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Generally, no. As others have mentioned, Mathematics isn't really a language. It's at the very least absolutely certainly not one language. Certain parts of Ma
by tel 9y ago
Generally, no.
As others have mentioned, Mathematics isn't really a language. It's at the very least absolutely certainly not one language. Certain parts of Mathematics use a typed language. Certain parts rely on other kinds of containment properties which serve nicely as types.
Finally, generally, math is very interested in being completely clear the properties of objects and very interested in speaking abstractly, so even if the language of use is untyped the logic is often very rigorous around typing.
Above it all, perhaps, is the idea that mathematics is concerned with proof and proofs may contain reference to the properties being discussed---metamathematical ideas pervade normal mathematical thought. This means that even absent of types the content of a mathematical utterance is often going to explicitly posit, discuss, and prove properties similar to type propositions.