Creatively tiling a bathroom floor isn’t just a stressful task for DIY home renovators. It is also one of the hardest problems in mathematics. For centuries, experts have been studying the special ...

And it all began with a hobbyist “messing about and experimenting with shapes.” An “aperiodic monotile,” or einstein, is a shape that tiles an infinite flat surface in a nonrepeating pattern. The ...

Mathematicians have discovered a pattern known as the einstein tile — a single shape that can cover an infinite plane without ever repeating. Long thought impossible, the discovery rewrote what ...