian Branch, now bearing the name S.The Moscow group of this laboratory became a core in the creation of the Central Economic and Mathematics Institute of the Academy of Sciences, gave an impetus to the creation of groups at Moscow State University and in a state plan, and one of the members of this group reached the post of First Deputy Minister of Economy of Russia.

Even before moving to Novosibirsk under the leadership of L. Kantorovich in Leningrad, research on the theory and numerical methods of mathematical programming, as well as in the field of theory and practical use of optimal planning models, were deployed. In particular, the optimal taxi tariffs developed here were implemented on a country scale and brought a great economic effect.