> But if you're trying to apply the math, if you're studying linear algebra because it's useful rather than for its own sake, then you don't need proofs. To follow the same analogy, it's like learning enough English to be conversational and get around America, without knowing what an "appositive" is.
Sure, but then you're not studying math, you're studying applications of math or perhaps you're even studying some other subject like engineering which is built on top of applications of math.
To add an extra analogy to the pile, its like learning to drive a car vs learning how to build a car. Sure, its completely valid to learn how to drive a car without knowing how to build one, but no one says they're learning automotive engineering when they're studying for their driving test. Its a different subject.
Sure, but then you're not studying math, you're studying applications of math or perhaps you're even studying some other subject like engineering which is built on top of applications of math.
To add an extra analogy to the pile, its like learning to drive a car vs learning how to build a car. Sure, its completely valid to learn how to drive a car without knowing how to build one, but no one says they're learning automotive engineering when they're studying for their driving test. Its a different subject.