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Each mathematics field defines a language, a set of terms each defined in terms of some basic truths (axioms) and a way of building sentences, often with adjunction of the language of logic. Any sentence you speak in this language is Always True, because logic often uses universal quantification. It's possible to make truths which hold in specific cases using the idea of existential quantification, but they are less interesting/celebrated because they are specific applications.

@chexxor The other hotness is Type Theory and HOTT in particular.

chexxor@chexxor@functional.cafeSo, mathematics becomes interesting when you read a sentence written by someone else who speaks that language and you are surprised by something it entails in the specific cases to which you are applying these universal truths. Each statement spoken in this language can be trusted to be true, because logic. You can apply the language to any problem you encounter, so long as you can properly encode the problem in that language. Learn once, apply anywhere.