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Einstein problem - mklabgr - 08-04-2026
Einstein problem
Summary
The Einstein problem is a famous question in mathematics about whether there exists a single shape that can tile an infinite plane only in a non-repeating pattern (an aperiodic monotile, or “einstein” from the German phrase ein Stein, meaning “one stone”). For decades, mathematicians searched for such a shape, and in 2023 researchers discovered the first true example: a 13-sided shape called the “hat”, which can cover a plane without ever forming a repeating pattern.
Later work found simpler versions, including an “einstein” shape that is connected and does not require using mirror images. The discovery solved a long-standing problem in tiling theory and had connections to geometry, computer science, crystallography, and the study of aperiodic structures found in nature, such as quasicrystals.
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