[kindfellow92]

You only need multi volumes to prove 1 + 1 = 2 if you start with first order logic. If you start with the rules of basic arithmetic, it takes less than a page.

There is no fundamental difference when changing your starting assumptions other than one set of assumptions might prove more things than the other. From the perspective of single proof, either is equally as good. We axiomatically know basic arithmetic to be true, just as we axiomatically know first order logic to be true.

[dboreham]

Boy, I didn't realize I needed to set the explicit "irony flag" on that post! The idea is that my math teacher was making a math joke, stimulating his students' curiosity to think about deep things like "what does it mean to add and how do you prove things that seem intuitive" and informing the class that people have written serious and long books on the foundations of mathematics. None of my kids' math teachers (so far) have made any math jokes...

[posterboy]

It's not really a joke, just an understatement. Very dry humor indeed. Could be modesty or exageration, but at its core, it's true.