One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Proving the “discrete” periodic tiling conjecture for high-dimensional lattices is a slightly different problem than proving the continuous version of the conjecture, as there are tilings that are ...

Earlier this spring, tiling aficionados thought maybe they’d found the shape of their dreams. Now they’re certain. By Siobhan Roberts In March, a team of mathematical tilers announced their solution ...