Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) is due to David Hilbert`s attempt of proving the consistency of mathematical theories by provi....
[n] - the logical analysis of mathematical reasoning
metamathematics The branch of mathematics that deals with the logic and consistency of mathematical proofs, formulas, and equations.
noun the logical analysis of mathematical reasoning
See Proof theory, and Syntax, logical.