maths

The title is a pun actually, as the E8 group is technically both "exceptional" and "simple", in the mathematical sense of those terms, if i recall correctly.

so the title is a joke of sorts.

i just want to point out that einstein wasn't 'arrogant' here. he said what he did because he 'knew' GR had to be right -- it was just the generalization of special relativity, which was already known to be right.

of course, it turns out that GR is wrong, at least at small-scales. while special relativity is compatible with quantum field theory (indeed, SR was the motivation for moving from quantum mechanics to QFT, as quantum mechanics does not respect SR), general relativity is not.

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.