The discovery of the 15 types of convex pentagons that monohedrally tile the plane started
in 1918 when the first five types were described by Reinhardt. Fifty years later Kershner added three
more types to this list and claimed that it was complete. Since then, amateur and professional
mathematicians have found seven more pentagonal prototiles.
In this talk, we want to retrace the discovery by looking at the actors involved and their methods. The
search for a new tile culminated when Michael Rao announced a computer-based proof of
completeness in 2017. We will briefly present the core ideas of his exhaustive search