Its central ideas were developed by Danish mathematician Jakob Nielsen, and bear his name.
The theory developed in the study of the so-called minimal number of a map f from a compact space to itself, denoted MF[f].
Nielsen's approach is to group the fixed-point set into classes, which are judged "essential" or "nonessential" according to whether or not they can be "removed" by a homotopy.
Nielsen proved that making his invariant a good tool for estimating the much more difficult MF[f].
This leads immediately to what is now known as the Nielsen fixed-point theorem: Any map f has at least N(f) fixed points.