Being able to represent the same things in different ways is simply captured by the syntax/semantics dichotomy from disciplines like programming language theory

Being able to represent the same things in different ways is simply captured by the syntax/semantics dichotomy from disciplines like programming language theory. There is no need to invoke philosophy. Programmers care about syntax, too. But it's not like we've collectively figured it out yet. But I wouldn't be surprised if it turned out that we were further ahead than mathematicians in some ways. :o)