"A problem adequately stated is a problem well on its way to being solved." (R Buckminster Fuller, "I Seem to be a Verb", 1970)
"Deep in the human nature there is an almost irresistible tendency to concentrate physical and mental energy on attempts at solving problems that seem to be unsolvable." (Ragnar Frisch, "From Utopian Theory to Practical Applications", [Nobel lecture] 1970)
"The definition of a problem and the action taken to solve it largely depend on the view which the individuals or groups that discovered the problem have of the system to which it refers. A problem may thus find itself defined as a badly interpreted output, or as a faulty output of a faulty output device, or as a faulty output due to a malfunction in an otherwise faultless system, or as a correct but undesired output from a faultless and thus undesirable system. All definitions but the last suggest corrective action; only the last definition suggests change, and so presents an unsolvable problem to anyone opposed to change." (Herbert Brün, "Technology and the Composer", 1971)
"The matter of the normalcy or non-normalcy of π will never, of course, be resolved by electronic computers. We have here an example of a theoretical problem which requires profound mathematical talent and cannot be solved by computations alone. The existence of such problems ought to furnish at least a partial antidote to the disease of computeritis, which seems so rampant today." (Howard Eves, "Mathematical Circles Revisited", 1971)
"Extrema is the generic term for the concepts 'maximum' and 'minimum' , like 'parents' is the generic term for 'father' and 'mother'. Extremal problems have to do with finding maxima and minima. We encounter them everywhere. It is hardly an exaggeration to say that all problems solved by living organisms are those involving a search for extrema." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"The synthetic mode of thought, when applied to systems problems, is called the systems approach. In this approach a problem is not solved by taking it apart but by viewing it as a part of a larger problem." (Russell L Ackoff, "Redesigning the future", 1974)
"It is one of our most exciting discoveries that local discovery leads to a complex of further discoveries. Corollary to this we find that we no sooner get a problem solved than we are overwhelmed with a multiplicity of additional problems in a most beautiful payoff of heretofore unknown, previously unrecognized, and as-yet unsolved problems." (Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)"
"A solution of newly appearing economic problems, and in particular those connected with the scientific-technical revolution often cannot be based on existing methods but needs new ideas and approaches. Such one is the problem of the protection of nature. The problem of economic valuation of technical innovations efficiency and rates of their spreading cannot be solved only by the long-term estimation of direct outcomes and results without accounting peculiarities of new industrial technology, its total contribution to technical progress." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives", [Nobel lecture]1975)
"The philosophical emphasis here is: to solve a geometrical problem of a global nature, one first reduces it to a homotopy theory problem; this is in turn reduced to an algebraic problem and is solved as such. This path has historically been the most fruitful one in algebraic topology." (Brayton Gray, Homotopy Theory", Pure and Applied Mathematics Vol. 64, 1975)
"One of the lessons that the history of mathematics clearly teaches us is that the search for solutions to unsolved problems, whether solvable or unsolvable, invariably leads to important discoveries along the way." (Carl B Boyer & Uta C Merzbach, "A History of Mathematics", 1976)
"All mathematical problems are solved by reasoning within a deductive system in which basic laws of logic are embedded." (Martin Gardner,"Aha! Insight", 1978)
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