“Mathematics Are Made Up”

That's not true. We didn't make up mathematics. Mathematics are a language, that describe the way the world works. Yes, the language is made up, but the things they describe aren't. Like any language, it requires context to fully understand, and through context we describe the real world. Math is also a form of logic, and like language, there's true and false statements and valid and invalid methods of reasoning to further principles. A math problem, that relates to no context, is like a novel, that it's fictitious, but still the logic works, and is proven to work.