The shape behind the Einstein problem just revealed strange new physics

A mathematical shape famous for covering a surface without ever repeating revealed an unexpected ability to twist light into unusual chiral patterns. The discovery could lead to new ways of controlling light, polarization, and advanced optical devices. The shape behind the Einstein problem just revealed strange new physics.

Researchers have found that structures based on the shape can make light form unusual chiral patterns, pointing to new ways of exploring how geometry can influence optical behavior. In a study published in Nature Communications, researchers from the Institute of Industrial Science, The University of Tokyo, and collaborating institutions built optical structures inspired by the "Smith hat." This unusual shape is known for solving the so-called Einstein problem in mathematics. When the team illuminated the structures with laser light, they observed diffraction effects unlike those seen in conventional quasicrystals.

The Shape That Solved the Einstein Problem The Einstein problem asks whether a single tile shape, known as a "monotile," can cover an entire surface without creating a repeating pattern. Familiar tilings such as checkerboards and honeycombs repeat in a regular way. An aperiodic monotile, by contrast, can fill a surface without ever settling into a repeating arrangement.