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.

From *Nobel Lectures, Economics 1969-1980*, Editor Assar Lindbeck, World Scientific Publishing Co., Singapore, 1992

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.*

Copyright © The Nobel Foundation 1975

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