That's obvious if you program, though (to me). What you can do in one language, you can do faster, slower, more concise, more verbose, more symbolic, more literal, and so on, in another. You can build constructions and you can break them apart, depending on what layer of abstraction you can get to. You can call it by it's specific name and functionality, in how the part interacts in relation to the parts around it, or you can call it objects and morphisms.
I might be totally wrong, again, or using the wrong words and confusing everyone including myself (which is why I like to study formal languages, too). But I think that no matter where you start from, you will eventually find yourself in a place where you are scratching your head, confused about what you know, what you don't know, what everyone knows, and what everyone doesn't know.
Oh, and it's probably totally obvious if write proofs, believe in induction, and get very philosophical.
Does it even make sense for someone to not believe in induction? It's a perfectly valid logical rule.
using Haskell now as a side effect
https://www.youtube.com/watch?v=Vetg7vWitTU
(In case you don't know Lehrer, he did PhD studies in math at Harvard, and taught at Harvard and MIT, often performing his songs during his lectures (or composing songs FOR his lectures.))
... and Santa Cruz! I was one course shy of taking his last course (Infinity) before he retired.
In the early '70s, there was a global movement in math pedagogy that took this angle to elementary learning.
Instead of arithmetic, first graders were taught set theory. Elements and unions became the first mathematical concepts introduced to 6-year-olds.
In the US, I think they called it "New Math". Here in Finland, set theory was included in the national educational system's grand redesign. Regardless of country, set theory as elementary math seems to have gone out of fashion as quickly as it gained traction, and by the early '80s was out everywhere.
Maybe, if they had stuck with it, we would all be using Haskell now as a side effect :)
(Here's a picture of a very '70s styled Finnish math teacher doing set theory: http://1.bp.blogspot.com/-vWW22FRIdfc/TobxIw3xF3I/AAAAAAAAHa... -- "Now tell me children, what is the union of green swans and red bears?")