The Necessity of Grinding Through 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.

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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.

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.

The way you come to understand life is not by just reading quotes. You have to actually accumulate lots of life experiences.

And you might think you understand the quotes when you’re young, but after you accumulate more life experience, you realize that you really had only the most naive, surface-level understanding of the quotes back then, and you really had no idea what the hell you were talking about.

It’s the same way in math. 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.

If you shy away from grinding some messy math then you will never truly know what the hell you’re talking about.

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