08-04-2026, 11:35 PM
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.
ARTICLE
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.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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│ KONSTANTINOS MICHAILIDIS │
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