Leonid Kantorovich: Use

“In our time mathematics has penetrated into economics so solidly, widely and variously, and the chosen theme is connected with such a variety of facts and problems that it brings us to cite the words of which are very popular in our country: "One can not embrace the unembraceable". The appropriateness of this wise sentence is not diminished by the fact that the great thinker is only a pen-name.”

Leonid Kantorovich

Lead paragraph
"Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975

Mathematics , Problem , Time , Country

“The university immediately published my pamphlet, and it was sent to ﬁfty People’s Commissariats. It was distributed only in the Soviet Union, since in the days just before the start of the World War it came out in an edition of one thousand copies in all.
Soviet Union, since in the days just before the start of the World War it came out in an edition of one thousand copies in all. The number of responses was not very large. There was quite an interesting reference from the People’s Commissariat of Transportation in which some optimization problems directed at decreasing the mileage of wagons was considered, and a good review of the pamphlet appeared in the journal "The Timber Industry."
At the beginning of 1940 I published a purely mathematical version of this work in Doklady Akad. Nauk [76], expressed in terms of functional analysis and algebra. However, I did not even put in it a reference to my published pamphlet—taking into account the circumstances I did not want my practical work to be used outside the country
In the spring of 1939 I gave some more reports—at the Polytechnic Institute and the House of Scientists, but several times met with the objection that the work used mathematical methods, and in the West the mathematical school in economics was an anti-Marxist school and mathematics in economics was a means for apologists of capitalism. This forced me when writing a pamphlet to avoid the term "economic" as much as possible and talk about the organization and planning of production; the role and meaning of the Lagrange multipliers had to be given somewhere in the outskirts of the second appendix and in the semi Aesopian language.”

Leonid Kantorovich

L.V. Kantorovich (1996) Descriptive Theory of Sets and Functions. p. 41; As cited in: K. Aardal, ‎George L. Nemhauser, ‎R. Weismantel (2005) Handbooks in Operations Research and Management Science, p. 19-20

War , People , World , School

“The accounting methods based on mathematical models, the use of computers for computations and information data processing make up only one part of the control mechanism, another part is the control structure.”

Leonid Kantorovich

"Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975

Mathematics , Parting

“Once some engineers from the veneer trust laboratory came to me for consultation with a quite skilful presentation of their problems. Diﬀerent productivity is obtained for veneer-cutting machines for diﬀerent types of materials; linked to this the output of production of this group of machines depended, it would seem, on the chance factor of which group of raw materials to which machine was assigned. How could this fact be used rationally?
This question interested me, but nevertheless appeared to be quite particular and elementary, so I did not begin to study it by giving up everything else. I put this question for discussion at a meeting of the mathematics department, where there were such great specialists as Gyunter, Smirnov himself, Kuz’min, and Tartakovskii. Everyone listened but no one proposed a solution; they had already turned to someone earlier in individual order, apparently to Kuz’min. However, this question nevertheless kept me in suspense. This was the year of my marriage, so I was also distracted by this. In the summer or after the vacation concrete, to some extent similar, economic, engineering, and managerial situations started to come into my head, that also required the solving of a maximization problem in the presence of a series of linear constraints.
In the simplest case of one or two variables such problems are easily solved—by going through all the possible extreme points and choosing the best. But, let us say in the veneer trust problem for ﬁve machines and eight types of materials such a search would already have required solving about a billion systems of linear equations and it was evident that this was not a realistic method. I constructed particular devices and was probably the ﬁrst to report on this problem in 1938 at the October scientiﬁc session of the Herzen Institute, where in the main a number of problems were posed with some ideas for their solution.
The universality of this class of problems, in conjunction with their difficulty, made me study them seriously and bring in my mathematical knowledge, in particular, some ideas from functional analysis.
What became clear was both the solubility of these problems and the fact that they were widespread, so representatives of industry were invited to a discussion of my report at the university.”

Leonid Kantorovich

L.V. Kantorovich (1996) Descriptive Theory of Sets and Functions. p. 39; As cited in: K. Aardal, ‎George L. Nemhauser, ‎R. Weismantel (2005) Handbooks in Operations Research and Management Science, p. 15-26

Marriage , Search , Mathematics , Idea

“The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration ofjkbni semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.”

Leonid Kantorovich

"On one class of functional equations" (1936), as cited in: O'Connor, John J.; Robertson, Edmund F., " Leonid Kantorovich http://www-history.mcs.st-andrews.ac.uk/Biographies/Kantorovich.html", MacTutor History of Mathematics archive, University of St Andrews

Study , Success

“In planning the idea of decentralization must be connected with routines of linking plans of rather autonomous parts of the whole system. Here one can use a conditional separation of the system by means of fixing values of flows and parameters transmitted from one part to another. One can use an idea of sequential recomputation of the parameters, which was successfully developed by many authors for the scheme of Dantzig-Wolfe and for aggregative linear models.”

Leonid Kantorovich

"Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975

Idea , Wolf , Parting