I have never understood why proofs are always required. Usually when you have an unproven theorem and it works often enough, to me it's good enough for most of what you're doing, for example in applied math. Of course if you find places where an unproven theorem doesn't work, it becomes interesting to why it doesn't work, and it's usually a big discovery, but it doesn't really disprove a theorem, it just helps to refine it.
I remember that in school teachers were often insisting about giving a proof to something, but to me it often made enough sense and it was often right, and it was often frustrating to have teachers tell you "no". It felt like a burden of proof.
If some claim is not proved but believed to be true it's called a conjecture. If a claim is known to be false but "works often enough" it's called a heuristic.
Well, broadly speaking, pure mathematics is picking some axioms, and then proving rigorous results based on them. If that doesn't sound like a fun game to you, you don't need to play it or watch it.
Not saying it's not fun, but to me proofs don't seem to help me understanding mathematics.
Not saying proofs are not important, but it seems that proving a theorem is important at a higher levels of mathematics, not in high school or university.
I remember that in school teachers were often insisting about giving a proof to something, but to me it often made enough sense and it was often right, and it was often frustrating to have teachers tell you "no". It felt like a burden of proof.