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Eliezer_Yudkowsky comments on You don't need Kant - Less Wrong
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Most science classes aren't about practicing science, but memorizing science that's already done. Most math classes are the same way.
If you're not going to be extending math theory, is remaining ignorant of the process really a detriment?
Even high school geometry requires you to construct your own proofs.
It may be different abroad, but in the UK state system, we were never taught the idea of a proof untill sixth form (age 16-18).
Most people hate geometry and not only promptly forget it once they're out of the class but develop an aversion to it.
Also, there's barely any historical discussion of how the geometrical results were first found, with a few colorful anecdotes as exceptions.
Knowing how to construct a proof has nothing to do with knowing how the ancient Greeks viewed geometry. Knowing how to solve a math problem has nothing to do with knowing how the method was originally worked out.