Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself. Instead of studying the objects of a particular mathematical theory, it examines the mathematical theories as such, especially with respect to their logical structure. It concentrates mainly on the way in which theorems are derived from axioms.
See alsoLogic, Mathematics, Metatheorem, Proof
Portions of this entry contributed by Margherita Barile