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Math can be defined as formalizing ways to notice aspects of abstractions/models. This definition of math leads to a recognition of the myriad of ways of noticing aspects of abstractions - different styles of math. Probability models can be recast as diagrams and pseudo-random variables can be inefficiently but validly drawn using those diagrams. This transforms the understanding of probability into experiments performed on diagrams. Simulation is then understood as each sample being an index of the model it is logically connected to by the way it was drawn.
Statistics can be defined as formalizing ways to learn from observations using math (i.e. using models). It is always the case that given we have no direct access to reality, reality must be represented abstractly in our heads. Given that we must think about reality using abstractions, we can only notice aspects of those abstractions.
Simulation provides a profitable way of noticing aspects of probability/statistics where the learning about a model is fully distinguished from what to make of observations in hand. This requires transporting what repeatedly happens given a model to what reality happened to produce this time.
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