“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

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Albert Einstein 702
German-born physicist and founder of the theory of relativi… 1879–1955

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Albert Einstein photo

“The mere formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and makres real advances in science.”

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

http://umich.edu/~scps/html/01chap/html/summary.htm
Attributed in posthumous publications, Einstein and Religion (1999)

Russell L. Ackoff photo

“When a mess, which is a system of problems, is taken apart, it loses its essential properties and so does each of its parts. The behavior of a mess depends more on how the treatment of its parts interact than how they act independently of each other. A partial solution to a whole system of problems is better than whole solutions of each of its parts taken separately.”

Russell L. Ackoff (1919–2009) Scientist

Cited in: Can Alpaslan, Ian Mitroff (2011) Swans, Swine, and Swindlers: Coping with the Growing Threat of Mega-Crises and Mega-Messes. p. 16.
1970s, The future of operational research is past, 1979

“The concern of OR with finding an optimum decision, policy, or design is one of its essential characteristics. It does not seek merely to define a better solution to a problem than the one in use; it seeks the best solution… [It] can be characterized as the application of scientific methods, techniques, and tools to problems involving the operations of systems so as to provide those in control of the operations with optimum solutions to the problems.”

C. West Churchman (1913–2004) American philosopher and systems scientist

Source: 1940s - 1950s, Introduction to Operations Research (1957), p. 8, cited in: R.L. McCown (2001) "Learning to bridge the gap between science-based decision support and the practice of farming". In: Aust. J. Agric. Res., Vol 52, p. 560-561

George Dantzig photo

“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.

Russell L. Ackoff photo

“Successful problem solving requires finding the right solution to the right problem. We fail more often because we solve the wrong problem than because we get the wrong solution to the right problem.”

Russell L. Ackoff (1919–2009) Scientist

Source: 1970s, Redesigning the future, 1974, p. 8.

David Hilbert photo

“It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

David Hilbert photo

“This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

“The systems approach to problems does not mean that the most generally formulated problem must be solved in one research project. However desirable this may be, it is seldom possible to realize it in practice. In practice, parts of the total problem are usually solved in sequence. In many cases the total problem cannot be formulated in advance but the solution of one phase of it helps define the next phase. For example, a production control project may require determination of the most economic production quantities of different items. Once these are found it may turn out that these quantities cannot be produced on the available equipment in the available time. This, then, gives rise to a new problem whose solution will affect the solution obtained in the first phase.”

C. West Churchman (1913–2004) American philosopher and systems scientist

Source: 1940s - 1950s, Introduction to Operations Research (1957), p. 7

“Sometimes it is more difficult to formulate the criterion for a problem than to state the question itself.”

Robert E. Machol (1917–1998) American systems engineer

Source: Information and Decision Processes (1960), p. xi

Leonid Kantorovich photo

“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 (1912–1986) Russian mathematician

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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