The Y combinator shows that self-reference need not begin with a self

The Y combinator is a higher-order function from lambda calculus that enables recursion without giving a function an explicit name. It works by feeding a function into a carefully constructed self-referential pattern, allowing that function to invoke itself indirectly. The result is a fixed point: a function whose behavior remains unchanged when transformed by another function. Though compact and abstract, the Y combinator demonstrates that recursion can emerge from pure function application alone, with no built-in looping mechanism required. It is a classic example of computation reduced to its logical bones. It is used primarily in functional programming, lambda calculus, and programming language theory.