The tricky bit is that "simplest" has no formal definition. Here Wolfram claims to simplicity is having the least number of axiom, even if that axiom is very co

The tricky bit is that "simplest" has no formal definition. Here Wolfram claims to simplicity is having the least number of axiom, even if that axiom is very complicated. Unfortunately, that is a perversion of the idea of axiom. An axiom should be as simple as it can be and ideally self-evident. Being self-evident is a strong requirement because axioms are not proven but accepted as true. Clearly, no-one would say that Wolfram's axiom is self-evident. As a matter of fact, even Wolfram does not find it self-evident: that it is equivalent and sufficient as a basis needed to be proven, via proving it can generate all other set of axioms. Basically, once a field has matured enough and we found a simple set of axioms, one can come up with a new set. All set of axioms must encode the same information, so you can either have multiple simple one or a single complex one. The quantity of information that is encoded must be constant. So having a single axiom is not simpler, except by the very naive measurement of count.