Why should all mathematics be written using exactly the same language and conventions? Should all computer programs be written in the same language? People modi

Why should all mathematics be written using exactly the same language and conventions? Should all computer programs be written in the same language? People modify the language (natural, mathematical, programming) they are using to suit their problem. It is unreasonable to expect that the kind of language you use at the foundations of mathematics for example (set axioms and so on) would be efficient and useful for stating properties of much more complex objects: this exactly parallels computer programming languages. Admittedly, there are no big tables containing "definitions" of these languages. But I think it is common opinion that if you don't understand the language a paper is using, then there is a very large chance you don't know the underlying theory, and the paper will make no sense anyway.