In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate ...

The cosmos may have something in common with a doughnut. In addition to their fried, sugary goodness, doughnuts are known for their shape, or in mathematical terms, their topology. In a universe with ...

Physicists recently mapped the hidden shape that underlies the quantum behaviors of a crystal, using a new method that’s expected to become ubiquitous. Famously, at the quantum scale, particles can be ...