Origins
The English word 'recur' entered the language around 1390, from Latin 'recurrere' (to run back, to return, to hasten back). The Latin verb combines 're-' (back, again) and 'currere' (to run), creating the image of running back — returning to a starting point, retracing a path.
The physical sense of 'running back' was primary in Latin. A messenger who recurred was one who ran back with a reply. A road that recurred was one that doubled back on itself. But the figurative senses developed early: a thought that recurred was one that ran back into the mind; a fever that recurred was one that ran back after an interval of relief; a theme that recurred in a speech was one that returned repeatedly.
In English, the physical sense of 'running back' faded quickly, and the figurative senses dominated from the start. The main modern meanings are: to happen again or repeatedly (the problem recurs every winter), to return to the mind (the memory kept recurring), and to go back to something in thought or discussion (let me recur to my earlier point). All three rest on the same Latin image: something running back, returning.
Scientific Usage
The adjective 'recurrent' (happening repeatedly, returning periodically) dates to the seventeenth century and is especially common in medical and scientific contexts. A recurrent infection returns after apparent resolution. A recurrent dream repeats. Recurrent neural networks in machine learning feed their output back as input — they literally run back, processing information in loops rather than in a single forward pass.
The noun 'recurrence' followed the adjective and has become standard vocabulary in medicine (recurrence of cancer), mathematics (recurrence relations), and everyday life (to prevent a recurrence of the error).
The computing term 'recursion' deserves special attention. In computer science, recursion is a technique in which a function calls itself — the program runs back to its own beginning, executing the same code with different inputs until a base condition is met. Recursive algorithms solve problems by breaking them into smaller instances of the same problem. The mathematical concept of recursion (defining a sequence or function in terms of its own earlier values) predates computing, but the word became ubiquitous with the rise of programming languages like LISP and Haskell that rely heavily on recursive techniques.
Latin Roots
The etymology is perfect: a recursive function literally 'runs back' (re- + currere) to itself. The classic computer science humor — 'To understand recursion, see: recursion' — accidentally illustrates the Latin meaning. The word migrated from Latin through English into mathematics and then into computing, retaining at each stage the core idea of returning to a starting point.
In music, 'recurrence' describes the return of a theme, motif, or section. Sonata form, rondo form, and variations all involve recurrence — musical material that runs back, presenting itself again in modified or unmodified form. Wagner's leitmotifs are recurring musical ideas associated with characters, objects, or concepts. The musicological use of 'recurrence' is essentially the Latin meaning applied to sound rather than motion.
The relationship between 'recur' and its siblings in the 'currere' family follows the standard prefix logic. 'Occur' (ob- : run toward) is about events approaching. 'Incur' (in- : run into) is about encountering consequences. 'Concur' (con- : run together) is about agreement. 'Recur' (re- : run back) is about return and repetition. Each prefix reshapes the same verb of motion into a distinct conceptual domain.