Kac M. Statistical independence in Probability, Analysis & Number Theory

Dover Publications, 2018. — 112 p. — (Dover Books in science and mathematics). — ISBN: 978-0-486-82158-0, 0-486-82158-7.This book "does math". It does not have the dry presentation of Theorem, proof, lemma, "assume that" and a huge inventory of formal symbols. It starts with an amusing derivation of formula which Kac attributes to Vieta. It takes another look at it from a different, more intuitive point of view. It does this repeatedly until one begins to see how the notion of statistical independence arises. Not as some dry formal construct following the Hilbert program or some such but as something living and organic growing naturally from intuitive roots. Kac recognizes what he calls a price that must be paid for "unrestrained abstraction". The price is that "it tends also to divert attention from whole areas of application whose very discovery depends on features that the abstract point of view rules out as being accidental."