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The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

If you go directly to the most abstract ideas then you’re basically like a kid who reads a book of famous quotes about life and thinks they understand everything about life by way of those quotes.

What a lot of math learners fail to understand is that grinding through concrete examples imbues you with intuition that you will not get if you jump directly to studying the most abstract ideas. In general, the purpose and power of an abstract idea is that it compresses a zoo of concrete examples. But if you haven’t built up that zoo of concrete examples then you miss out on that power.

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