"A central problem in teaching mathematics is to communicate a reasonable sense of taste - meaning often when to, or not to, generalize, abstract, or extend something you have just done." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)
"Experience without theory teaches nothing." (William E Deming, "Out of the Crisis", 1986)
"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", 1991)
"Probability does pervade the universe, and in this sense, the old chestnut about baseball imitating life really has validity. The statistics of streaks and slumps, properly understood, do teach an important lesson about epistemology, and life in general. The history of a species, or any natural phenomenon, that requires unbroken continuity in a world of trouble, works like a batting streak. All are games of a gambler playing with a limited stake against a house with infinite resources. The gambler must eventually go bust. His aim can only be to stick around as long as possible, to have some fun while he's at it, and, if he happens to be a moral agent as well, to worry about staying the course with honor!" (Stephen J Gould, 1991)
"Whoever teaches learns in the act of teaching, and whoever learns teaches in the act of learning." (Paulo Freire, "Pedagogy of Freedom", 1996)
"A teacher who cannot explain any abstract subject to a child does not himself thoroughly understand his subject; if he does not attempt to break down his knowledge to fit the child's mind, he does not understand teaching." (Fulton J Sheen, "Life Is Worth Living", 1999)
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