The widely accepted axiomatic basis for the natural numbers is the first order Peano Axioms. Very few children are capable of understanding how to prove 1+1=2

The widely accepted axiomatic basis for the natural numbers is the first order Peano Axioms. Very few children are capable of understanding how to prove 1+1=2 in this axiomatic system. In this system an axiom says that each element has a successor. 1 is called the successor of 0. 2 is called the successor of 1. So on and so forth. Now we need to define a binary operation called +. Now show that the successor of 0 plus the successor of 0 is the successor of the successor of 0. How many children are capable of this level of abstract thinking? People without training in statistics don’t understand how to properly design trials. I’m a mathematician and I don’t understand this since it is not something I’ve studied. I need to rely on the expert knowledge of others to tell what is and is not a good study design. The large group of people that distrust certain vaccines rather than all of them are ignoramuses.