Proof theory is a branch of mathematical logic that focuses on the structure and nature of mathematical proofs. It investigates how theorems can be derived from axioms using formal rules, emphasizing the relationship between syntax (formal expressions) and semantics (meaning). In various contexts, proof theory is essential for understanding the foundations of logic, such as in establishing the correctness of algorithms or systems, and plays a crucial role in areas like automated theorem proving and programming language design.
congrats on reading the definition of Proof Theory. now let's actually learn it.