**Leonid Vital'evich Kantorovich** studied mathematics at Leningrad State University, receiving his doctorate in mathematics in 1930 at the age of eighteen. From 1934 to 1960 he was a professor of mathematics at Leningrad University. He held the chair of mathematics and economics in the Siberian branch of the USSR Academy of Sciences (1961-1971), then directed research at Moscow's Institute of National Economic Planning (1971-76).

Kantorovich's background was entirely in mathematics but he showed a considerable feel for the underlying economics to which he applied the mathematical techniques. He was one of the first to use linear programming as a tool in economics and this appeared in a publication *Mathematical methods of organising and planning production* which he published in 1939. Makarov writes in [24]:-

This may be considered a historic document, containing the facts about discovery of the linear programming. The mathematical formulation of production problems of optimal planning was presented here for the first time and the effective methods of their solution and economic analysis were proposed.

Kantorovich introduced many new concepts into the study of mathematical programming such as giving necessary and sufficient optimality conditions on the base of supporting hyperplanes at the solution point in the production space, the concept of primal-dual methods, the interpretation in economics of multipliers, and the column-generation method used in linear programming.

One of his most fundamental works on economics was *The best use of economic resources* which he wrote in 1942 but was not published until 1959. In this work Kantorovich applies optimisation techniques to a wide range of problems in economics.

He also proposed a theory to handle the economics of technological innovations. This had three components namely the effect on the producer, the effect on the consumer and, the novel part of the theory, the effect derived from the increasing economic potential arising from the innovation.

Kantorovich was a joint winner of the 1975 Nobel Prize for economics for his work on the optimal allocation of scarce resources. The article [12] is the autobiography which Kantorovich had to submit to the Nobel Prize committee who were considering him for the award.

In [8] Belykh examines the opinions of Western scholars on Kantorovich as a mathematical economist and concludes that:-

Despite the differences of opinion and attempts to assign Kantorovich to one economic school or another, all the scientists under consideration here emphasise his outstanding contribution to the development of economic sciences.

The work of Kantorovich which we have looked at up until now has been on the application of mathematical methods, particularly mathematical programming, to economics. It is this work for which Kantorovich is most famous, but he also worked in many other areas of mathematics. These other areas include functional analysis and numerical analysis and within these topics he published papers on the theory of functions, the theory of complex variables, approximation theory in which he was particularly interested in using Bernstein polynomials, the calculus of variations, methods of finding approximate solutions to partial differential equations, and descriptive set theory.

From 1929 he worked on the theory of analytic sets and the Baire classification of functions. This work continued through the early 1930s then in the late 1930s he studied ordered topological vector spaces. However later in his career he also became interested in computer architecture. For example in [9] Fet writes:-

We describe briefly computers created on the basis of Kantorovich's suggestions. We note the significance of the concept, put forth by Kantorovich, of the large-block organisation of computing processes and the influence of this concept on the development of the architecture of computer systems.

Makarov writes in [24] of Kantorovich's:-

... mathematical genius and the vast range of his interests and knowledge.

His remarkable contributions to mathematics, economics and computers was published in over 300 papers and books.

List of References (33 books/articles)

Article by: *J.J. O'Connor and E.F. Robertson*

Source: MacTutor History of Mathematics archive