Look carefully! Mathematicians have invented a new 13-sided shape that can be tiled infinitely without ever repeating a pattern. They call it "the einstein." For decades, mathematicians wondered if it ...

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 ...

In November 2022 a colleague of mine casually asked what I was working on. My dazed answer reflected the swirl of ideas that was consuming all my mental energy at the time: “Actually, I think the ...

The recently discovered “hat” aperiodic monotile admits tilings of the plane, but none that are periodic [SMKGS23]. This polygon settles the question of whether a single shape—a closed topological ...