@Jirikiha @futurebird @whknott I'm *far* from an expert in math / stats. I took 2 years of honours math as part of my looong ago comp sci degree, and have been generally interested in mathy stuff since.
My impression is that the math behind statistics (at least the foundations) is deep: measure theory, the Lebesgue integral, and other terms I recognize as topics, but do not have even a basic understanding of.