[maths]

Actually it took Whitehead and Russell a lot of work just to prove 1+1=2. not kidding. see http://en.wikipedia.org/wiki/Image:Principia_Mathematica_the...

It all depends on the axioms you use, iirc. I can think of cases where 2+2 does not equal 4. For example (very roughly -- this example isn't really 100% accurate, but you get the idea), 2 protons plus 2 protons != 4 protons. in fact, you get the helium nucleus, I believe, 2 protons plus 2 neutrons. before you say this is an esoteric example, i might point out that this is the reaction that powers the sun and you wouldn't be alive right now without it. (for the actual reaction see here: http://en.wikipedia.org/wiki/Proton-proton_chain_reaction)

Someone with more maths training might correct me here, but 2+2=4 is true because you're using the usual axioms you learned in school. you might also say it's obvious that 3 times 3 = 9, or that ab = ba, but there is a lot of interesting math around anti-commutative algebras where ab=-ba, for example. it's all about the axioms you use.