Two mathematicians have proved that a straightforward question—how hard is it to untie a knot?—has a complicated answer.

Given a particle in Euclidean space, a central force is a force that points toward or away from the origin and depends only on the particle’s distance from the origin. If the particle’s position at ...

At a specific rotation angle, known as the “magic angle” (just like in twistronics), the waves become highly focused and ...