### Leonid Vitaliyevich Kantorovich – Autobiography

I was born in Petersburg (Leningrad) on 19th January 1912. My father, Vitalij Kantorovich, died in 1922 and it was my mother, Paulina (Saks), who brought me up. Some of the first events of my childhood were the February and the October Revolutions of 1917, and a one-year trip to Byelorussia during the Civil War.

My first interest in sciences and the first displays of self-dependent thinking manifested themselves about 1920. On entering the Mathematical Department of the Leningrad University in 1926, I was mainly interested in sciences (but also in political economy and modern history, thanks to the most vivid lectures of academician E. Tarle).

At the University, I attended lectures and worked in seminars of V.I. Smirnov, G.M. Fichtengolz, B.N. Delaunay; my University friends were I.P. Natanson, S.L. Sobolev, S.G. Michlin, D.K. and V.N. Faddeevs.

My scientific activities started in my second university year covering the rather more abstract fields of mathematics. I think my most significant research in those days was that connected with analytical operations on sets and on projective sets (1929-30) where I solved some N.N. Lusin problems. I reported these results to the First All-Union Mathematical Congress in Kharkov (1930).

My participation in the work of the Congress was an important episode in my life; here I met such outstanding Soviet mathematicians as S.N. Bernstein, P.S. Alexandrov, A.N. Kolmogorov, A.O. Gelfond, *et al*, and some foreign guests, among whom were J. Hadamard, P. Montel, W. Blaschke.

The Petersburg mathematical school combined theoretical and applied research. On graduating from the university in 1930, simultaneously with my teaching activities at the higher school educational institutions, I started my research in applied problems. The ever expanding industrialization of the country created the appropriate atmosphere for such developments. It was precisely at that time such works of mine, *A New Method of Approximate Conformal Mapping ,* and *The New Variational Method* were published. This research was completed in *Approximate Methods of Higher Analysis*, a book that I wrote with V.I. Krylov (1936). By that time I was a full professor confirmed in this rank in 1934, and in 1935, when the system of academic degrees was restored in USSR, I received my doctoral degree. At that time I worked at the Leningrad University and in the Institute of Industrial Construction Engineering.

The Thirties was a time of intensive development of functional analysis which became one of the fundamental parts of modern mathematics.

My own efforts in this field were concentrated mainly in a new direction. It was the systematical study of functional spaces with an ordering defined for some of pairs of elements. This theory of partially-ordered spaces turned out to be very fruitful and was being developed at approximately the same time in the USA, Japan and the Netherlands. On this subject I contacted J. von Neumann, G. Birkhoff, A.W. Tucker, M. Frechet and other mathematicians whom I met at the Moscow Topological Congress (1935). One of my memoires on functional equations was published as a result of the invitation extended to me by T. Carleman in *Acta Mathematica*. *Functional Analysis in Semiordered Spaces*, the first complete book of our contributions in this field, was published in 1950 by my colleagues, B.Z. Vulikh and A.G. Pinsker, and myself.

In those days, my theoretical and applied research had nothing in common. But later, especially in the postwar period, I succeeded in linking them and showing broad possibilities for using the ideas of functional analysis in Numerical Mathematics. This I proved in my paper, the very title of which, *Functional Analysis and Applied Mathematics*, seemed, at that time, paradoxical. In 1949, the work was awarded the State Prize and later was included in the book, *Functional Analysis in Normed Spaces*, written with G.P. Akilov (1959) .

The Thirties was also important for me as I began my first economics. The very starting point was rather accidental. In 1938, as professor of the university, I acted as a consultant for the Laboratory of the Plywood Trust in a very special extreme problem. Economically, it was a problem of distributing some initial raw materials in order to maximize equipment productivity under certain restrictions. Mathematically, it was a problem of maximizing a linear function on a convex polytope. The well-known general recommendation of calculus to compare the function values in the polytope vertices lost its force since the vertices number was enormous even in very simple problems.

But this accidental problem turned out to be very typical. I found many different economic problems with the same mathematical form: work distribution for equipment, the best use of sowing area, rational material cutting, use of complex resources, distribution of transport flows.* This was reason enough to find an efficient method of solving the problem. The method was found under influence of ideas of functional analysis as I named the “method of resolving multipliers”.

