In 2023, a long-standing problem in mathematics was solved with the discovery of the “hat” tile, an aperiodic monotile.
The 13-sided shape can cover an infinite plane completely, with no gaps or overlaps, using copies of just this one shape. However, the resulting pattern can never become periodic—it does not repeat in a regular pattern.
The shape was discovered by David Smith, a retired print technician and tiling enthusiast from Yorkshire, England. He then worked with mathematicians Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss to prove its properties.
The term “einstein” comes from the German ein Stein, meaning “one stone,” and has nothing to do with Albert Einstein.
The discovery solved a problem mathematicians had studied for decades: whether a single shape could tile the plane only in a non-repeating way.