"The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively comprehensible. A more abstract presentation is only possible in the upper classes."

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The life of a thinking man will probably be divided into two parts -- the first in which he desires to exterminate modern thinkers, and the second in which he desires to watch them exterminating each other. ... Suppose, for instance, there is an old story and a new skeptic who is skeptical of the story. We have only to wait a little while for a yet newer skeptic who is skeptical of the skeptic. He will probably find the old notion actually a help in his new notion. This process is an abstract truth applying to anything, apart from agreement or disagreement.

— Gilbert K. Chesterton