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How important is it to learn the backgrounds/how the formulas came about in math and physics? Obviously you need a general understanding, but does one really need to know exactly how these formulas came about/work? Since that doesn't make too make much sense, here are two examples.

Math: We are doing centers of mass in calculus II. The teacher spent about 1/3 of the class explaining the formulas before he even got to writing them on the board. Taking averages of the f(x) + g(x) doing this and that until eventually arriving at the actual formula.

Physics: Conservation of momentum. We spent around 20 minutes going through derivatives, expanding stuff, solving for different things, etc etc until arriving at (for example) m1vi + m2vi = m1vf + m2vf.

It is much easier for me just to remember the formulas. I suck at memorizing but formulas I can remember without much work.

Is this going to hurt me in the long run by doing this or is it ok to vaguely remember how the formulas are derived but just stick to the actual formulas?

p.s. If this in the wrong spot, sorry. It fits about four sections but not completely in any.