"A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some ‘dreaming’ time." (Howard W Eves)
"A problem is not solved in a laboratory. It is solved in some fellow's head. All the apparatus is for is to get his head turned around so that he can see the thing right." (Charles F Kettering)
"A problem well-defined is a problem half solved." (John Dewey)
"Each problem that I solved became a rule which served afterwards to solve other problems." (Descartes, Oeuvres, vol. VI)
"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)
"Indeed, when in the course of a mathematical investigation we encounter a problem or conjecture a theorem, our minds will not rest until the problem is exhaustively solved and the theorem rigorously proved; or else, until we have found the reasons which made success impossible and, hence, failure unavoidable. Thus, the proofs of the impossibility of certain solutions plays a predominant role in modern mathematics; the search for an answer to such questions has often led to the discovery of newer and more fruitful fields of endeavour." (David Hilbert)
"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 reason, for in mathematics there is no ignorabimus." (David Hilbert)
"What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved." (Julia Robinson)
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