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 ...

A new theory proposes that the universe’s fundamental forces and particle properties may arise from the geometry of hidden extra dimensions. These dimensions could twist and evolve over time, forming ...

Three mathematicians just proved a famous 30-year-old conjecture in geometry, with only a tiny assist from AI. The conjecture says that even within enormous, scattered and chaotic assemblages of ...

Polyhedra are three-dimensional shapes made from flat polygonal faces and straight edges. Cubes, pyramids and octahedrons are ...