Leonid Kantorovich

Picture of Leonid Kantorovich

Date of Birth: 01/19/1912

Age: 74

Place of birth: St. Petersburg

Citizenship: Russia

About the wonderful man - Leonid Kantorovich

Part I. mathematician.

Father Kantorovich, and later the older brother, were doctors. Sam L. He showed a bright tendency for mathematics and entered the University of Leningrad for this specialty.

Close to the university years and his friends I.P.Natanson D.K.Faddeev, his senior by six years and three courses, a long time his name was Lenechka. 15 years old, he went to the scientific seminars of senior courses, and co-author on the first work E.M.Livenson two course ahead of him. After graduating from the university in 18 years, LV Two years was a graduate student at G.M.Fihtengoltsa, with 20 years - lecturer, and 22 - a full professor of native faculty.

Many features are inherent in his scientific work, his books, teaching style, its penetration into the application threads to communicate with his students and colleagues, and finally - its resistance to public conflicts.

LV He considered that a reasonable generalization, integration problems can give its solution more than analyze the details. It is in this way they had solved a number of difficult problems in the theory of functions set out in the Moscow school of Academician Luzin. It is too early to strengthen the scientific authority LV

When a group established on the initiative of the leading mathematicians of the Leningrad mathematician VI Smirnov organized "workshop without a conductor", to explore and develop a new branch of mathematics - functional analysis, LV Soon came the leaders of the general theoretical branches of functional analysis. In particular, L. He created the theory of partially ordered spaces, called in his honor K-space.

LV always seen, sometimes distant, links to different areas of mathematics and its possible applications of the theoretical results.

For computational mathematics have become classics of his book "Methods of approximate solutions of partial differential equations" (1936), in the completion of the form, "Approximate methods of higher analysis" (1941). And his great article "Functional analysis and applied mathematics" (1948) literally changed the face of computing mathematics. This article has been marked by the award of LVKantorovich Stalin Prize in 1949 At the same time he received the award for individual government involved in the atomic project.

The abundance of ideas worked out in LV ability to work in parallel on different themes, and these themes enthrall group of employees. Therefore, in most books LV He had co-authors. In this it is similar to one of the most famous mathematicians of Moscow - Israel Moiseevich Gelfand, now living in the United States.

Often LV I gave orders that for the first time to the Executive seemed prohibitive. But clarity of intent and support of praise when the first successes have inspired. His staff and colleagues grew from communicating with him. (I myself had the opportunity to carry out these orders, LV - in 1940 and in 1948-53 gg.).

It was peculiar and pedagogical activity LV Having become in 20 years an assistant professor at the university, he was elected Professor of parallel, Head. the Department of Mathematics of industrial and construction university, where he taught from the age of 18. When LV came to the first lecture, the students pair screamed to him, "Man, get to your place! Professor will "now. By 1941 this institution was formed Higher Military Engineering Technical School. Ordinary LV assigned once the rank of Major. With this school, he spent the war years in Yaroslavl, performing and applied research, and wrote a course in probability theory, focused on military matters (published in 1946). Who is this building, now the Military Engineering University in St. Petersburg have a plaque that is from 1930 to 1948. I worked Leonid Kantorovich.

But his main work in the 1932-1941 and 1945-1960 years. (Before leaving for Novosibirsk) was on the Mathematics and Mechanics Faculty of the University and in the LOMI (the Leningrad section of the Mathematical Institute. Steklov, Academy of Sciences of the USSR).

As a lecturer for mathematicians LV I did not have the artistry inherent in his teacher G.M.Fihtengoltsu. But LV It gives us more: he seems to be thinking out loud in front of us. And we understand not only prove the theorem, but also the "why and how it is made," and often find themselves able to prove the following.

On examination he did not forgive misunderstanding. When our student group he put a deuce, and a good student, close to LV the house, asked him to reexamine that, he replied: "You work out with her. And when she will know, tell me. That`s when I pereekzamenuyu it. " LV He insisted on high standards for training on practical exercises on the analysis. Not by chance the head of the Department of Analysis at Moscow University noted that passed into the Moscow State University of LSU students distinguish strong skills in mathematical analysis. And in 1938 LV He led the student group of 1st course. According to the choices we make forward-looking report, we discussed unsolved problems, learn scientific communication. They put in the universities of Leningrad and Novosibirsk a number of new courses were created new specialties.

