It's a lot harder when you try to prove that 2+2=4: http://us.metamath.org/mpegif/mmset.html#trivia
That's right, there are 25,933 steps in that one if you trace 2+2=4 all the way back to axioms.
One obvious exception to this is Einstein coming up with relativity before it was ever observed in nature and approximated by people. But if you think about it, Einstein wasn't proving aximos; he was presenting a theoretical model (a guess) which turned out to precisely correspond with nature. It was still a guess.
So my point is... "results" are subjective, and don't require proofs. Proofs are very useful for checking your theories, but probably not for discovering new phenomena.
Physics is different. Yes, you can assume axioms and see what follows in the context of a physical situation, but that's a different game.
Speculation about physics is interesting in this case, but really, the question is about math.
They're taking 2 and 4 to be complex numbers (2 + 0i), where as he was taking 2 to be a cardinal number.