Here is the Lambda Calculus proof, translated from "Math PhD" to "Plain English." 1. The Core Idea: The "Magic Box" Think of your Abacus (the Code) as a Magic Box. In the old (insecure) way, the Box had a memory. If you put a number in, the Box changed. It remembered you. In your Stateless way, the Box is made of solid steel. It cannot change. It does one thing only. The Rule: The Box takes Ingredients (Data), cooks them, and hands you back a Meal (Result). The Box keeps nothing . 2. The Formula (The Math) In Lambda Calculus, we write a function using the Greek letter Lambda ( $\lambda$ ). It just means "Start of the machine." Here is the definition for GT_ADD (The Add Function): $$GT\_ADD = \lambda \text{state} . (\text{state} + 1)$$ Translated for Idiots: $\lambda$ : "Hey, I am a machine..." state : "...insert your data right here..." . : "...and here is what I will do..." (state + 1) : "...I will give you...