In LOMI parallel with theoretical and partly - applied problems (for example, - the approximate realization of conformal mappings) LV He led a small group of computing trends. He knew how to choose the methods and ways of accounts available to available computational tools. Under his leadership and M.K.Gavurin V.N.Faddeeva created a table of Bessel functions. necessary at the time for a table of applications have also been developed for the calculation of the bottoms gateways.

Not by chance in 1948 LV assigned to head the new Department of Computing, which fulfilled one of the calculations for the atomic project. Then he joined a group of seven university graduates. Among them it was and I later ran out of school due to stay at the front in 1941-45. But two LV not included in the atomic project: V.P.Ilina he attracted to theoretical work on functional analysis, and I - to the cutting tasks related to mathematical and economic work of the LV

Computing means confined to his department while mechanical adding machines of the "Mercedes" and tabs. It - relay devices, working with punch cards. Once they have served a population census, and then used for urban and trade statistics.

In an effort to expedite the bill, LV for the first time included in the programming of the parallelism of action, and also invented a "function generator" that allowed Tabs, in the course of the account, look in the function table. This converter is the size of a piano, contained a 8000 semiconductor valves. Set tables simultaneously connected, sealed on the replacement board, was very great. The device has been manufactured and used. Somewhat later, LV He proposed a scheme for electric desk calculator. It was finalized and issued long Podolsky plant. Of course, the international development of computers in a short time has made unnecessary the like. But I kept the value of the proposed LV "Conveyor processor" for solving problems of linear algebra.

If the innovative idea of ??parallel accounts LV I realized even in primitive conditions, his work on the block programming by alphabetic calculations on a computer ahead of time. They appeared before there was technology, now allows it to carry out.

Striking organizational skillfulness LV Crowded designs he created for each topic a separate small team, sometimes all of 2-3 people (including himself). They were a group of close scientific communication, and when the question makes it clear that clearly separate private jobs each. Maybe this manner were observed in LV still a student when he wrote to E.M.Livensonom (who moved to Ufa in 1931 in connection with his father`s link), the first work on the theory of functions, or when they I.P.Natansonom and D.K.Faddeevym (later - the outstanding scientists and top-notch lecturers) created the mathematics course for industrial and construction Institute.

The theory of partially ordered spaces LV developed with other friends and B.Z.Vulihom A.G.Pinskerom (later - headed the department in other universities).

Books on approximate methods he wrote with V.I.Krylovym (later academician of Belarus).

A classic was his course "Functional Analysis", written jointly with G.P.Akilovym (later Akilov already with their graduate students V.P.Havinym B.M.Makarovym and modernize the program to analyze at LSU and later Akilov left with LV . in Novosibirsk, where he taught at the university, even after the loss of the legs).

On the problem of the atomic project became his right-hand V.S.Vladimirov (later Academician and director of MIAN). Other members of this group became the leading masters of the programming and V.P.Ilin was awarded the State Prize for his theoretical studies.

To work on LV function generator drew M.K.Gavurina and student of the Polytechnic Institute V.L.Epshteyna for which it was the design of the thesis. Even the writer of these lines took part - was a quadratic interpolation algorithm for the device.

By designing a calculator LV drew N.P.Posnova and Yu.P.Petrova.

Separate groups of employees under the direction of LV developed promising areas of programming mentioned above: K.V.Shahbazyan and moved along with the LV 60 years in Novosibirsk L.T.Petrova, V.A.Bulavsky, M.A.Yakovleva.

Important for the development of mathematics of his work "On the mass transfer" LV wrote in 1957 together with G.Sh.Rubinshteynom, then also moved to Novosibirsk.

The book "A rational cutting of industrial materials" (1951, 1972) LV co-wrote the geometry V.A.Zalgallerom, the author of this article.

