Definition
Metamathematics is the study of mathematics itself. It examines the assumptions, foundations, and implications of mathematical systems, rather than solving specific problems within those systems. It's like stepping back to analyze the rules of a game rather than playing the game. It asks questions like: What makes a mathematical proof valid? Are there inherent limitations to what mathematics can prove? It's not about calculating answers but about understanding the nature of calculation itself. Think of it as the philosophy of mathematics.