Elusive ‘einstein’ solves a long-standing math problem

Last November, after a decade of failed attempts, David Smith, a self-described shape hobbyist of Bridlington in East Yorkshire, England, suspected that he might have finally solved an open problem in the mathematics of tiling: That is, he thought he might have discovered an "einstein."

In less poetic terms, an einstein is an "aperiodic monotile," a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term "einstein" comes from the German "ein stein," or "one stone" - more loosely, "one tile" or "one shape.") Your typical wallpaper or tiled floor is part of an infinite pattern that repeats periodically; when shifted, or "translated," the pattern can be exactly superimposed on itself. An aperiodic tiling displays no such "translational symmetry," and mathematicians have long sought a single shape that could tile the...