Computer Scientist Solves Decades-Old Mathematical Mysteries

Computer scientist Craig Kaplan, who had been searching for a shape that could fill an entire plane without forming regular patterns for decades, has finally found it with the help of a hobbyist named David Smith. The shape, called the 'hat', shattered records for both Heesch and isohedral numbers, proving itself to be an Einstein tile. Kaplan used computational methods to analyze the tiling properties of the hat, and the researchers used computation to construct a complete list of all possible neighborhoods to prove aperiodicity. While there is no immediate application identified to this tiling, new and interesting connections are expected to emerge as more researchers fiddle around with it.