You cannot understand ideas without understanding the problems they solve.
This sounds like it means no one can understand math, which doesn't seem right.
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I would counter that you can never truly understand math until you use it in practice. I passed high school and college math but it was not until I derived its usage myself in practice (in this case, computer graphics) that I really understood it. : )
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I'd add that using math in practice won't deepen your knowledge, it just adds examples to your "oh, I've seen that before" memory. Example: trigonometry is used in astrophysics, mechanics, electrodynamics, etc ... 1/
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Well, for example, I don't think I really understood calculus until I studied mechanics. (Some of my friends do retort that "the REST of us understand ideas without problems", so maybe it's just me!)
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Sure, my linear math college textbooks suddenly became a while lot more relevant when it became my job. But people still pass their math classes without that motivation.
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