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the transition from pure math to the application of statistics to the real world (or science) requires a philosophical adjustment.

In math, the model and axioms are sound (by definition) within the mathematician's world.

However, in order to make judgments about reality by using statistics, one has to come up with reasonable models and assumptions, otherwise the resulting deductions can be worthless. The leads to a lot of subjectivity and grey areas for debate that a mathematician may not be accustomed to.