"2 + 2 = 4" "the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2." Most of us conflate arithmeti

"2 + 2 = 4" "the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2." Most of us conflate arithmetic with mathematics. In arithmetic, things start getting 'conceptual' as soon as we no longer can map certain measures and operations to a realizable physical construct. At that precise juncture, math becomes a semantic system and is therefore subject to social consensus. For example, consider introducing infinity, or even zero, into 'shopkeepers' sense of numbers. Before, you could never add something to a number and end up with the same number, but now 0 + 0 = 0, and a + \infty = \infty . And to the shopkeepers' surprise, some mathematicians may even argue over it.