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.
Born Marjorie Jeuck in Florida, Rice went to a one-room country school where she skipped two grades and studied with the older kids. Though she loved learning and particularly her brief exposure to math, poverty and cultural norms prevented her family from even considering that she might attend college. In 1945, she married Gilbert Rice, a deeply Christian conscientious objector, and they moved to Washington, D.C., where Gilbert was to work in a military hospital. Marjorie Rice worked for a time as a commercial artist, until the couple moved to San Diego with their infant son. That child died but five other children survived.
For Rice, math was an indulgence. “We were kind of raised with the importance of the Scriptures and studying that way,” Kathy said, “and you didn’t want to waste your time on other endeavors.” Still, Rice read avidly and used her mind “actively, deeply and regularly,” as her son David wrote in an obituary shared among friends and family. “She was fascinated with the golden ratio” and pyramids, he wrote, and studied them “with extensive drawings and calculations.”
Rice gave one of her sons a subscription to Scientific American partly so she could peruse it while the children were at school. When she read Gardner’s column about tiling, as she later recalled in an interview on David Suzuki’s “The Nature of Things”: “I thought, my, that must be wonderful that someone could discover these things which no one had seen before, these beautiful patterns.” She also wrote in an essay, “I became fascinated by the subject and wanted to understand what made each type [of pentagon] unique. Lacking a mathematical background, I developed my own notation system and in a few months discovered a new type.”