It is not a devolution. The discussion whether 1+1=2 is a definition, an axiom, or a theorem is very similar to the discussion of "0^0=1". In each case we are l

It is not a devolution. The discussion whether 1+1=2 is a definition, an axiom, or a theorem is very similar to the discussion of "0^0=1". In each case we are looking at different way to construct a useful mathematic out of different sets of definitions and axioms. Regarding 0^0 there is no clear winner, as - like the blog shows - there are many incompatible advantages one would get from 0^0:=1 or 0^0:=0. With "1+1=2" there is no controversy, as the many different definitions or axioms essentially result in the same nomenclature. But as an example of a rather unintuitive result regarding "1+1" look at the field F_2 (or GF(2)). It has two elements, 0 and 1. So when I'm writing "1" or "0" I am referring to these elements. Nonetheless with a typical definition used in many branches of mathematics I define 2:=1+1, 3:=1+1+1,… In F_2 the addition operation is defined as 0+0=0, 0+1=1, 1+0=1, and… 1+1=0. I thus get 0=1+1=2, 1=(1+1)+1=3, 0=((1+1)+1)+1)=4. Note that this is essentially calculation mod 2. But whereas outside of algebra this is often seen as a different set of equalities ("1+1≡0 mod 2") in algebra F_2 is just another field alongside of the rational, the real and the imaginary numbers.