Here are characteristic of the organizational abilities LV episode, narrated by today`s president of the St. Petersburg Mathematical Society Anatolii Moiseevich Vershik. In 1958 Vershik already was a graduate student at Akilov and was a member of the youth environment LV Then in Leningrad revised tariffs for buses and taxis. Moscow has already changed the bus fare badly. In Leningrad, a taxi used unevenly and many were idle. We seek the advice of LV, the newly elected member of the Academy of Sciences in Economics.

To study the question of LV gathered a group of young mathematicians, he gave different orders. It was a kind of "action" in which LV He acted as a director. Some things were his spontaneous inventions. On the bus fares know little. A taxi for LV, familiarized with the structure of fleet costs and knowing from personal observations of taxi drivers desire to avoid short trips, offered to reduce pokilometrovy fare, but the initial fee to enter the "landing". For a quantitative analysis of this proposal required statistics range trips. LV He organized the survey. In addition was the general meeting of the drivers. It turned disparate drivers in a single expert. Each of them were asked to answer questions on a wide range of profiles, drawn LV and printed in the desired number of copies of his wife.

Transportation officials, unlike the drivers did not understand why the proposed measure will help. And added that it is impossible to trust the drivers, who will "lie in the questionnaires." LV He replied: "Yes. But they will not know which way to lie. And on average, we get the correct data. " Officials also considered it impossible to convert taxis to include initial fees. LV He asked his nephew Yu.B.Arkhangelskogo, and he gave the scheme a simple modification of the taximeter.

It was clear that the reduction in tariff pokilometrovogo increase the demand for taxis. But the "elasticity of demand" - consumer response to price change - has been little studied, and LV He came from his hypothesis of the logarithmic nature of elasticity. Tariff was adopted and was a complete success. The most surprising is that the reaction of the population forecast proved to be accurate, the error was in the minimum limits.

Part II. The Economist.

In 1937, to the Kantorovich turned to the next task. For the production of plywood used in a certain ratio assortment veneer 8 grades. Each of the 5 machines for the production of veneer has each class its performance. How to distribute the tasks among the machines to get veneers in the desired range with the highest performance? LV I saw that for the solution of such problems there is no ready method, and this method is invented. This method has been associated with the introduction of auxiliary factors, which he called "resolving multipliers".

With its depth of thinking L. immediately I realized that such problems arise whenever necessary the most economical use of limited resources. And he wrote, and the university in the same 1939 published the brochure "Mathematical methods of organizing and planning." It describes a method and listed many of the economic issues, in which it can be useful.

This booklet LV I created the branch of mathematics, which was later called linear programming.

I do not think that this is - an unexpected and highly complex problem of inaccessible mathematics. Even when he was mayor of Fourier province during the Great French Revolution I met them. Whatever LV this kind of problem for the transport networks becoming an engineer-economist in 1941, Alexei Tolstoy describe all these tasks can be geometrically (on multidimensional convex polyhedra) and, using the terminology of Minkowski, to trace the geometric meaning of the method of L.

Deepest merit LV It was that he immediately realized that the emerging factors are the nature of value. With the expansion of tasks on macroeconomics suggests a rational structure of economic indicators. What is in this way possible in a planned economy to upgrade pricing. And to overcome the disadvantages of excessive centralization of economic decision-making on the basis of such prices.

I read this booklet in 1939, and at the same time from Professor I.P.Natansona heard that "L. He wrote a brilliant job. "

The brochure was sent to all ministries, but the response was not followed. In 1940-41. LV already wrote a separate work on the sawmill and, in conjunction with Gavurin, - optimization of freight traffic. These articles lay in the offices of almost 9 years old, but still were published in 1949, when the LV He was awarded the Stalin Prize for mathematical work.

In 1942, already in Yaroslavl, LV I wrote most of the manuscript "Economic calculation, providing the most appropriate use of resources." With support from Acad. Sobolev she was transferred to the State Planning Committee. In September 1942, Vice-Chairman of the State Planning Commission and V.N.Starovsky G.P.Kosyachenko it did not approve. (This was followed in the office of Chairman of the State Planning Committee NA Voznesensky even discussed whether to arrest LVKantorovich necessary). At the same LV I gave a talk in the seminar of Acad. K.V.Ostrovityanova. And there has been a sharp critic. One of those present said: "Optimum Pareto offers even fascist, Mussolini`s favorite." This phrase was in the genre of political denunciations of those times. It would not be wrong to generalize the advice of the workshop saying, do not imagine yourself Marx and better burn his manuscripts.

