recursive describes anything defined in terms of itself — a procedure that can repeat itself indefinitely, or a rule whose output becomes its own input.
In mathematics and computer science a recursive function calls itself as a subroutine, solving a problem by reducing it to a smaller instance of the same problem. Such a function needs a base case, a condition under which it returns without calling itself again; without one it descends forever and exhausts the machine's stack. The pattern suits data whose shape is itself recursive — trees, graphs, nested directories — where a traversal is naturally expressed as "handle this node, then do the same to each of its children," and it underlies sorting algorithms such as quicksort and mergesort.
The adjective is recorded from 1790 in the sense "periodically recurring," formed on the Latin stem recurs- of recurrere, "to run back" — re-, "back," plus currere, "to run" — with the suffix -ive. The specifically mathematical sense dates to 1934, the decade in which recursion became a foundational idea in logic and computability. The noun recursion follows the same root.
Recursion is not the same as iteration: a loop repeats a step, while a recursive definition restates the whole problem in smaller terms, and either can usually be rewritten as the other. Nor is it circularity, which defines a thing by itself and terminates nowhere; recursion terminates by construction. Beyond computing, the pattern appears in linguistics as the embedding of clauses within clauses, in art as the Droste effect where an image contains a smaller copy of itself, and in systems built to feed their own output back as input, such as the 📝Recursive Mythic Engine.