Hyperbolic knot theory concerns itself with the study of knots and links embedded in three‐dimensional spaces that admit hyperbolic structures. The geometry of a link complement—the manifold that ...

Complex hyperbolic geometry studies spaces that combine the rich structure of complex manifolds with the intriguing features of hyperbolic curvature. At its heart lies the complex hyperbolic space, a ...

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...

Atomic interactions in everyday solids and liquids are so complex that some of these materials’ properties continue to elude physicists’ understanding. Solving the problems mathematically is beyond ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

Building on previous work that realized Euclidean lattice models using circuit quantum electrodynamics (QED) and interconnected networks of superconducting microwave resonators, researchers at ...

Our gallery gets to grips with hyperbolic space through mathematical artist Vi Hart’s visualisations in balloons, beads, clothes and more. See more in our gallery here. The one diet that’s good for ...

Researchers have built an electronic array on a microchip that simulates particle interactions in a hyperbolic plane, a geometric surface in which space curves away from itself at every point. Atomic ...