Some economists, which LV gave his manuscript to read, then avoided meeting him.

LV very upset by the result of the visit to Moscow. For a while he did his work even links to the brochure 1939

Also in 1942 LV publishes the work "On the movement of the masses."

The transport problems "permitting factors" Kantorovich turned into potentials. Not only clear surface that appear in the famous Monge geometric work "On the cut and fill" written even under Napoleon, were none other than the potential level surfaces Kantorovich. Now the task of the economical movement of soil is called Monge-Kantorovich.

The article "On the mass transfer" was the first mathematical-economic work LV, translated into English. Translation it is true, was made only in 1959. At the same time he began his correspondence with T.Kupmansom.

Times have changed gradually. Even in 1954, the same Starovsky writes in his review that offers LV on the application of mathematics to the specific issues should be dealt with the involvement of the relevant industries. A proposal LV the revision of the system of economic indicators are completely unacceptable. However, in 1958 LV was elected a corresponding member of the Academy of Sciences of the USSR on the economic branch.

In LV was the creed, which expresses one of his phrase: "Scientists have the right and duty to speak the truth." And he said impartially on department meetings, and, importantly, the General Meeting of the Academy of Sciences of the USSR, the backwardness of the Soviet economic science and void speeches and publications.

If LV defended his awards and titles, the educated economist V.V.Novozhilova for the development of the same as that of the LV views, disqualified from running a department of Economics of the Leningrad Polytechnic Institute.

In the 1958-59 biennium. LV He decides to publish the manuscript of his great 1942. He edited it. I remember how he explained to me that he had decided to replace the term "resolving multipliers" to "objectively determined valuations". He wanted to publish a book in the Leningrad University. The final word was for the vice-rector for Social Sciences Tyulpanov. He said that the book is very interesting, but take it for publication Party card he will not. The book was published in 1959 in Moscow publishing house of the Academy of Sciences.

I remember how, after its publication I was summoned to a special department to introduce the article appeared in the US Campbell "Marx, Kantorovich, Novozhilov." I was struck by the words of the article: "Interestingly, the term" objectively determined valuations ". Apparently, it is - the most that we can say today in the USSR. " (By this time, the United States views LV independently developed T.Kupmans, used the term "shadow prices").

In 1964, LV as a mathematician was elected Academician of the Siberian Branch of the USSR and moved to Novosibirsk.

Domestic persecutors LV, however, were not appeased. One of them, L.M.Gatovsky, editor of "Issues of Economics", offended once recall LV of his works, published in the journal "Communist" an article on the book of L. Article entirely fit into the already aging genre of political denunciations. It caused mass protests of scientists. (Even I have sent to the address of the then ideologue Suslov letter in which he wrote that the employees of "Communist" magazine it would be necessary to pull up for the fact that they, as the organ of the Central Committee of the CPSU, are opposed to objective science).

Sam L. I never became a pose offended. It is only time and again explained his position. And LV sent to the "Communist" is such an explanatory article. Revision arranged a meeting of scientists, but not to parse the infamous article Gatovsky, and for the discussion of article L. The invitation I received phrase was deleted, "the article is attached." They were afraid to send it.

Sensing the mood of the vast majority - for "LV", chief editor for discussion did not come, entrusting management of the Deputy Assembly.

I remember that first climbed on stage Academician A.I.Berg full admiral and form a strong voice began: "For us there is no doubt that the Kantorovich rights. The question is how to use it. "

Gatovsky and a couple of his supporters at the meeting looked pitiful. But the article L. magazine "Communist" was never published.

