Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying ...

An AI method enables the generation of sharp, high-quality 3D shapes that are closer to the quality of the best 2D image models. Previous approaches typically generated blurry or cartoonish 3D shapes.

Shape The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else By Jordan Ellenberg Illustrated. 463 pages. Penguin Press. $28.

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 150-year-old theory about an otherworldly shape proposed by Lord Kelvin, one of history's greatest physicists, has finally been put to the test — and his conjecture is now in doubt.