1. A certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems specifically associated with David Hilbert.

2. In economic anthropology, formalism is the theoretical perspective that the principles of neoclassical economics can be applied to our understanding of all human societies.

3. A certain rigorous mathematical method: see formal system.

4. A set of notations and rules for manipulating them that yield results in agreement with experiment or other techniques of calculation. These rules and notations may or may not have a corresponding mathematical semantics. In the case no mathematical semantics exists, the calculations are often said to be purely formal.

5. In the study of the arts and literature, formalism refers to the style of criticism that focuses on artistic or literary techniques in themselves, in separation from the work's social and historical context.

6. A school of thought in law and jurisprudence that emphasises the fairness of process over substantive outcomes.