At the end of 1959 LV He began work on a new generation of economists. In the fall of 1959 under the auspices of the Rector and Academician Aleksandrov Yu.V.Linnik at the economic faculty of Leningrad University was created by the efforts of LV and V.V.Novozhilova disposable sixth year. On his left the best part of graduating fifth year and added the young employees of the State Planning Commission, several foreigners from socialist countries and even the young teachers of the faculty; there were also a volunteer. They were to look deeper into the math, to learn linear programming and its relationship with the already known to them the economy. I had a chance to read them a lecture on geometry.

Of course this came from Moscow A.Anchishkin future academicians and S.Shatalin; Moscow scientists and Yu.Shvyrkov A.Smertin; a number of heads of departments of the future of the economy of St. Petersburg universities; A.Laschyak and Yu.Fetsianin from Czechoslovakia (the last one was the minister in Slovakia). A large group of graduates of the sixth course went to LV in Novosibirsk, where they continued to work under his leadership.

Since linear programming included gradually in the programs of all universities.

Times continue to change, and in 1965 LVKantorovich, V.V.Novozhilovu V.S.Nemchinovu and was awarded (jointly) Lenin Prize. This is partly due to the desire to fix the priority in the creation of linear programming, which has been rediscovered and began to be used in the United States.

Finally, in 1975 LVKantorovich T.Kupmansu and American scientists were awarded a joint Nobel Prize in Economics.

It may be interesting for the reader to know that before the award of the Nobel Prize Committee, the representative read out a description of the merits of each of the winners. Here is the text of the pronounced LV

(Speech Sciences Professor Ragnar Bentzelya Royal Academy).

Your Majesties, Your Royal Highnesses, ladies and gentlemen.

The main economic problems are the same for any company, regardless of its political organization, whether it is capitalist, socialist or any other. Since the stock of productive resources is limited everywhere, every society faces a range of issues relating to the optimal use of existing resources and the equitable distribution of income among citizens. Point of view from which can be considered similar regulatory issues, does not depend on the political organization of society under consideration. This fact is well illustrated by the two winners of this year - Professor Leonid Kantorovich and Koopmans Tjalling. While one of them lived and worked in the Soviet Union, and the other - in the United States, the two researchers showed striking similarities in their choice of problems and methods. For both production efficiency took center stage in their studies, and independently of each other, they have developed a similar production model.

In the late thirties stood before Kantorowicz specific routine problem: how to combine the existing factory production resources so as to maximize productivity. He solved this problem by creating a new type of analysis, later called linear programming. This method of finding the maximum value of a linear function under constraints consist of linear inequalities. A characteristic feature of this method is that the computation gives as a byproduct, some expressions called "shadow prices" which have certain properties that make them suitable for use as the estimated prices.

In the next two decades Kantorowicz continued to develop his method of analysis, and in a book published in 1959, he applied it also to macroeconomic problems. In addition, he made a further and very important step, aligning the theorem of linear programming and the theory of optimal planning of the socialist economy. He came to the conclusion that rational planning should be based on the results obtained during the optimization calculations concerning the type of linear programming, and further that the production decisions could be decentralized without loss of efficiency - the level of decision-makers, can be reduced if the use "shadow prices" as the basis for determining the profitability of these decisions. These studies Kantorowicz strongly influenced economic discussions ongoing in the Soviet Union. He emerged as the leader of the "mathematical school" Soviet economists, and, consequently, the group of researchers who recommend planning to reform the foundations of art. An important part of their argument is the thesis consists in the fact that, including a special interest rate of successful decentralization of production decisions in a centrally planned economy to depend on the existence of the rationally constructed system of prices.

This was followed by the transfer of merit T.Kupmansa and the phrase:

"Dr. Kantorovich and Koopmans, on behalf of the Royal Academy of Sciences, I ask you to take your reward from His Majesty the King`s hands."

On the 90th anniversary of the birth of L. published the book "Leonid Kantorovich man and scholar.", Novosibirsk, 2002, 542 pages In it the reader may find interesting documents, the memories of many people of the LV, the memories of the LV and information about its work in Moscow, where he moved in the early 1970s.

Pictures of Leonid Kantorovich more

Leonid Kantorovich picture
Leonid Kantorovich photo