“I discovered that a whole range of problems of the most diverse character relating to the scientiﬁc organization of production (questions of the optimum distribution of the work of machines and mechanisms, the minimization of scrap, the best utilization of raw materials and local materials, fuel, transportation, and so on) lead to the formulation of a single group of mathematical problems (extremal problems). These problems are not directly comparable to problems considered in mathematical analysis. It is more correct to say that they are formally similar, and even turn out to be formally very simple, but the process of solving them with which one is faced [i. e., by mathematical analysis] is practically completely unusable, since it requires the solution of tens of thousands or even millions of systems of equations for completion.
I have succeeded in ﬁnding a comparatively simple general method of solving this group of problems which is applicable to all the problems I have mentioned, and is sufﬁciently simple and effective for their solution to be made completely achievable under practical conditions.”

— Leonid Kantorovich

Kantorovich (1960) "Mathematical Methods of Organizing and Planning Production." Management Science, 6(4):366–422, 1960, p. 368); As cited in: Cockshott, W. Paul. " Mises, Kantorovich and economic computation http://www.dcs.gla.ac.uk/publications/PAPERS/8707/standalonearticle.pdf." (2007).

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Leonid Kantorovich8

Russian mathematician 1912–1986

Charles Perrow (1925–2019) American sociologist

Source: 1960s, "A Framework for the Comparative Analysis of Organizations", 1967, p. 195

“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 (1912–1986) Russian mathematician

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

“All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it.”

George Dantzig (1914–2005) American mathematician

Source: Linear programming and extensions (1963), p. vii.

“If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

“So the real problem in this whole question relates to utilization of national resources for productive and social welfare against the burden of defense expenditure which a country can bear at any particular time.”

Vikram Sarabhai (1919–1971) (1919-1971), Indian physicist

On the issue of priority to internal development vis-a-vis external defense.
The Making of the Indian Atomic Bomb: Science, Secrecy and the Post-colonial State

“In mathematics the art of asking questions is more valuable than solving problems.”
In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.

Georg Cantor (1845–1918) mathematician, inventor of set theory

Doctoral thesis (1867); variant translation: In mathematics the art of proposing a question must be held of higher value than solving it.

“As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity.”

William Winwood Reade (1838–1875) British historian

Source: The Martyrdom of Man (1872), Chapter II, "Religion", pp. 143-4.

“Chess problems are the hymn-tunes of mathematics.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

“The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

“The problem is the fake products today are of better quality and better price than the real names … They are exactly the same factories, exactly the same raw materials but they do not use the names.”

Jack Ma (1964) Chinese businessman

Responding to the accusation that Alibaba sells fake merchandise. "Jack Ma Says Fakes 'Better Quality and Better Price Than the Real Names'” http://blogs.wsj.com/chinarealtime/2016/06/15/jack-ma-says-fakes-better-quality-and-better-price-than-the-real-names/, CHINA REAL TIME REPORT, The Wall Street Journal (June 15, 2016)

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Leonid Kantorovich8

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