High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible. If you’ve ever been stuck in traffic on a rainy afternoon, you’ve probably watched raindrops ...

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

Tiling a two-dimensional bathroom floor is a straightforward home renovation, but researchers have found that in higher dimensions it could blossom into a baffling mess of nonrepeating chaos. New ...