The study of four-dimensional manifolds occupies a central role in modern topology, uniquely bridging purely topological classification with differential and gauge-theoretic methods. Unlike in ...

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 ...

We all know we live in three-dimensional space. But what does it mean when people talk about four dimensions? Is it just a bigger kind of space? Is it “space-time”, the popular idea which emerged from ...

A new study from the University of Eastern Finland (UEF) explores the behavior of photons, the elementary particles of light, as they encounter boundaries where material properties change rapidly over ...

Can you imagine the imprint a four-dimensional hexagon might leave as it passes through your three-dimensional kitchen table? Probably not, but some people can. One such person was mathematician ...

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,” ...