Once you apply arbitrary rules, you get algebras, so natural numbers, integers, rational numbers, algebraic numbers, continuous fractions, geometry, topology, ...

The view that the physics we experience is a subset of mathematics is obviously not proven, but not original or controversial.

Wolfram has a lot of good ideas. Many of which already existed, but he obscures, renames or ignores that.

He is a genuinely brilliant individual, and if he clearly demarcated what he did that was genuinely original, I think he would both get more respect, and be likelier to not distract himself from doing better work with his own grandiose abstractions.

A lot of great work starts out by solving something small but highly original, and following up every loose end, so that you end up somewhere interesting that neither you or anyone else might have expected. Maybe somewhere profound.

Starting out with grandiose publicly disclosed project definitions creates enormous pressure to confabulate.