An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German),
is a single tile which tiles the plane only aperiodically. It was an open problem
for a long time to either find such a tile or show that none exists. The problem
was solved by Smith et al. (2023), who found a simple polykite
known as a hat that is an aperiodic monotile.
In addition to the hat, Smith et al. (2023)
also found a continuum of aperiodic polygonal monotiles.
