Researchers have solved a long-standing problem in topology by helping classify four-dimensional shapes (4-manifolds) that ...

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in two-dimensional (2D) and three-dimensional (3D) settings. The rules of Euclidean ...

A mathematical problem solved by Susanna Heikkilä relates to the classification of quasiregularly elliptic 4-manifolds, ...

In 1963 it was proved that a celebrated mathematical hypothesis put forward by Georg Cantor could not be proved. This profound development is explained by analogy with non-Euclidean geometry ...