Theoretically, it’s impossible for us to perceive a 4D creature. That is, unless it broke into our three-dimensional reality.

Tie a trefoil knot in a piece of string, seal the ends together, and try to wiggle it free without cutting. In three-dimensional space, the knot holds firm. Add a fourth spatial dimension, however, ...

Van Vleck’s largest lecture hall was filled to the brim for popular YouTuber Grant Sanderon’s talk on high-dimensional spheres.

The cosmos seems to have a preference for things that are round. Planets and stars tend to be spheres because gravity pulls clouds of gas and dust toward the center of mass. The same holds for black ...

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it. One of the most important pieces of ...

In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible. The cosmos seems to have ...