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[usually treated as singular] The 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.’
- ‘Furthermore, Hilbert's work on metamathematics has greatly improved our understanding of the nature of mathematical reasoning.’
- ‘Thus, only in his early sixties did Hilbert truly proceed to create proof theory and metamathematics.’
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