Ralph P. Boas, Jr. Quotes
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Suppose that you want to teach the 'cat' concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I'll bet not. You probably show the kid a lot of different cats, saying 'kitty' each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience.
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Somebody came up to me after a talk I had given, and say, "You make mathematics seem like fun." I was inspired to reply, "If it isn't fun, why do it?"
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Only professional mathematicians learn anything from proofs. Other people learn from explanations.
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