In 1939, the Leningrad University Press printed my booklet called *The Mathematical Method of Production Planning and Organization* which was devoted to the formulation of the basic economic problems, their mathematical form, a sketch of the solution method, and the first discussion of its economic sense. In essence, it contained the main ideas of the theories and algorithms of linear programming. The work remained unknown for many years to Western scholars. Later, Tjalling Koopmans, George Dantzing, *et al*, found these results and, moreover, in their own way. But their contributions remained unknown to me until the middle of the 50s.

I recognized the broad horizons offered by this work at an early stage. It could be carried forward in three directions:

1) The further development of methods of solving these extremal problems and their generalization; their application to separate classes of problems;

2) A mathematical generalization of these problems such as, non-linear problems, problems in functional spaces, the application of these methods to extremal problems of mathematics, mechanics and technical sciences;

3) The spreading of the method of description and analysis from separate economic problems to general economic systems with their application to planning problems on the level of an industry, a region, the whole national economy as well as the analysis of the structure of economic indices.

Some activity took place in the first two directions (the results were published partly immediately, partly after the war), but the third one lured me most. I hope that the reasons were clarified enough in my Nobel lecture.

The studies were interrupted by the war. During the war, I worked as Professor of the Higher School for Naval Engineers. But even then I found time to continue my deliberations in the realm of economics. It was then that I wrote the first version of my book. Having returned to Leningrad in 1944, I worked at the University and at the Mathematical Institute of the USSR Academy of Sciences, heading the Department of Approximate Methods. At that time, I became interested in computation problems, with some results in the automation of programming and in computer construction.

My economics studies progressed as well. I particularly wish to mention the work done in 1948-1950 at the Leningrad Carriage-Building Works by geometrist V.A. Zalgaller under my guidance. Here the optimal use of steel sheets was calculated by linear programming methods and saved material. Our book of 1951 summarized our experience and gave a systematic explanation of our algorithms including the combination of linear programming with the idea of dynamic programming (independently of R. Bellman).

In the middle of the 50s, the interest in the improvement of economic control in the USSR increased significantly, and conditions for studies in the use of mathematical methods and computers for general problems of economics and planning became more favourable. At that time, I made a series of reports and publications and prepared the above-mentioned book for publication. It appeared in 1959 under the title, *The Best Use of Economic Resources*, and contained a broad exposition of the optimal approach to such central problems of economics as planning, pricing, rent valuations, stock efficiency, “hozraschet” problems and decentralization of decisions. Precisely at that time, I contacted foreign scholars in this field. As a particular result, thanks to the initiative of Tjalling Koopmans, my 1939 booklet was published in *Management Science*, and, somewhat later, the 1959 book was translated as well.

Some of the Soviet economists met the new methods guardedly. Together with the book, I must mention the special Conference on Mathematical Methods in Economics and Planning held by the Academy of Science. The participants of the conference were some prominent Soviet mathematicians and economists. The conference approved the new scientific direction. But this time we had obtained some positive experience of its applications.

The field attracted a number of young talented scientists, and the preparation of such hybrid specialists (mathematician-economist) began in Leningrad, Moscow, and some other cities. It is worth noting that in the newly-organized Siberian Branch of the Academy of Sciences, conditions for new scientific directions were especially favourable. A special laboratory on the application of mathematics in economics headed by Nemchinov V.S. and me was created. Its main body belonged to the Leningrad and Moscow schools. In Akademgorodok it was integrated into Institute of Mathernatics as a department.

I was elected Corresponding-Member of the Academy in 1958 and came to Novosibirsk in 1960. Out of my group in Novosibirsk, a number of talented mathematicians and economists emerged.

In spite of continual discussions and some critique, the scientific direction gained recognition more and more by both the scientific community and governmental bodies. The token of this recognition was the Lenin Prize which I was awarded in 1965.

Now I head the Research Laboratory at the Institute of National Economy Control, Moscow, where high-ranking executives are introduced to new methods of control and management. I act as consultant to various governmental bodies.

I was married in 1938. My wife, Natalie, is a physician. We have two adult children (d. and s.), both working in mathematical economy.

* A. Tolstoy had stated this problem before me (1930). He gave an approximate method of its solution. Later, the same problem was stated by F. Hitchcock.

This autobiography/biography was written
at the time of the award and first
published in the book series *Les Prix Nobel*.
It was later edited and republished in *Nobel Lectures*. To cite this document, always state the source as shown above.

*Leonid Kantorovich died on April 7, 1986.*

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