This is not snobbery, some subjects just have prerequisites.
You can't learn computer science without having a good sense of what an "algorithm" is, you have to know how to read and write and understand algorithms. Similarly you can't learn math without having a good sense of what a proof is, reading, writing and understanding proofs is the heart of what math is.
Even more strongly, trying to learn math without a solid understanding of how proofs work is something like studying English literature while refusing to learn how to read English.
> Even more strongly, trying to learn math without a solid understanding of how proofs work is something like studying English literature while refusing to learn how to read English.
It depends why you're trying to learn math. Are you interested in math for math's sake, or are you trying to actually do something with it?
If it's the former, then yeah, you need proofs. Otherwise, like in your analogy, it's like studying English literature without knowing any english grammar rules.
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.
The software industry, similarly, is full of people who make use of computer science concepts, without having rigorously studying computer science. You can't learn true "computer science" without an understanding of discrete math, but you can certainly get a job as an entry-level SWE without one. You don't need discrete math to learn python, see that it's useful, and do something interesting with it.
The same applies to linear algebra. Everyone who does vector math doesn't need to be able to prove that the tools they are using work. If everyone who does vector math is re-deriving their math from first principles, then something's gone terribly wrong. There's a menu of known, well-defined treatments that can be applied to vectors, and one can read about them and trust that they work without having proven why they work.
EDIT: it occurs to me, an even stronger analogy of this point, is that it is entirely possible to study computer science, without having any understanding of electrical engineering or knowing how a transistor works.
> 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.
You can't learn computer science without having a good sense of what an "algorithm" is, you have to know how to read and write and understand algorithms. Similarly you can't learn math without having a good sense of what a proof is, reading, writing and understanding proofs is the heart of what math is.
Even more strongly, trying to learn math without a solid understanding of how proofs work is something like studying English literature while refusing to learn how to read English.