We all know we live in three-dimensional space. But what does it mean when people talk about four dimensions? Is it just a ...

The book Flatland: A Romance of Many Dimensions by Edwin A. Abbott explores the concept of physical dimensions through characters who encounter higher-dimensional beings. The protagonist, “A. Square,” ...

Put a ball in a box. In two dimensions, the ball (a circle) fills most of the box (a square). In three dimensions, a sphere still takes up a good chunk of its cube. But keep adding dimensions, and ...

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 ...