p-adic numbers are an elaboration of the arithmetic one uses to reckon days of the week. p-adic AdS/CFT is a formulation of the gauge-string duality where the conformal field theory is defined over p-adic numbers, and anti-de Sitter space is replaced by an infinite regular tree, sometimes called the Bethe lattice. I will explain this new version of AdS/CFT, illustrate with a few computations, and at the end also explain how some old ideas like Kadanoff's spin-blocking fit in elegantly to the p-adic picture.