Fibonacci numbers date back to the 13th century Italian mathematician Leonardo of Pisa a.k.a Fibonacci who seems to have devised them as a way of modelling the growth in rabbit populations. I guess their popularity is down to the numerous and varied situations in which they occur. They occur in several ways in nature, for example the arrangement of nodules on a pine cone, and are used in computing for designing algorithms for recursive programming (i.e. a kind of step-by-step recipe for a programming technique where a particular function is repeatedly triggered by itself until a certain stopping point is reached).