...and even newer methods make old math insanely complicated, but much more generalized. Like building definitions for things like numbers and basic arithmetic using set theory.

To be fair, the first 100 pages of that was justifying the set theory definition for what numbers are. The following two hundred papers are proving that a process of iterative counting we call addition functions in a consistent and useful way, given the set theory way of defining numbers. Once we get to that point, 1+1 is easy. Then we get to start talking more deeply about iteration as a process, leading to considering iterating addition (aka multiplication), iterating multiplication (aka exponents), etc. But that stuff is for the next thousand pages.

Remember, 0 is defined as the amount of things in the empty set {}. 1 is defined as the amount of things in a set containing the empty set {{}}. Each following natural number is defined as the amount of things in a set containing each of the previous nonnegative integers. So for example 2 is the amount of things in a set containing the empty set and a set containing the empty set {{}, {{}}}, 3 is the amount of things in a set containing the empty set, a set containing the empty set, and a set containing the empty set and a set containing the empty set {{}, {{}}, {{}, {{}}}}, etc. All natural numbers are just counting increasingly recursively labeled nothing. Welcome to math.