The standard interpretation of a null state, or empty state, posits it as devoid of structure. This paper introduces a ...

The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists ...

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 ...

Plastics, by and large, are well-understood materials. Not as strong as most metals, but often much lighter, these man-made polymers have found innumerable applications that have revolutionized the ...