Metamathematics

Metamathematics is the study of mathematics itself using mathematical methods. It explores the foundations and structures of mathematical systems, including formal logic, which focuses on the rules of valid reasoning; proof theory, which examines the nature of mathematical proofs; and paraconsistent logic, which allows for contradictions without collapse. By analyzing these aspects, metamathematics helps us understand the principles and limitations of mathematical reasoning, assessing the consistency and completeness of various mathematical theories and systems, thus deepening our understanding of mathematical truth and knowledge.