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treated as singularThe field of study that deals with the structure and formal properties of mathematics and similar formal systems.

‘Proof theory, a form of metamathematics, studies the ways in which proofs are used in mathematics.’

‘In conjunction with the twenty-fourth problem, this shows that, even at the time, he had at least a vague idea of metamathematics.’

‘Tarski made important contributions in many areas of mathematics: set theory, measure theory, topology, geometry, classical and universal algebra, algebraic logic, various branches of formal logic and metamathematics.’

‘Thus, only in his early sixties did Hilbert truly proceed to create proof theory and metamathematics.’

‘Furthermore, Hilbert's work on metamathematics has greatly improved our understanding of the nature of mathematical reasoning.’