This question has been going on in my mind for a while. I've been having an interest in reading about higher mathematics, ever since I was into trying to solve math olympiads from the national and international level (though majority of them I couldn't even solve but it was fun). Anyways this led me into looking into famous unsolved problems and one which caught my attention was the Collatz Conjecture as it doesn't require that much mathematical background to understand and its notoriety for being an extremely hard problem to solve. So, my question is this: If someone were to prove that it's true / false, what would it mean to the math community and how would it revolutionize the way we see how numbers relate with each other?