"Metaphors deny distinctions between things: problems often arise from taking structural metaphors too literally. Because unexamined metaphors lead us to assume the identity of unidentical things, conflicts can arise which can only be resolved by understanding the metaphor (which requires its recognition as such), which means reconstructing the analogy on which it is based. […] The unexplained extension of concepts can too often result in the destruction rather than the expansion of meaning." (David Pimm,"Metaphor and Analogy in Mathematics", For the Learning of Mathematics Vol. 1" (3), 1981)
"In various fields of knowledge the problem of the relationship between cause and condition is solved in different ways, depending mainly on the complexity of the relationships that are being studied, their uniformity or, on the contrary, the distinctness and comparative importance of separate factors." (Alexander Spirkin, "Dialectical Materialism", 1983)
"There are, roughly speaking, two kinds of mathematical creativity. One, akin to conquering a mountain peak, consists of solving a problem which has remained unsolved for a long time and has commanded the attention of many mathematicians. The other is exploring new territory." (Mark Kac, "Enigmas Of Chance", 1985)
"To learn mathematics is to learn mathematical problem solving." (Patrik W Thompson, 1985)
"One never knows how hard a problem is until it has been solved. You don’t necessarily know that you will succeed if you work harder or longer." (Linus Pauling, [interview] 1986)
"Linear relationships are easy to think about: the more the merrier. Linear equations are solvable, which makes them suitable for textbooks. Linear systems have an important modular virtue: you can take them apart and put them together again - the pieces add up. Nonlinear systems generally cannot be solved and cannot be added together. [...] Nonlinearity means that the act of playing the game has a way of changing the rules. [...] That twisted changeability makes nonlinearity hard to calculate, but it also creates rich kinds of behavior that never occur in linear systems." (James Gleick, "Chaos: Making a New Science", 1987)
"A scientific problem can be illuminated by the discovery of a profound analogy, and a mundane problem can be solved in a similar way." (Philip Johnson-Laird, "The Computer and the Mind", 1988)
"The successes of the differential equation paradigm were impressive and extensive. Many problems, including basic and important ones, led to equations that could be solved. A process of self-selection set in, whereby equations that could not be solved were automatically of less interest than those that could." (Ian Stewart, "Does God Play Dice? The Mathematics of Chaos", 1989)
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