metamathematics
/ˌmɛtəˌmæθəˈmætɪks/
noun
- The study of mathematics itself, using mathematical methods to examine the foundations, structure, and limits of mathematical systems.
- She wrote her doctoral thesis on the philosophy of metamathematics.
- Metamathematics explores questions about what can and cannot be proven within a mathematical system.
- Gödel's incompleteness theorems are famous results in metamathematics.