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In 1975, a San Diego homemaker named Marjorie Rice came across a column in Scientific American about tiling, a problem that has fascinated mathematicians since ancient Greek times. The problem, as Martin Gardner explained in the column, asks which shapes “tile” the plane, locking together with copies of themselves in endless patterns called tessellations. Gardner reported that the classification of all tessellating convex polygons had been completed by a 1968 proof that claimed to have found the remaining convex pentagons that tile the plane.

After Rice’s chance encounter with pentagon tilings, family members often saw her in the kitchen covertly sketching shapes on the tile countertops. “I thought she was just doodling,” her daughter Kathy Rice told me. But Rice, who took only one year of math in high school, was actually discovering new families of tessellating pentagons, and never-before-seen patterns, beyond those listed in Gardner’s column.

Rice died on July 2 at the age of 94. Dementia prevented her from learning that the pentagon tiling story has finally come to a close, decades after Gardner first called it. As I report in Quanta today, a new computer-assisted proof by the French mathematician Michaël Rao establishes that there are precisely 15 families of convex pentagons that tile the plane — including the four that Rice discovered.

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