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Learn about the exciting recent discoveries of the Hat (also known as the “einstein tile”) and its close relative, the Spectre. The Hat is the first-ever shape in mathematics to tile the plane endlessly without ever quite repeating the pattern. In tiling the plane, the Hat mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. This question is answered with the exciting discovery of the Spectre, an aperiodic monotile that is “chiral,” meaning that reflected copies of the tile are not needed to form a tiling and no tiling with unreflected copies has a repeating pattern.
The New York Times has applauded this advancement in the world of mathematics, noting in a recent article that an Elusive ‘Einstein’ Solves a Longstanding Math Problem.