Lambda Calculus

Definitions

A formal system for expressing computation using function abstraction (λx.body) and application (f x). Equivalent in power to Turing machines but models computation as function evaluation rather than state transitions. The theoretical foundation of functional programming, closures, and anonymous functions.
In plain English: A mathematical system from the 1930s that defines computation as applying functions to arguments — the theory behind all functional programming.
Example: "Every time you write an arrow function in JavaScript, you're using lambda calculus — (x) => x + 1 is λx.x+1."

1932: Alonzo Church introduced lambda calculus at Princeton as a formal system for mathematical logic.
1936: Church used lambda calculus to give a negative answer to the Entscheidungsproblem, independently of Turing.
1958: John McCarthy created Lisp, the first programming language directly inspired by lambda calculus.