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 to prove the
consistency of mathematical theories by proving
a proposition about a theory itself, i.e. specifically about all possible proofs of theorems in the theory; in particular, both a proposition
A and its negation
not A should not be theorems (Kleene 1952, p. 55). However, metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic, among which the consistency problem is only one" (Kleene 1952, p. 59).