I think the incomprehensibility of high level mathematics is as much a planned feature as is incomprehensibility of Haskell to a common programmer. And yet, peo

I think the incomprehensibility of high level mathematics is as much a planned feature as is incomprehensibility of Haskell to a common programmer. And yet, people who know Haskell find it actually more expressive than e.g. Java, precisely because it is more abstract, and neatly unifies some concepts. I think what I realized from being a programmer, just like in programming, there is no single language of mathematics. Different sub-fields invented different languages, and since everybody wants to remain productive, the effort to unify the languages is extremely difficult and unrewarding. Yet is much more accepted activity in mathematics than in programming. But it's not really intentional, it's just a side effect of natural tendency of various research groups to have somewhat different languages.