"We can scarcely imagine a problem absolutely new, unlike and unrelated to any formerly solved problem; but if such a problem could exist, it would be insoluble. In fact, when solving a problem, we should always profit from previously solved problems, using their result or their method, or the experience acquired in solving them." (George Polya, 1945)
"The problems are solved, not by giving new information, but by arranging what we have known since long." (Ludwig Wittgenstein, "Philosophical Investigations", 1953)
"A great many problems are easier to solve rigorously if you know in advance what the answer is." (Ian Stewart, "From Here to Infinity", 1987)
"An important symptom of an emerging understanding is the capacity to represent a problem in a number of different ways and to approach its solution from varied vantage points; a single, rigid representation is unlikely to suffice." (Howard Gardner, "The Unschooled Mind", 1991)
"[By understanding] I mean simply a sufficient grasp of concepts, principles, or skills so that one can bring them to bear on new problems and situations, deciding in which ways one’s present competencies can suffice and in which ways one may require new skills or knowledge." (Howard Gardner, "The Unschooled Mind", 1991)
"Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley." (Yōko Ogawa, "The Housekeeper and the Professor", 2003)
"Framing the right problem is equally or even more important than solving it." (Pearl Zhu, "Change, Creativity and Problem-Solving", 2017)
"A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery." (George Polya)
"A great many problems are easier to solve rigorously if you know in advance what the answer is." (Ian Stewart, "From Here to Infinity", 1987)"Every problem has a solution; it may sometimes just need another perspective.” (Rebecca Mallery et al, “NLP for Rookies”, 2009)
"Mostly we rely on stories to put our ideas into context and give them meaning. It should be no surprise, then, that the human capacity for storytelling plays an important role in the intrinsically human-centered approach to problem solving, design thinking."
"One of the broad truths we’ve seen to be true is the idea that finding problems earlier in the developer workflow usually reduces costs." (Titus Winters, "Software Engineering at Google: Lessons Learned from Programming Over Time", 2020)
"A problem thoroughly understood is always fairly simple." (Charles Kettering)
"A problem well-defined is a problem half solved." (John Dewey)
"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity." (Howard W Eves)
"Finding the right answer is important, of course. But more important is developing the ability to see that problems have multiple solutions, that getting from X to Y demands basic skills and mental agility, imagination, persistence, patience." (Mary H Futrell)
"I have not seen any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated." (Paul Anderson)
"I knew nothing, except how to think, how to grapple with a problem and then go on grappling with it until you had solved it." (Sir Barnes Wallis)
"Man is not born to solve the problems of the universe, but to find out where the problems begin, and then to take his stand within the limits of the intelligible." (Johann Wolfgang von Goethe)
"One is always a long way from solving a problem until one actually has the answer." (Stephen Hawking)
"One measure of our understanding is the number of independent ways we are able to get to the same result." (Richard P Feynman)
“Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice.” (George Polya)
"Some problems are just too complicated for rational logical solutions. They admit of insights, not answers." (Jerome B Wiesner)
"The best way to escape from a problem is to solve it." (Brendan Francis)
"The greatest challenge to any thinker is stating the problem in a way that will allow a solution." (Bertrand Russell)
"The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems." (Charles W Churchman)
"The mere formulation of a problem is often far more essential than its solution. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advances in science." (Albert Einstein)
"The worst thing you can do to a problem is solve it completely." (Daniel Kleitman)
"There is no such thing as a problem without a gift. We seek problems because we need their gifts." (Richard Bach)
"To ask the right question is harder than to answer it." (Georg Cantor)
"When the answer to a mathematical problem cannot be found, then the reason is frequently that we have not recognized the general idea from which the given problem only appears as a link in a chain of related problems." (David Hilbert)
"You are never sure whether or not a problem is good unless you actually solve it." (Mikhail Gromov)
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